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Subtracting fractions word problems
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Let children work on our printable adding fractions word problems worksheets hammer and tongs! Whether it's sharing a meal with your friends or measuring the ingredients for a recipe, adding fractions is at the heart of it all, hence our worksheets. A wealth of real-life scenarios that involve addition of fractions with whole numbers and addition of two like fractions, two unlike fractions, and two mixed numbers, our pdf worksheets are indispensable for grade 3, grade 4, grade 5, and grade 6 students. The free fraction addition word problems worksheet is worth a try!
Adding Fractions with Whole Numbers
Dazzle 3rd grade kids with a gift of lifelike story problems! If you're a novice up against fraction addition, don't miss our pdf adding fractions word problems worksheets using whole numbers and fractions!
Download the set
Adding Like Fractions Word Problems
Gerald ate 5/9 of an apple, and Garry ate 4/9 of it. How many apples did they eat in all? Good going! They both ate one whole apple. Simply combine the numerators and solve the like fraction word problems here!
Adding Unlike Fractions
A potpourri of word problems that involve adding unlike fractions, these pdfs mean that 4th grade and 5th grade students will breeze through addition of fractions with different denominators in their day-to-day lives.
Adding Mixed Numbers | Same Denominators
See in your mind's eye adding mixed numbers with same denominators riding on the several real-life scenarios in our printable worksheets! Convert the mixed numbers to fractions, and add them as usual.
Adding Mixed Numbers | Different Denominators
Steal a march on your 5th grade and 6th grade peers by getting your act together to power through the real-world situations featured in this set of printable adding mixed numbers word problems worksheets.
Addition of fractions is typically taught starting in 4th grade, with like fractions (same denominator, such as 3/8 + 2/8). Children start out by using manipulatives so they can understand the concept, and then they can go on to abstract problems.
Next, in 5th grade, students tackle adding fractions (fractions with different denominators, such as 3/4 + 2/5) and mixed numbers with unlike fractional parts. The procedure for this involves converting the fractions to be added to with a common denominator. After the conversion, you have (fractions with the same denominator) which you can add easily. To understand how this is done, please see on my other site (MathMammoth.com)
In 6th and 7th grades, students simply practice addition of fractions using larger denominators and more complex problems.
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Each worksheet is randomly generated and thus unique. The and is placed on the second page of the file.
You can generate the worksheets — both are easy to print. To get the PDF worksheet, simply push the button titled " " or " ". To get the worksheet in html format, push the button " " or " ". This has the advantage that you can save the worksheet directly from your browser (choose File → Save) and then in Word or other word processing program.
Sometimes the generated worksheet is not exactly what you want. Just try again! To get a different worksheet using the same options:
Fraction addition worksheets: grade 4
The fractions in grade 4 addition problems are limited to fractions — fractions with a same denominator.
Add two fractions, same denominators, easy denominators of 2, 3, 4, 6, and 8 (the child can use a manipulative)
Add two fractions, same denominators
Add three fractions (same denominators)
Add two mixed numbers (same denominators)
Add a fraction with tenths
Add three fractions with
Allow improper fractions
Add a fraction and a mixed number (easy)
Add fractions - missing number
Add fractions or mixed numbers - missing number - same denominators
Here are some more fraction worksheets you can use in grade 4. They also use only fractions with a same denominator (like fractions).
Add four fractions - same denominators ( )
Add four fractions, some are improper ( )
Add three fractions; missing number
Add two mixed numbers; missing number
Add three mixed numbers
Add mixed numbers, whole numbers,
Fraction addition worksheets: grade 5
In grade 5, students learn to add unlike fractions — fractions with different denominators.
Add two unlike fractions, easy denominators of 2, 3, 4, 6, and 12 (the student can use a manipulative)
Add two unlike fractions,
Add two unlike fractions,
Add two unlike fractions,
Add two mixed numbers,
Add two mixed numbers,
Add three fractions,
Challenge: a missing fraction
Here are some more fraction worksheets for grade 5.
Add two unlike fractions, allow improper fractions, denominators 2-12
Add three fractions, allow improper fractions, denominators 2-12
Add a mixed number and a fraction, denominators 2-12
Add two mixed numbers and a fraction, denominators 2-12
Challenge: add four fractions, mixed numbers, and whole numbers )
Challenge: a missing mixed number
Fraction addition worksheets: grades 6-7
In grades 6 and 7, students simply practice addition with fractions that have larger denominators than in grade 5.
Add two fractions, select (easier) denominators within 2-25
Add three fractions, select (easier) denominators within 2-25
Add two fractions, denominators 2-25
Add two fractions, allow improper fractions, denominators 2-25
Add two mixed numbers, select (easier) denominators within 2-25
Add three mixed numbers, select (easier) denominators within 2-25
Add two mixed numbers, denominators 2-25
Challenge: a missing fraction, denominators 2-25
Add four fractions, select (easier) denominators within 2-25
Add four fractions and/or mixed numbers, select (easier) denominators within 2-25 (print in landscape)
Add 3 fractions and mixed numbers, missing number (print in landscape)
Add four fractions, missing fraction (print in landscape)
Fraction worksheets generator
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Solving Word Problems by Adding and Subtracting Fractions and Mixed Numbers
Learn how to solve fraction word problems with examples and interactive exercises.
Example 1: Rachel rode her bike for one-fifth of a mile on Monday and two-fifths of a mile on Tuesday. How many miles did she ride altogether?
Analysis: To solve this problem, we will add two fractions with like denominators.
Solution:
Answer: Rachel rode her bike for three-fifths of a mile altogether.
Analysis: To solve this problem, we will subtract two fractions with unlike denominators.
Answer: Stefanie swam one-third of a lap farther in the morning.
Analysis: To solve this problem, we will add three fractions with unlike denominators. Note that the first is an improper fraction.
Answer: It took Nick three and one-fourth hours to complete his homework altogether.
Analysis: To solve this problem, we will add two mixed numbers, with the fractional parts having like denominators.
Answer: Diego and his friends ate six pizzas in all.
Analysis: To solve this problem, we will subtract two mixed numbers, with the fractional parts having like denominators.
Answer: The Cocozzelli family took one-half more days to drive home.
Analysis: To solve this problem, we will add two mixed numbers, with the fractional parts having unlike denominators.
Answer: The warehouse has 21 and one-half meters of tape in all.
Analysis: To solve this problem, we will subtract two mixed numbers, with the fractional parts having unlike denominators.
Answer: The electrician needs to cut 13 sixteenths cm of wire.
Analysis: To solve this problem, we will subtract a mixed number from a whole number.
Answer: The carpenter needs to cut four and seven-twelfths feet of wood.
Summary: In this lesson we learned how to solve word problems involving addition and subtraction of fractions and mixed numbers. We used the following skills to solve these problems:
Add fractions with like denominators.
Subtract fractions with like denominators.
Find the LCD.
Add fractions with unlike denominators.
Subtract fractions with unlike denominators.
Add mixed numbers with like denominators.
Subtract mixed numbers with like denominators.
Add mixed numbers with unlike denominators.
Subtract mixed numbers with unlike denominators.
Directions: Subtract the mixed numbers in each exercise below. Be sure to simplify your result, if necessary. Click once in an ANSWER BOX and type in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR.
Note: To write the fraction three-fourths, enter 3/4 into the form. To write the mixed number four and two-thirds, enter 4, a space, and then 2/3 into the form.
RESULTS BOX:
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Adding Fractions Worksheets
Welcome to our Adding Fractions Worksheets page. We have a range of worksheets designed to help students learn to add two fractions together.
Our sheets range in difficulty from easier supported sheets with like denominators to harder sheets with different denominators and three fractions to add.
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All Adding Fractions Worksheets
Adding Fractions with Like Denominators Worksheets
Here you will find a selection of Fraction worksheets designed to help your child practice how to add two or three fractions.
The sheets are carefully graded so that the easiest sheets come first, and the most difficult sheet is the last one.
Next to each sheet is a description of the math skills involved.
Using these sheets will help your child to:
apply their understanding of equivalent fractions;
add 2 fractions with like denominators;
add 2 or 3 fractions with different denominators;
These skills and worksheets are aimed at 3rd through to 7th grade.
The easiest sheets with like denominators are suitable for 3rd graders (sheet 1)
The hardest sheets with adding 3 fractions with different denominators are more suitable for 7th graders.
Adding Fractions (like denominators) Worksheets
If you are looking to add fractions which have the same denominator, take a look at our sheets below.
Like Denominators
Sheet 1: the easiest sheet, no simplifying or converting needed.
Adding Fractions like denominators Sheet 1
PDF version
Sheet 2: Fractions need adding then simplifying.
Adding Fractions like denominators Sheet 2
Sheet 3: fractions need simplifying and/or converting from an improper fraction into a mixed number.
Adding Fractions like denominators Sheet 3
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This quick quiz tests your knowledge and skill at adding fractions with like denominators.
Adding Fractions (unlike denominators) Worksheets
Sheet 1: easy to convert denominators with one denominator a multiple of the other; no simplifying or converting needed
Adding Fractions Worksheet 1
Sheet 2: easy to convert denominators with one denominator a multiple of the other; simplifying needed but no converting
Adding Fractions Worksheet 2
Sheet 3: easy to convert denominators with one denominator a multiple of the other; simplifying needed and converting to mixed numbers
Adding Fractions Worksheet 3
Sheet 4: harder to convert denominators - supported sheet; no simplifying or converting needed
Adding Fractions Worksheet 4
Sheet 5: harder to convert denominators; some simplifying needed but no converting
Adding Fractions Worksheet 5
Sheet 6: harder to convert denominators; simplifying needed and also converting to mixed numbers
Adding Fractions Worksheet 6
Sheet 7: adding 3 fractions; easier sheet - simplifying needed but no converting
Adding Fractions Worksheet 7
Sheet 8: adding 3 fractions; harder sheet - simplifying and converting to mixed numbers needed
Adding Fractions Worksheet 8
Adding Fractions (with unlike) Denominators Quiz
This quick quiz tests your knowledge and skill at adding a range of fractions.
More Recommended Math Resources
Take a look at some more of our resources similar to these.
More Adding Subtracting Fractions
The sheets in this section will help you practice both adding and subtracting a range of fractions.
Some of the sheets also involve simplifying the fractions and converting the answers to mixed fractions.
Adding Fractions with Like Denominators
Adding Improper Fractions
Subtracting Fractions Worksheets
Adding Subtracting Fractions Worksheets
Fractions Adding and Subtracting Worksheets (randomly generated)
Least Common Multiple Calculator
Our Least Common Multiple Calculator will find the lowest common multiple of 2 or more numbers.
It will tell you the best multiple to convert the denominators of the fractions you are adding into.
There are also some worked examples.
Equivalent Fractions Worksheets
This is a pre-requisite for knowing how to add and subtract fractions.
develop an understanding of equivalent fractions;
know when two fractions are equivalent;
find a fraction that is equivalent to another.
Multiplying and Dividing Fractions
multiply and divide fractions by whole numbers and other fractions;
multiply and divide mixed fractions.
Multiplying Fractions Worksheets
Multiplying Mixed Fractions
How to Divide Fractions
Dividing Fractions by whole numbers
How to Divide Mixed Numbers
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Learn about adding fractions., adding fractions lesson, how to add fractions.
To add fractions, we follow three simple steps. They are as follows:
Make the denominators the same if they aren't already.
Add the numerators, keeping the denominator the same.
Simplify the resulting fraction.
The same three steps apply for adding mixed fractions (such as 4 1 / 2 + 1 2 / 3 ) except that we will simply add the whole number and fraction components separately.
In this lesson we will go through how to add fractions and show examples of adding fractions with like and unlike denominators.
Adding Fractions with Like Denominators
Let's go through how to add fractions with like denominators first, since it is most simple type of fraction addition. Here's an example of adding fractions with like denominators, using the three steps from earlier.
Find the sum of 3 / 5 + 1 / 5 .
The denominators are already the same, so we can skip step 1.
Let's add the numerators. 3 + 1 = 4, so the sum of our numerators is 4. The denominator is still 5, so our result is 4 / 5 .
4 / 5 is already in its simplest form, so there is no simplifying needed here.
The solution is 3 / 5 + 1 / 5 = 4 / 5 .
Adding Fractions with Unlike Denominators
Now let's go through another example but this time with unlike denominators. We will use the same exact three steps.
Find the sum of 1 / 4 + 2 / 3 .
Let's find the lowest common denominator and convert these fractions to like denominators to make them addable. Multiplying the top and bottom of each fraction by the other fraction's denominator gives us 1 / 4 · 3 / 3 = 3 / 12 and 2 / 3 · 4 / 4 = 8 / 12 .
Now let's add the numerators. 3 + 8 = 11, so the sum of our numerators is 11. The denominator is still 12, so our result is 11 / 12 .
11 / 12 is already in its simplest form, so there is no simplifying needed here.
The solution is 1 / 4 + 2 / 3 = 11 / 12 .
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Fraction Word Problems: Addition, Subtraction, and Mixed Numbers
In today’s post, we’re going to see how to solve some of the problems that we’ve introduced in Smartick: fraction word problems. They appear during the word problems section at the end of the daily session.
We’re going to look at how to solve problems involving addition and subtraction of fractions, including mixed fractions (the ones that are made up of a whole number and a fraction).
Try and solve the fraction word problems by yourself first, before you look for the solutions and their respective explanations below.
Fraction Word Problems
Problem nº 1.
Problem nº 2
Problem nº 3
Solution to Problem nº 1
This is an example of a problem involving the addition of a whole number and a fraction.
The simplest way to show the number of cookies I ate is to write it as a mixed number. And the data given in the word problem gives us the result: 9 biscuits and 5 / 6 of a biscuit = 9 5 / 6 biscuits.
Solution to Problem nº 2
In this example, we have to subtract two fractions with the same denominator.
To calculate how full the gas tank is, we have to subtract both fractions. Since we are given fractions, the best way to present the solution is in the form of a fraction. Additionally, we’re dealing with two fractions with the same denominator, so we just have to subtract the numerators of both fractions to get the result. 8 / 10 – 4 / 10 = 4 / 10
Solution to Problem nº 3
This problem requires us to subtract a mixed number and a fraction.
To solve this problem, we need to subtract the number of episodes that were downloaded this morning from the total number of episodes that are now downloaded.
To do this, we need to change the mixed number into a fraction: the 5 becomes 60 / 12 (5 x 12 = 60) and we add it to the fraction 60 / 12 + 8 / 12 = 68 / 12 .
We’ve converted the mixed number 5 8 / 12 to 68 / 12 . Now we just have to subtract the number of episodes that were downloaded yesterday ( 7 / 12 ), 68 / 12 – 7 / 12 = 61 / 12 .
Hopefully, you didn’t need the explanations and were able to solve them yourself without any help!
Fraction Video Tutorials
In the following video tutorials, you can learn a bit more about fractions. And if you would like to learn more math concepts, check out Smartick’s Youtube channel !
Simplifying Fractions
Simplification Using the GCD
Equivalent Fractions
If you would like to practice more fraction word problems like these and others, log in to Smartick and enjoy learning math.
Learn More:
Word Problems with Fractions
What Is a Fraction? Learn Everything There Is to Know!
Using Mixed Numbers to Represent Improper Fractions
Learning How to Subtract Fractions
Learn How to Subtract Fractions
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Easy-to-Follow Methods for Adding Fractions
Last Updated: April 7, 2024 Fact Checked
Practice Problems
Adding fractions with like denominators, adding fractions with unlike denominators, adding mixed numbers.
This article was written by David Jia and by wikiHow staff writer, Ali Garbacz, B.A. . David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 462,379 times.
Adding fractions is an incredibly handy skill to know not only in school but also for everyday things like calculating cooking measurements. This article will guide you step-by-step through adding like fractions, unlike fractions, and mixed numbers—accompanied by tons of examples, of course. By the time you’re finished reading, you’ll be a pro at adding all types of fractions. This article is based on an interview with our academic tutor, David Jia, founder of LA Math Tutoring. Check out the full interview here.
Adding Fractions Together
Make sure the bottom numbers (denominators) are the same. If they aren’t, change them by adjusting the top numbers (numerators) so the bottom numbers are identical.
Add the top numbers together and place the sum over the common denominator (the bottom number).
Simplify the final fraction by dividing the numerator and denominator by their greatest common factor.
Ex. 1 : 1/4 + 2/4
Ex. 2 : 3/8 + 2/8 + 4/8
Ex. 1 : In the equation 1/4 + 2/4 , the numbers 1 and 2 are the numerators. Add the numerators together to get a sum of 3 (1 + 2 = 3).
Ex. 2 : For the equation 3/8 + 2/8 + 4/8 , the numerators are 3 , 2 and 4 . Add the 3 numerators together to get a sum of 9 (3 + 2 + 4 = 9).
Ex. 1 : For the equation 1/4 + 2/4 , the new numerator is 3 (1 + 2 = 3), and the denominator will still be 4 . This gives us an answer of 3/4 (1/4 + 2/4 = 3/4).
Ex. 2 : In the equation 3/8 + 2/8 + 4/8 , the new numerator is 9 (3 + 2 + 4 = 9), and the denominator is still 8 . This yields the answer 9/8 (3/8 + 2/8 + 4/8 = 9/8).
For example, the GCF of the numerator and denominator in the fraction 5/20 is 5 . After dividing both 5 and 20 by 5, you’re left with the reduced fraction 1/4 .
To turn the improper fraction 9/8 into a mixed number, divide the top number by the bottom number. When you divide 9 by 8, you get 1 as a whole number and a remainder of 1 .
Place the whole number in front of the fraction and the remainder in the numerator of the new fraction. Leave the denominator the same. The simplified version of 9/8 will thus be 1 1/8 .
Joseph Meyer
Simplifying a fraction just changes the way the fraction is written. To simplify a fraction, you can cancel out the greatest common factor from the numerator and denominator or convert an improper fraction to a mixed number. This doesn't change the inherent value of the fraction.
Here are 3 example problems we'll work on in this section:
Ex. 1 : 1/3 + 3/5
Ex. 2 : 2/7 + 2/14
Ex. 5 : 1/8 + 1/6
Ex. 1 : Between the denominators 3 and 5, the lowest common denominator is 15 .
Ex. 2 : Between the denominators 7 and 14, the lowest common denominator is 14 .
Ex. 3 : Between the denominators 8 and 6, the lowest common denominator is 24 .
Ex. 1 : The lowest common denominator in the equation 1/3 + 3/5 is 15 . Multiply both the numerator and denominator of 1/3 by 5 to get 5/15 . Then, multiply the numerator and denominator of 3/5 by 3 to get 9/15 .
Ex. 2 : The lowest common denominator in the equation 2/7 + 2/14 is 14 . Multiply both the numerator and denominator of 2/7 by 2 to get 4/14 . Leave 2/14 as is since it already has 14 as its denominator.
Ex. 3 : The lowest common denominator in the equation 1/8 + 1/6 is 24 . Multiply both the numerator and denominator of 1/8 by 3 to get 3/24 . Then, multiply the numerator and denominator of 1/6 by 4 to get 4/24 .
Then, multiply the numerator and denominator of 3/5 by 3 (the denominator of 1/3) to get 9/15 . Both fractions now have a common denominator of 15 .
Then, multiply the numerator and denominator of 2/14 by 7 (the denominator of 2/7) to get 14/98 . Both fractions now have a common denominator of 98 .
Then, multiply the numerator and denominator of 1/6 by 8 (the denominator of 1/8) to get 8/48 . Both fractions now have a common denominator of 48 .
Ex. 1 : The new equation with the lowest common denominator is 5/15 + 9/15 . Add the numerators together to get 14 (5 + 9 = 14).
Ex. 2 : The new equation with the lowest common denominator is 4/14 + 2/14 . Add the numerators together to get 6 (4 + 2 = 6).
Ex. 2 : The new equation with the lowest common denominator is 3/24 + 4/24 . Add the numerators together to get 7 (3 + 4 = 7).
Ex. 1 : For the equation 1/3 + 3/5 , the common denominator is 15 and the new numerator is 14 (5 + 9 = 14). This gives us an answer of 14/15 .
Ex. 2 : For the equation 2/7 + 2/14 , the common denominator is 14 and the new numerator is 6 (4 + 2 = 6). This gives us an answer of 6/14 .
Ex. 2 : For the equation 1/8 + 1/6 , the common denominator is 24 and the new numerator is 7 (4 + 3 = 7). This gives us an answer of 7/24 .
Ex. 2 : The GCF between the numerator and denominator in 6/14 is 2 . Divide the numerator and denominator by 2 to get the reduced answer of 3/7 (6 / 2 = 3 and 14 / 2 = 7).
If you got a final answer like 13/7, divide 13 by 7. This gives you a whole number of 1 and a remainder of 6 . Place the whole number next to the fraction and the remainder over the denominator to get an answer of 1 6/7 .
For example, let’s say we have the equation 5 3/4 + 1 1/8 .
To convert 5 3/4 to an improper fraction, multiply 5 x 4 to get 20 . Then, add 20 to the numerator (3) to get a new numerator of 23 (20 + 3 = 23).
Your new fraction is 23/4 .
To convert 1 1/8 to an improper fraction, multiply 1 x 8 to get 8 . Then, add 8 to the numerator (1) to get a new numerator of 9 (8 + 1 = 9).
The new improper fraction is 9/8 .
For the equation 5 3/4 + 1 1/8 , we changed the mixed numbers into the improper fractions 23/4 and 9/8 to give us the new equation 23/4 + 9/8 .
The two fractions have a lowest common denominator of 8 .
For the equation 23/4 + 9/8 , the common denominator is 8. In that case, multiply both the numerator and denominator of 23/4 by 2 to get a fraction that has the denominator 8.
The resulting fraction will be 46/8 ((23 x 2)/(4 x 2)).
9/8 will remain unchanged since it already has a denominator of 8.
In the new equation 46/8 + 9/8 , add the numerators 46 and 9 together to get 55 .
The final answer for 46/8 + 9/8 is 55/8 .
For the improper fraction 55/8, 8 goes into 55 a total of 6 times. The whole number for the mixed number is 6 .
To find the remainder, subtract 48 (6 x 8) from 55. This yields a remainder of 7 .
To add fractions, start by checking the denominator of each fraction to make sure it’s the same number. If not, multiply each fraction by the other fraction’s denominator to give them a common denominator. For example, when adding ⅓ and ⅗, your new denominator would be 15, and the new multiplied fractions would be 5/15 and 9/15. Once you have the same denominator, add only the numerators together, and put them over the new denominator. For the example, the answer would be 14/15. If you want to learn how to simplify your answers, keep reading the article! Did this summary help you? Yes No
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Fraction Addition Word Problems Worksheets
Pre-Algebra >
Fractions >
Addition >
Look to your laurels by answering our pdf fraction addition word problems worksheets, a collage of well-researched real-world word problems. Adding fractions or mixed numbers is not an alien concept. Whether it's cooking recipes; measuring lengths, weights, etc.; or sharing something among many, fraction addition and mixed-number addition are never too far away. Witness adding fractions and mixed numbers with like and unlike denominators leap into life as you solve this collection of word problems! Begin your learning journey with some of our free worksheets!
Adding Like Fractions
Pump up your practice with a pleasant potpourri of everyday situations in these adding fractions word problems worksheets for 3rd grade, 4th grade, and 5th grade. Keep at it, and summing up two like fractions will soon be a cakewalk!
Adding Unlike Fractions
An eclectic collection of word problems centering around fractions with unlike denominators, this pdf resource proves an imperative addition to your repertoire! Find equivalent like fractions and whizz through the problems!
Adding Fractions with Whole Numbers
Are you a novice wondering how to add fractions to whole numbers? Take a look at the real-life scenarios in these pdf worksheets and say goodbye to all your doubts! Put the numbers together as mixed numbers, and that's your sum.
Adding Mixed Numbers | Same Denominators
Natasha brewed a 1 1/2-ounce shot of espresso for latte and another 1 1/2-ounce shot for Americano. How much coffee did Natasha make in all? 3 shots! Keen to be explored in our printable set are a wealth of such situations!
Adding Mixed Numbers | Different Denominators
Evaluate 5th grade and 6th grade students' skills in adding mixed numbers with different denominators in this part of the fraction addition word problems worksheets. Convert to mixed numbers with the same denominators, and press on!
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Addition and Subtraction of Fraction: Methods, Examples, Facts, FAQs
What is addition and subtraction of fractions, methods of addition and subtraction of fractions, addition and subtraction of mixed numbers, solved examples on addition and subtraction of fractions, practice problems on addition and subtraction of fractions, frequently asked questions on addition and subtraction of fractions.
Addition and subtraction of fractions are the fundamental operations on fractions that can be studied easily using two cases:
Addition and subtraction of like fractions (fractions with same denominators)
Addition and subtraction of unlike fractions (fractions with different denominators)
A fraction represents parts of a whole. For example, the fraction 37 represents 3 parts out of 7 equal parts of a whole. Here, 3 is the numerator and it represents the number of parts taken. 7 is the denominator and it represents the total number of parts of the whole.
Adding and subtracting fractions is simple and straightforward when it comes to like fractions. In the case of unlike fractions, we first need to make the denominators the same. Let’s take a closer look at both these cases.
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Before adding and subtracting fractions, we first need to make sure that the fractions have the same denominators.
When the denominators are the same, we simply add the numerators and keep the denominator as it is. To add or subtract unlike fractions, we first need to learn how to make the denominators alike. Let’s learn how to add fractions and how to subtract fractions in both cases.
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Addition and Subtraction of Like Fractions
The rules for adding fractions with the same denominator are really simple and straightforward.
Let’s learn with the help of examples and visual bar models.
Addition of Like Fractions
Here are the steps to add fractions with the same denominator:
Step 1: Add the numerators of the given fractions.
Addition and subtraction of fractions with unlike denominators can be a little bit tricky since the denominators are not the same. So, we need to first convert the unlike fractions into like fractions. Let’s look at a few ways to do this!
Addition of Unlike Fractions
We can make the denominators the same by finding the LCM of the two denominators. Once we calculate the LCM, we multiply both the numerator and the denominator with an appropriate number so that we get the LCM value in the denominator.
Example: $\frac{3}{5} + \frac{3}{2}$
Step 1: Find the LCM (Least Common Multiple) of the two denominators.
The LCM of 5 and 2 is 10.
Step 2: Convert both the fractions into like fractions by making the denominators same.
$\frac{3 \times 2}{5 \times 2} = \frac{6}{10}$
$\frac{3 \times 5}{2 \times 5} = \frac{15}{10}$
Step 3: Add the numerators. The denominator stays the same.
$\frac{6}{10} + \frac{15}{10} = \frac{21}{10}$
Step 4: Convert the resultant fraction to its simplest form if the GCF of the numerator and denominator is not 1.
In this case, GCF (21,10) $= 1$
The fraction $\frac{21}{10}$ is already in its simplest form.
Thus, $\frac{3}{5} + \frac{3}{2} = \frac{21}{10}$
Subtraction of Unlike Fractions
Let’s learn how to subtract fractions when denominators are not the same. To subtract unlike fractions, we use the LCM method. The process is similar to what we discussed in the previous example.
Example: $\frac{5}{6} \;-\; \frac{2}{9}$
Step 1: Find the LCM of the two denominators.
LCM of 6 and $9 = 18$
Step 2: Convert both the fractions into like fractions by making the denominators same.
$\frac{5 \times 3}{6 \times 3} = \frac{15}{18}$
$\frac{2 \times 2}{9 \times 2} = \frac{4}{18}$
Step 3: Subtract the numerators. The denominator stays the same.
A mixed number is a type of fraction that has two parts: a whole number and a proper fraction. It is also known as a mixed fraction. Any mixed number can be written in the form of an improper fraction and vice-versa.
Adding and subtracting mixed fractions is done by converting mixed numbers into improper fractions .
Addition and Subtraction of Mixed Fractions with Same Denominators
The steps of adding and subtracting mixed numbers with the same denominators are the same. The only difference is the operation.
Step 1: Convert the given mixed fractions to improper fractions.
Step 2: Add/Subtract the like fractions obtained in step 1.
Step 3: Reduce the fraction to its simplest form.
Step 4: Convert the resulting fraction into a mixed number.
We cannot add or subtract fractions without converting them into like fractions.
Like fractions are fractions that have the same denominator, and unlike fractions are fractions that have different denominators.
Equivalent fractions are two different fractions that represent the same value.
The LCD (least common denominator) of two fractions is the LCM of the denominators.
In this article, we have learned about addition and subtraction of fractions (like fractions, unlike fractions, mixed fractions), methods of addition and subtraction of these fractions along with the steps. Let’s solve some examples on adding and subtracting fractions to understand the concept better.
Solve: $\frac{2}{4} + \frac{1}{4}$ .
Solution:
Here, the denominators are the same.
Thus, we add the numerators by keeping the denominators as it is.
$\frac{2}{4} + \frac{1}{4} = \frac{2 + 1}{4}$
$\frac{2}{4} + \frac{1}{4} = \frac{3}{4}$
2. Find the sum of the fractions $\frac{3}{5}$ and $\frac{5}{2}$ by using the LCM method.
$\frac{3}{5}$ and $\frac{5}{2}$ are unlike fractions.
Converting it into a mixed fraction, $\frac{19}{4}$ becomes $4 \frac{3}{4}$.
Thus, the length of the remaining rope is $4\frac{3}{4}$ ft.
Attend this quiz & Test your knowledge.
Find $\frac{2}{4} + \frac{2}{4}$.
$\frac{7}{24} + \frac{5}{16} =$, what is the least common denominator of $\frac{1}{2}$ and $\frac{1}{3}$, $\frac{3}{6} \;-\; \frac{1}{6} =$, what equation does the following figure represent.
How do we add and subtract negative fractions?
Negative fractions are simply fractions with a negative sign. The steps to add and subtract the negative fractions remain the same. We need to follow the rules for addition/subtraction with negative signs.
How can we convert an improper fraction into a mixed number?
To convert an improper fraction into a mixed number, we divide the numerator by the denominator. The denominator stays the same. The quotient represents the whole number part. The remainder represents the numerator of the mixed number.
Example: $\frac{14}{3} = 4\; \text{R}\; 2$
Quotient $= 4$
Remainder $= 2$
$\frac{14}{3} = 4\frac{2}{3}$
How do we divide two fractions?
To divide one fraction by another, we multiply the first fraction by the reciprocal of the second fraction.
For example, $\frac{1}{2} \div \frac{3}{5} = \frac{1}{2} \times \frac{5}{3} = \frac{5}{6}$
What are the rules of adding and subtracting fractions?
Before adding or subtracting, we check if the fractions have the same denominator.
If the denominators are equal, then we add/subtract the numerators keeping the common denominator.
If the denominators are different, then we make the denominators equal by using the LCM method. Once the fractions have the same denominator, we can add/subtract the numerators keeping the common denominator as it is.
How do we add and subtract fractions with whole numbers?
Convert the whole number to a fraction. To do this, give the whole number a denominator of 1.
Convert to fractions of like denominators.
Add/subtract the numerators. Now that the fractions have the same denominators, you can treat the numerators as a normal addition/subtraction problem.
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In the previous lessons, you learned that a fraction is part of a whole. Fractions show how much you have of something, like 1/2 of a tank of gas or 1/3 of a cup of water.
In real life, you might need to add or subtract fractions. For example, have you ever walked 1/2 of a mile to work and then walked another 1/2 mile back? Or drained 1/4 of a quart of gas from a gas tank that had 3/4 of a quart in it? You probably didn't think about it at the time, but these are examples of adding and subtracting fractions.
Click through the slideshow to learn how to set up addition and subtraction problems with fractions.
Let's imagine that a cake recipe tells you to add 3/5 of a cup of oil to the batter.
You also need 1/5 of a cup of oil to grease the pan. To see how much oil you'll need total, you can add these fractions together.
When you add fractions, you just add the top numbers, or numerators .
That's because the bottom numbers, or denominators , show how many parts would make a whole.
We don't want to change how many parts make a whole cup ( 5 ). We just want to find out how many parts we need total.
So we only need to add the numerators of our fractions.
We can stack the fractions so the numerators are lined up. This will make it easier to add them.
And that's all we have to do to set up an addition example with fractions. Our fractions are now ready to be added.
We'll do the same thing to set up a subtraction example. Let's say you had 3/4 of a tank of gas when you got to work.
If you use 1/4 of a tank to drive home, how much will you have left? We can subtract these fractions to find out.
Just like when we added, we'll stack our fractions to keep the numerators lined up.
This is because we want to subtract 1 part from 3 parts.
Now that our example is set up, we're ready to subtract!
Try setting up these addition and subtraction problems with fractions. Don't try solving them yet!
You run 4/10 of a mile in the morning. Later, you run for 3/10 of a mile.
You had 7/8 of a stick of butter and used 2/8 of the stick while cooking dinner.
Your gas tank is 2/5 full, and you put in another 2/5 of a tank.
Solving addition problems with fractions
Now that we know how to write addition problems with fractions, let's practice solving a few. If you can add whole numbers , you're ready to add fractions.
Click through the slideshow to learn how to add fractions.
Let's continue with our previous example and add these fractions: 3/5 of cup of oil and 1/5 of a cup of oil.
Remember, when we add fractions, we don't add the denominators.
This is because we're finding how many parts we need total. The numerators show the parts we need, so we'll add 3 and 1 .
3 plus 1 equals 4 . Make sure to line up the 4 with the numbers you just added.
The denominators will stay the same, so we'll write 5 on the bottom of our new fraction.
3/5 plus 1/5 equals 4/5 . So you'll need 4/5 of a cup of oil total to make your cake.
Let's try another example: 7/10 plus 2/10 .
Just like before, we're only going to add the numerators. In this example, the numerators are 7 and 2 .
7 plus 2 equals 9 , so we'll write that to the right of the numerators.
Just like in our earlier example, the denominator stays the same.
So 7/10 plus 2/10 equals 9/10 .
Try solving some of the addition problems below.
Solving subtraction problems with fractions
Subtracting fractions is a lot like regular subtraction. If you can subtract whole numbers , you can subtract fractions too!
Click through the slideshow to learn how to subtract fractions.
Let's use our earlier example and subtract 1/4 of a tank of gas from 3/4 of a tank.
Just like in addition, we're not going to change the denominators.
We don't want to change how many parts make a whole tank of gas. We just want to know how many parts we'll have left.
We'll start by subtracting the numerators. 3 minus 1 equals 2 , so we'll write 2 to the right of the numerators.
Just like when we added, the denominator of our answer will be the same as the other denominators.
So 3/4 minus 1/4 equals 2/4 . You'll have 2/4 of a tank of gas left when you get home.
Let's try solving another problem: 5/6 minus 3/6 .
We'll start by subtracting the numerators.
5 minus 3 equals 2 . So we'll put a 2 to the right of the numerators.
As usual, the denominator stays the same.
So 5/6 minus 3/6 equals 2/6 .
Try solving some of the subtraction problems below.
After you add or subtract fractions, you may sometimes have a fraction that can be reduced to a simpler fraction. As you learned in Comparing and Reducing Fractions , it's always best to reduce a fraction to its simplest form when you can. For example, 1/4 plus 1/4 equals 2/4 . Because 2 and 4 can both be divided 2 , we can reduce 2/4 to 1/2 .
Adding fractions with different denominators
On the last page, we learned how to add fractions that have the same denominator, like 1/4 and 3/4 . But what if you needed to add fractions with different denominators? For example, our cake recipe might say to blend 1/4 cup of milk in slowly and then dump in another 1/3 of a cup.
In Comparing and Reducing Fractions , we compared fractions with a different bottom number, or denominator. We had to change the fractions so their denominators were the same. To do that, we found the lowest common denominator , or LCD .
We can only add or subtract fractions if they have the same denominators. So we'll need to find the lowest common denominator before we add or subtract these fractions. Once the fractions have the same denominator, we can add or subtract as usual.
Click through the slideshow to learn how to add fractions with different denominators.
Let's add 1/4 and 1/3 .
Before we can add these fractions, we'll need to change them so they have the same denominator .
To do that, we'll have to find the LCD , or lowest common denominator, of 4 and 3 .
It looks like 12 is the smallest number that can be divided by both 3 and 4, so 12 is our LCD .
Since 12 is the LCD, it will be the new denominator for our fractions.
Now we'll change the numerators of the fractions, just like we changed the denominators.
First, let's look at the fraction on the left: 1/4 .
To change 4 into 12 , we multiplied it by 3 .
Since the denominator was multiplied by 3 , we'll also multiply the numerator by 3 .
1 times 3 equals 3 .
1/4 is equal to 3/12 .
Now let's look at the fraction on the right: 1/3 . We changed its denominator to 12 as well.
Our old denominator was 3 . We multiplied it by 4 to get 12.
We'll also multiply the numerator by 4 . 1 times 4 equals 4 .
So 1/3 is equal to 4/12 .
Now that our fractions have the same denominator, we can add them like we normally do.
3 plus 4 equals 7 . As usual, the denominator stays the same. So 3/12 plus 4/12 equals 7/12 .
Try solving the addition problems below.
Subtracting fractions with different denominators
We just saw that fractions can only be added when they have the same denominator. The same thing is true when we're subtracting fractions. Before we can subtract, we'll have to change our fractions so they have the same denominator.
Click through the slideshow to learn how to subtract fractions with different denominators.
Let's try subtracting 1/3 from 3/5 .
First, we'll change the denominators of both fractions to be the same by finding the lowest common denominator .
It looks like 15 is the smallest number that can be divided evenly by 3 and 5 , so 15 is our LCD.
Now we'll change our first fraction. To change the denominator to 15 , we'll multiply the denominator and the numerator by 3 .
5 times 3 equals 15 . So our fraction is now 9/15 .
Now let's change the second fraction. To change the denominator to 15 , we'll multiply both numbers by 5 to get 5/15 .
Now that our fractions have the same denominator, we can subtract like we normally do.
9 minus 5 equals 4 . As always, the denominator stays the same. So 9/15 minus 5/15 equals 4/15 .
Try solving the subtraction problems below.
Adding and subtracting mixed numbers
Over the last few pages, you've practiced adding and subtracting different kinds of fractions. But some problems will need one extra step. For example, can you add the fractions below?
In Introduction to Fractions , you learned about mixed numbers . A mixed number has both a fraction and a whole number . An example is 2 1/2 , or two-and-a-half . Another way to write this would be 5/2 , or five-halves . These two numbers look different, but they're actually the same.
5/2 is an improper fraction . This just means the top number is larger than the bottom number. Even though improper fractions look strange, you can add and subtract them just like normal fractions. Mixed numbers aren't easy to add, so you'll have to convert them into improper fractions first.
Let's add these two mixed numbers: 2 3/5 and 1 3/5 .
We'll need to convert these mixed numbers to improper fractions. Let's start with 2 3/5 .
As you learned in Lesson 2 , we'll multiply the whole number, 2 , by the bottom number, 5 .
2 times 5 equals 10 .
Now, let's add 10 to the numerator, 3 .
10 + 3 equals 13 .
Just like when you add fractions, the denominator stays the same. Our improper fraction is 13/5 .
Now we'll need to convert our second mixed number: 1 3/5 .
First, we'll multiply the whole number by the denominator. 1 x 5 = 5 .
Next, we'll add 5 to the numerators. 5 + 3 = 8 .
Just like last time, the denominator remains the same. So we've changed 1 3/5 to 8/5 .
Now that we've changed our mixed numbers to improper fractions, we can add like we normally do.
13 plus 8 equals 21 . As usual, the denominator will stay the same. So 13/5 + 8/5 = 21/5 .
Because we started with a mixed number, let's convert this improper fraction back into a mixed number.
As you learned in the previous lesson , divide the top number by the bottom number. 21 divided by 5 equals 4, with a remainder of 1 .
The answer, 4, will become our whole number.
And the remainder , 1, will become the numerator of the fraction.
These grade 5 worksheets provide practice in adding and subtracting fractions with both like and unlike denominators .
3/8 + 4/8 =
3/8 + 3 4/8 =
(like denominators)
4 3/8 + 3 4/8 =
2 3/4 + ___ = 5
2/5 + 2/3 =
5 2/5 + 2/3 =
5 2/5 + 4 2/3 =
5/7 - 3/7 =
6 - 3/7 =
3 2/7 - 3/7 =
(same denominators)
3 2/7 - 1 3/7 =
(missing number)
3 2/7 - ___ = 1 6/7
4/5 - 2/3 =
(harder)
17/25 - 2/3 =
(unlike denominators)
16 8/9 - 5 1/8 =
Sample Grade 5 Adding Fractions Worksheet
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Explore all of our fractions worksheets , from dividing shapes into "equal parts" to multiplying and dividing improper fractions and mixed numbers.
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Adding and Subtracting Fraction Word Problems
Subject: Mathematics
Age range: 7-11
Resource type: Worksheet/Activity
Last updated
16 June 2015
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Helpful sheet for practicing wordy fraction questions. Answers can sometimes be simplified further.
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Addition Lesson: Strategies, Techniques, and Practical Applications
Lesson overview, introduction to addition lesson, what is addition, how is addition classified, what are the basic principles of addition, what are the important addition rules, how do you add fractions, how do you add decimals, how do you add powers, how do you add reciprocal numbers, what are the properties of addition, how is addition used in real-world problems.
Addition is one of the four fundamental arithmetic operations, alongside subtraction, multiplication, and division. It forms the basis of many mathematical concepts and is essential for understanding how numbers interact. This addition lesson will guide you through the fundamental principles of addition, starting with the basics and progressing to more advanced techniques. We will cover addition with whole numbers, fractions, decimals, powers, and reciprocal numbers, ensuring you develop a comprehensive understanding of each concept.
Mastering addition is crucial for both academic success and practical applications in everyday life. From calculating totals while shopping to solving complex mathematical problems, addition is a skill that is frequently used. In this lesson, we will explore various addition strategies, techniques, and tips to help you solve addition problems efficiently and accurately.
Addition is a basic arithmetic operation that involves combining two or more numbers to find their total. This operation is essential for understanding relationships between quantities and is widely used in various mathematical and real-life applications. In addition, the numbers being combined are called addends, and the result is known as the sum.For example, in the equation, 4 + 3 = 7, 4 and 3 are the addends, and 7 is the sum. Understanding the basics of addition is crucial for tackling more complex problems and applying addition techniques in everyday situations. A solid grasp of addition forms the foundation for learning other mathematical operations and enhances overall mathematical skills.
Addition can be classified into different categories based on the types of numbers being added and the methods used. Here's how addition is classified
Addition of Whole Numbers Addition of whole numbers is the most basic form of addition, involving positive integers. This is often the first type of addition learned in early mathematics education. Example: 5 + 7 = 12
Addition of Fractions When adding fractions, it is important to have a common denominator. This classification deals with combining parts of whole numbers, focusing on ensuring that the fractions have a shared base before performing the addition.
Example: 1/2+1/3 = 3/6+2/6 = 5/6
Addition of Decimals Addition of decimals requires aligning the decimal points and then adding the numbers as with whole numbers. This classification handles numbers with fractional parts expressed in decimal form. Example: 3.75 + 2.5 = 6.25
Addition of Powers Adding powers typically involves combining terms with the same base and exponent. If the exponents or bases differ, the addition is handled differently, usually resulting in an expression that cannot be simplified further. Example : 4x 2 +3x 2 =7x 2
Addition of Reciprocal Numbers This classification deals with adding numbers that are inverses of each other. The addition of reciprocal numbers often involves finding a common denominator and then performing the addition.
Example: 1/4 + 1/6 = 3/12 + 2/12 = 5/12
The basic principles of addition provide the foundation for understanding how this operation works in various mathematical contexts. Here are the detailed explanations of these principles
Commutative Property The commutative property of addition states that changing the order of the addends does not change the sum. For example, 3 + 4 = 4 + 3 = 7. This property shows that addition can be performed in any order, making calculations flexible and straightforward.
Associative Property The associative property of addition indicates that when adding three or more numbers, the way the numbers are grouped does not affect the sum. For example, (2 + 3) + 4 = 2 + (3 + 4) = 9. This property is useful in simplifying complex addition problems by grouping numbers in a way that makes calculation easier.
Identity Property The identity property of addition states that adding zero to any number leaves the number unchanged. For example, 5 + 0 = 5. This property highlights the role of zero as the identity element in addition, maintaining the original value of the addend.
Additive Inverse The additive inverse principle states that for every number, there exists another number that when added together, equals zero. For example, 7 + (-7) = 0. This principle is essential for understanding subtraction as the inverse of addition.
Distributive Property The distributive property of addition over multiplication states that a(b + c) = ab + ac. This property is particularly useful in algebra and helps in simplifying expressions and solving equations.
Addition has several important rules that help in understanding and performing the operation correctly. Here are the detailed explanations of these rules
Order of Operations (PEMDAS/BODMAS) When addition is combined with other operations such as multiplication or division, the order of operations must be followed. Addition is typically performed after multiplication or division unless parentheses indicate otherwise.
Carrying Over In addition involving multi-digit numbers, when the sum of digits in a column exceeds 9, the extra value is carried over to the next column. For example, in adding 27 + 35, the sum of the units column (7 + 5 = 12) requires carrying over 1 to the tens column, resulting in 62.
Handling Negative Numbers When adding negative numbers, the process is similar to adding positive numbers, but with special attention to the signs. For example, adding -3 + 4 is equivalent to subtracting 3 from 4, resulting in 1.
Decimal Alignment When adding decimals, it is crucial to align the decimal points to ensure that digits are added in the correct place value columns. This alignment prevents errors and ensures accurate results.
Fraction Addition Adding fractions requires finding a common denominator before adding the numerators. This ensures that the fractions represent comparable quantities, making the addition accurate.
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Adding fractions involves several steps to ensure accuracy. Here is a detailed explanation along with three examples to illustrate the process
Find a Common Denominator Ensure both fractions have the same denominator. If they do not, find the least common denominator (LCD) and adjust the fractions accordingly.
Add the Numerators Once the fractions have the same denominator, add the numerators while keeping the denominator the same.
Simplify Reduce the fraction to its simplest form, if possible, by dividing both the numerator and the denominator by their greatest common divisor (GCD).
Example 1 Adding Fractions with the Same Denominator
3/8+4/8 = 7/8
The fractions already have the same denominator (8).
Add the numerators 3 + 4 = 7
The result is 7/8
Example 2 Adding Fractions with Different Denominators
3/4+1/6
Find a common denominator. The least common denominator of 4 and 6 is 12.
Adjust the fractions 3/4= 9/12 (by multiplying the numerator and denominator by 3).
Adjust the fractions 1/6= 2/12 by multiplying the numerator and denominator by 2).
Add the numerators 9 + 2 = 11.
The result is 11/12, which is already in its simplest form.
Example 3 Adding Mixed Numbers
2 1/3+ 1 1/2
Convert the mixed numbers to improper fractions.
2 1/3 = 2 X 3 + 1/3 = 7/3
1 1/2 = 1 X 2 + 1/2 = 3/2
Find a common denominator. The least common denominator of 3 and 2 is 6.
Adjust the fractions 7/3 = 14/6 (by multiplying the numerator and denominator by 2).
Adjust the fractions 3/2 = 9/6 (by multiplying the numerator and denominator by 3).
Subtract the numerators 14+9 = 23.
The result is 23/6
Adding decimals follows a similar process to adding whole numbers, with careful attention to the placement of the decimal point. Here is a detailed explanation along with three examples
Align the Decimal Points Ensure the decimal points of both numbers are aligned vertically. This helps to correctly place the digits in the right columns.
Add Normally Perform the addition as with whole numbers, starting from the rightmost digit and moving leftward.
Place the Decimal Point Ensure the decimal point in the result is aligned with the decimal points of the numbers being added.
Example 1 Adding Simple Decimals To add 4.25 and 3.6 Align the decimal points: 4.25 +3.60 Add normally 7.85 The decimal point in the result is aligned with the numbers being added.
Example 2 Adding Decimals with Different Numbers of Decimal Places To add 5.7 and 2.345 Align the decimal points and add zeros as necessary 5.700 +2.345 Add normally 8.045 The decimal point in the result is aligned with the numbers being added.
Example 3 Adding Larger Decimals To add 123.456 and 78.123 Align the decimal points: 123.456 +78.123 Add normally 201.579 The decimal point in the result is aligned with the numbers being added.
Adding powers involves specific rules when the powers share the same base and exponent. Here's a detailed explanation along with three examples
Ensure Same Exponents To add powers, the terms must have the same base and exponent. This allows for the coefficients to be added while keeping the base and exponent unchanged.
Add the Coefficients When the exponents are the same, add the coefficients of the terms.
Maintain the Base and Exponent The base and exponent of the terms remain unchanged after adding the coefficients.
Example 1 Adding Powers with the Same Base and Exponent To add 3x 2 and 5x 2 Ensure the exponents are the same. Here, both terms have the base x and exponent 2. Add the coefficients 3 + 5 = 8. Maintain the base and exponent 8x 2 .
Example 2 Adding Larger Powers with the Same Base and Exponent To add 6y 3 and 2y 3 Ensure the exponents are the same. Both terms have the base y and exponent 3. Add the coefficients 6 + 2 = 8. Maintain the base and exponent: 8y 3 .
Example 3 Adding Negative Powers with the Same Base and Exponent To add −4z 4 and −3z 4 Ensure the exponents are the same. Both terms have the base z and exponent 4. Add the coefficients -4 + (-3) = -7. Maintain the base and exponent −7z 4 .
Adding reciprocal numbers involves a few key steps to ensure the process is done correctly. Here is a detailed explanation along with three examples to illustrate the process
Find the Common Denominator Make the denominators of the fractions the same. This allows for straightforward addition of the numerators.
Add the Numerators Once the fractions have the same denominator, add the numerators.
Example 1 Adding Simple Reciprocal Numbers
Add 1/2 and 1/3
3/6 + 2/6 = 5/6
Final Answer 1/2 + 1/3 = 5/6
Example 2 Adding Reciprocal Numbers with Different Denominators
Add 1/4 and 1/5
5/20 + 4/20 = 9/20
Final Answer 1/4 + 1/5 = 9/20
Example 3 Adding Larger Reciprocal Numbers
Add 1/6 and 1/8
4/24 + 3/24 = 7/24
Final Answer 1/6 + 1/8 = 7/24
Addition has several important properties that help us understand and perform this operation correctly. Here are the detailed explanations of these properties
Both equations result in 8.
This property shows that the order in which you add numbers doesn't affect the result, making calculations flexible.
(2+3)+4=2+(3+4)
Both groupings result in 9.
This property is useful when simplifying addition problems by grouping numbers in a way that makes the calculation easier.
The result is 7.
This property highlights the role of zero as the identity element in addition, maintaining the original value of the addend.
The result is 0.
This property is essential for understanding subtraction as the inverse operation of addition.
2×(3+4)=(2×3)+(2×4)
Both sides result in 14.
This property is particularly useful in algebra for simplifying expressions and solving equations.
Addition is a fundamental operation that plays a critical role in many real-world scenarios. Here are detailed explanations and examples of how addition is applied in different contexts
Suppose you spent $45 on groceries, $30 on fuel, and $25 on dining out. To find the total amount spent, you add these expenses together:
$45 + $30 + $25 = $100
The total amount spent is $100.
Example Balancing a Checkbook
If you start with a balance of $1,200 and deposit $500, you add the deposit to your balance to find the new total
$1,200 + $500 = $1,700
Your new balance is $1,700.
If a recipe requires 2 cups of flour and you add another 1/2 cup, you calculate the total amount of flour used by adding the quantities together
2 cups + 1/2 cup = 2 1/2 cups
You now have a total of 2 1/2 cups of flour.
Example Calculating Total Distance Traveled
If you drive 60 miles to visit a friend and then another 30 miles to reach your final destination, the total distance traveled is:
60 miles + 30 miles = 90 miles
You traveled a total of 90 miles.
A store starts with 150 units of a product. After receiving a shipment of 50 more units, the new inventory level is calculated by adding the shipment to the existing stock:
150 units + 50 units = 200 units
The store now has 200 units in stock.
Example Tracking Sales and Stock Levels
If a store sells 30 units of a product on Monday and 40 units on Tuesday, the total number of units sold is
30 units + 40 units = 70 units
The store sold 70 units over two days.
If you worked 8 hours on Monday and 7 hours on Tuesday, the total number of hours worked is
8 hours + 7 hours = 15 hours
You worked a total of 15 hours over those two days.
Example Scheduling Appointments
If an appointment starts at 2:00 PM and lasts for 45 minutes, you add the duration to the start time to find the end time:
2:00 PM + 45 minutes = 2:45 PM
The appointment ends at 2:45 PM.
If a student scores 85 on a math test, 90 on a science test, and 88 on an English test, the total score across these subjects is:
85 + 90 + 88 = 263
The student's total score is 263.
Example Analyzing Survey Results
If a survey receives responses from 120 participants in one week and 150 participants in the next week, the total number of responses is
120 + 150 = 270
The survey received a total of 270 responses over the two weeks.
Great job on completing this addition lesson! You've now gained a comprehensive understanding of addition, one of the most essential mathematical operations. This lesson has taken you through the key concepts of addition, from the basics of combining numbers to more advanced techniques like adding fractions, decimals, and powers.
We explored the core properties of addition, such as commutativity, associativity, and the identity property, which are foundational to solving problems efficiently. You've also seen how addition plays a vital role in real-life situations, whether it's managing finances, calculating time, or analyzing data. With the knowledge and strategies you've acquired, you're now equipped to apply addition confidently in various contexts, making it a valuable skill both in and out of the classroom.
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What Do 2nd Graders Learn in Math | 9 Key Topics
After building foundational math skills in 1st grade, children move on to 2nd grade, where they learn new math concepts. In 2nd grade, your child will build on what they’ve already learned, delving deeper into numbers, operations, and problem-solving. This year, they’ll strengthen their skills in addition and subtraction and start to explore the basics of multiplication and division. They’ll work with larger numbers, understand place value more thoroughly, and begin to tell time to the nearest five minutes. Your child will also get hands-on with money and basic geometry and start learning about fractions.
Here’s an overview of what 2nd graders typically learn in math and how these concepts contribute to their overall growth.
9 Important Second-Grade Math Topics and Skills
1. mental addition and subtraction.
In 2nd grade, one of the key math skills your child will develop is mental addition and subtraction. This involves solving basic math problems in their head without needing a pencil and paper. By practicing these skills, your child will become faster and more confident in handling numbers.
At this stage, your child will start with simple addition and subtraction facts, working with numbers up to 20. They’ll gradually move on to larger numbers, learning to add and subtract within 100, and even explore the concept of carrying over (in addition) and borrowing (in subtraction).
To make mental math easier, your child will learn strategies like breaking down numbers into smaller parts and rounding numbers to the nearest ten. For example, instead of adding 47 and 26 all at once, they might break it down to add 40 + 20 and then 7 + 6, combining the sums to get the final answer. And for rounding numbers, your child might round 48 up to 50 or 72 down to 70, making the addition or subtraction simpler.
2. Place Value and Expanded Form
In 2nd grade, your child will continue to build on what they learned about numbers in 1st grade, diving deeper into the concept of place value. This year, they’ll better understand odd and even numbers, working with one-digit, two-digit, and even three-digit numbers. Place value helps them see that each digit in a number has a special role—whether in the ones, tens, or hundreds place.
Your child will practice figuring out which digit stands for ones, tens, or hundreds in various numbers. They’ll also learn how to write numbers in words, making the connection between the digits they see and the words they say.
A big focus this year is on the expanded form . This means breaking down a number to show the value of each digit. For example, 267 would be written as 200+60+7 in expanded form. It’s fun for kids to see how numbers are together and understand what each part represents.
3. Complex Addition and Subtraction
2nd grade math books present various problems that challenge your child to perform more complex addition and subtraction. They’ll also encounter word problems that require them to apply these skills in real-world situations, helping them see the practical side of math.
Your child will be introduced to the number line to make working with larger numbers easier. This tool helps them visualize how numbers move up and down as they add or subtract, making it easier to grasp the concept of working with bigger figures.
4. Coordination, Charts, and Graphs
In 2nd grade, your child will start exploring the world of coordination, charts, and graphs—an important step in developing their data interpretation skills. This year, they’ll be introduced to the basics of graphing on a coordinate grid, learning how to use coordinates to plot images on a graph. It’s a fun and engaging way to help them understand how data can be represented visually.
Through this introduction, your child will get hands-on experience with different types of graphs, including pictographs, bar graphs, and line plots. They’ll learn to read these graphs, interpret the data they show, and even create their own. By practicing with these tools, your child will develop the ability to understand, analyze, and present information clearly and organized.
5. Geometry and Fractions
In 2nd grade, your child will begin to explore the basics of geometry and fractions, two fundamental concepts that lay the groundwork for more advanced math in later years. They’ll start by learning to identify shapes based on the number of sides they have, which helps them recognize and categorize different types of shapes.
Your child will also be introduced to geometric concepts such as endpoints, line segments, and angles. These ideas help them understand how shapes are formed and how different parts of a shape relate to each other.
As they delve into geometry, your child will also learn about fractions . Using shapes, they’ll discover how to divide a whole into equal parts and how to describe these parts using fractions. They’ll get familiar with terms like numerator and denominator, which are key to understanding how fractions work.
6. Word Problems
In 2nd grade, word problems become a key part of your child’s math learning journey. Nearly every lesson in the 2nd-grade curriculum includes word problems directly related to the topic. These problems are designed to help your child apply the math concepts they’re learning to real-life situations, making the lessons more engaging and practical.
Your child will encounter word problems across various topics, including simple and complex addition and subtraction, the number line, fractions, telling time, and even an introduction to simple multiplication. By working through these problems, your child will develop critical thinking skills and learn how to break down a problem, figure out what’s being asked, and use the appropriate math operations to find the solution.
7. Measurement
In 2nd grade, your child will start learning about measurement —a key skill that helps them understand the sizes and lengths of objects around them. This year, they’ll be introduced to the ruler, discovering how the lines on one side measure in inches and on the other side in centimeters.
Through hands-on practice, your child will measure images in their books, gaining experience with inches and centimeters. They’ll learn when to use each type of measurement, helping them grasp the concept of different units of measurement and how they apply to various situations.
This measurement lesson teaches your child how to use a ruler and helps them understand the concept of size. It makes it easier for them to compare objects and see the world in a more structured way. By the end of 2nd grade, your child will be more comfortable with measurement, setting the foundation for more advanced math and science concepts.
8. Telling Time
In 2nd grade, your child will begin mastering the important skill of telling time . They’ll start by learning the basics of reading analog and digital clocks, an essential part of their daily routine. Through engaging exercises and clear illustrations, your child will practice identifying the hour hand, minute hand, and second hand on an analog clock.
2nd grade books provide plenty of opportunities for your child to practice telling time, whether reading a clock to the nearest hour, half-hour, or minute. Working with analog and digital clocks, your child will understand how time is measured and represented in different formats.
9. Multiplication
As 2nd grade comes to a close, your child will be introduced to the exciting world of multiplication. This new math operation is a big step forward, and it all starts with learning the times tables. Your child will begin by completing a chart that helps them understand and memorize the times tables for numbers 1 through 12.
The lessons in this section are designed to make multiplication approachable and engaging. Your child will be given plenty of practice to help them master this new skill, building a strong foundation for more advanced math in the future. Through these exercises, they’ll learn how multiplication works, how it relates to addition, and how to use it in real-life situations.
Parental Involvement Tips
Parental support is crucial in helping your 2nd grader succeed in math. The good news is you don’t need to be a math expert to make a big difference! Simple, everyday activities can become fun learning opportunities that show your child how math is used in real life.
For example, you can start by counting coins together. Whether you’re saving up for something special or just sorting loose change, this activity helps your child practice counting and understanding the value of money.
Maintaining a family calendar is another great way to involve your child in math. Let them help you mark important dates and count the days of a big event. It’s a fun way to teach them about time and planning.
When you’re in the kitchen, invite your child to help. Measuring ingredients and following a recipe are perfect ways to practice math skills like fractions and addition. Plus, it’s a great bonding experience!
Even sorting pantry items can become a math lesson. Ask your child to group items by size, weight, or category. This reinforces their understanding of measurement and classification and helps keep the pantry organized!
By incorporating these simple activities into your daily routine, you’ll make math fun and show your child how math is a part of everyday life.
End-of-Year Skills Checklist
As your child wraps up 2nd grade, it’s helpful to know what key math skills they should have mastered by the end of the year. Here’s a checklist of the essential abilities your child should be proficient in:
Adding and Subtracting within 100 : Your child should confidently add and subtract numbers up to 100 mentally and on paper.
Understanding Place Value : They should be able to break down numbers into hundreds, tens, and ones and understand the value of each digit in a number.
Mastering Basic Multiplication : By the end of 2nd grade, your child will have a solid introduction to multiplication and should know the times tables for 1 through 12.
Working with Simple Fractions : Your child should understand basic fractions, like halves, thirds, and quarters, and be able to identify them in shapes and numbers.
Telling Time : They should be able to read analog and digital clocks, tell time to the nearest five minutes, and understand the concepts of AM and PM.
Solving Word Problems : Your child should be comfortable solving word problems that involve addition, subtraction, and simple multiplication, applying their math skills to real-life scenarios.
Understanding and Creating Graphs : Students should know how to read and create simple graphs, such as bar graphs and pictographs, and interpret data using them.
Measurement Skills : Your child should be able to measure objects using inches and centimeters and understand when to use different units of measurement.
Identifying Shapes and Geometry Basics : They should be able to recognize and name various shapes, understand basic geometry terms like line segments and angles, and begin to explore 3D shapes.
Supporting Your Child With Second Grade Math At Genie Academy
At Genie Academy, second grade is a crucial time for your child to build a strong foundation in math. That’s why we’re here to help! Our tutoring center supports kids and teens with core subjects like math, abacus , reading , writing , and coding . But let’s be honest—math is one of our favorites, and we’re good at it!
Our expert tutors have a knack for making math fun and understandable. They use creative and engaging methods personalized to your child’s unique learning style so math becomes something they enjoy rather than struggle with. We’ve seen so many second graders flourish in math after working with us, and we’re proud to be a part of their success stories.
Whether you prefer online sessions or in-person tutoring, we’ve got you covered with flexible options that fit your family’s needs. Our curriculum is not just productive—it’s designed to be interactive and enjoyable, making learning a rewarding experience for your child.
We offer both in-person and online classes. Our locations include East Brunswick , Hillsborough , Marlboro , South Brunswick , Plainsboro , and South Plainfield , New Jersey.
Learn more about us , our core values , our philosophy , our numerous success stories , and our history . Also, read our reviews and testimonials and learn about the true benefits of Genie Academy.
Second grade is a crucial time for your child to build a strong foundation in maths that will prepare them for future success. These skills are essential to boosting their confidence and understanding, from mental arithmetic to mastering basic multiplication.
At Genie Academy, we’re here to make learning maths fun and effective. Our experienced tutors are dedicated to helping your child succeed, and with our flexible online and in-person options, we ensure they get the support they need. We’re excited to be a part of your child’s success in maths and see them grow into a confident prodigy!
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Grade 4 word problem worksheets on adding and subtracting fractions
Solving word problems associated with Fractions
Fraction Problem Solving Worksheet 2
Adding And Subtracting Fractions Word Problems Worksheets
32 Adding Fractions Word Problems Worksheet
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Problem Solving Involving Fractions
Addition and Subtraction of Fractions
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Adding fractions word problems
Solution. This word problem requires addition of fractions. Choosing a common denominator of 4, we get. 1/2 + 3/4 = 2/4 + 3/4 = 5/4. So, John walked a total of 5/4 miles. Example #2: Mary is preparing a final exam. She study 3/2 hours on Friday, 6/4 hours on Saturday, and 2/3 hours on Sunday. How many hours she studied over the weekend.
Add & subtract fractions word problems
Like & unlike denominators. Below are our grade 5 math word problem worksheet on adding and subtracting fractions. The problems include both like and unlike denominators, and may include more than two terms. Worksheet #1 Worksheet #2 Worksheet #3 Worksheet #4. Worksheet #5 Worksheet #6.
Fraction Addition Word Problems Worksheets
A wealth of real-life scenarios that involve addition of fractions with whole numbers and addition of two like fractions, two unlike fractions, and two mixed numbers, our pdf worksheets are indispensable for grade 3, grade 4, grade 5, and grade 6 students. The free fraction addition word problems worksheet is worth a try!
Worksheets for fraction addition
Fraction addition worksheets: grades 6-7. In grades 6 and 7, students simply practice addition with fractions that have larger denominators than in grade 5. Add two fractions, select (easier) denominators within 2-25. View in browser Create PDF. Add three fractions, select (easier) denominators within 2-25.
How to Add Fractions in 3 Easy Steps
To add fractions with different denominators, you need to find a common denominator. A common denominator is a number that both denominators can divide into evenly. You can solve problems involving adding fractions for either scenario by applying the following 3-step process: Step One: Identify whether the denominators are the same or different.
Solving Word Problems by Adding and Subtracting Fractions and Mixed
Answer: The carpenter needs to cut four and seven-twelfths feet of wood. Summary: In this lesson we learned how to solve word problems involving addition and subtraction of fractions and mixed numbers. We used the following skills to solve these problems: Add fractions with like denominators. Subtract fractions with like denominators.
Adding Fractions
Adding Fractions. A fraction like 3 4 says we have 3 out of the 4 parts the whole is divided into. To add fractions there are Three Simple Steps: Step 1: Make sure the bottom numbers (the denominators) are the same. Step 2: Add the top numbers (the numerators), put that answer over the denominator. Step 3: Simplify the fraction (if possible)
Adding Fractions Worksheets
If you are looking to add fractions which have the same denominator, take a look at our sheets below. Sheet 1: the easiest sheet, no simplifying or converting needed. Sheet 2: Fractions need adding then simplifying. Sheet 3: fractions need simplifying and/or converting from an improper fraction into a mixed number.
Adding and Subtracting Fractions Worksheets
Whenever you are adding or subtracting fractions, the key is having both fractions having common denominators. If both fractions share a common denominator, you can simply add/subtract the numerators together, keep the denominator as is, and simplify the result if possible. For example, we could solve the problem: 1/4 + 2/4 as follows:
Adding Fractions Lesson (Examples + Practice Problems)
Here's an example of adding fractions with like denominators, using the three steps from earlier. Find the sum of 3 / 5 + 1 / 5. Solution: The denominators are already the same, so we can skip step 1. Let's add the numerators. 3 + 1 = 4, so the sum of our numerators is 4. The denominator is still 5, so our result is 4 / 5.
Fraction Word Problems: Addition, Subtraction, and Mixed Numbers
Problem nº 1. Problem nº 2. Problem nº 3. Solution to Problem nº 1. This is an example of a problem involving the addition of a whole number and a fraction. The simplest way to show the number of cookies I ate is to write it as a mixed number. And the data given in the word problem gives us the result: 9 biscuits and 5 / 6 of a biscuit = 9 ...
How to Add Fractions: A Step-by-Step Guide (with Examples)
Add the 3 numerators together to get a sum of 9 (3 + 2 + 4 = 9). 3. Put the new numerator on top and leave the denominator as is. Take the sum of the numerators and place it on the top of the fraction. When you add like fractions, you don't add the denominators together.
Adding Fractions Practice Questions
The Corbettmaths Practice Questions on Adding Fractions. Welcome; Videos and Worksheets; Primary; 5-a-day. 5-a-day GCSE 9-1; 5-a-day Primary; 5-a-day Further Maths; More. ... Addition, Adding. Practice Questions. Previous: Solving Quadratics Practice Questions. Next: Dividing Fractions Practice Questions. GCSE Revision Cards. 5-a-day Workbooks ...
Addition of Fractions (Adding like and unlike fractions with Examples)
Solved Examples. Let us solve some problems based on adding fractions. Q. 1: Add 1/2 and 7/2. Solution: Given fractions: 1/2 and 7/2 Since the denominators are the same, hence we can just add the numerators here, keeping the denominator as it is.
Fraction Addition Word Problems Worksheets
Evaluate 5th grade and 6th grade students' skills in adding mixed numbers with different denominators in this part of the fraction addition word problems worksheets. Convert to mixed numbers with the same denominators, and press on! Grab Worksheet 1. Try our free fraction addition word problems worksheets, replete with refreshing real-world ...
How to Add Fractions with Different Denominators (Step-by-Step)
Step Two: Add the numerators together and keep the denominator. Now we have a new expression where both fractions share a common denominator: 1/4 + 1/2 → 2/8 + 4/8. Next, we have to add the numerators together and keep the denominator as follows: 2/8 + 4/8 = (2+4)/8 = 6/8. Step Three: Simplify the result if possible.
Addition and Subtraction of Fraction: Methods, Facts, Examples
Here are the steps to add fractions with the same denominator: Step 1: Add the numerators of the given fractions. Step 2: Keep the denominator the same. Step 3: Simplify. a c + b c = a + b c … c ≠ 0. Example 1: Find 1 4 + 2 4. 1 4 + 2 4 = 1 + 2 4 = 3 4. We can visualize this addition using a bar model:
Adding & subtracting fractions word problems
Word problem worksheets: Addition & subtraction of fractions. Below are three versions of our grade 4 math worksheet on adding and subtracting fractions and mixed numbers. All fractions have like denominators. Some problems will include irrelevant data so that students have to read and understand the questions, rather than simply recognizing a pattern to the solutions.
Fractions: Adding and Subtracting Fractions
Now that we know how to write addition problems with fractions, let's practice solving a few. If you can add whole numbers, you're ready to add fractions. Click through the slideshow to learn how to add fractions. Let's continue with our previous example and add these fractions: 3/5 of cup of oil and 1/5 of a cup of oil.
Add & Subtract Fractions Worksheets for Grade 5
5th grade adding and subtracting fractions worksheets, including adding like fractions, adding mixed numbers, completing whole numbers, adding unlike fractions and mixed numbers, and subtracting like and unlike fractions and mixed numbers. No login required.
Word Problems Worksheets
Include Word Problems Worksheet Answer Page. Now you are ready to create your Word Problems Worksheet by pressing the Create Button. If You Experience Display Problems with Your Math Worksheet. Click here for More Word Problems Worksheets. This Fractions Word Problems worksheet will produce problems involving adding two fractions.
Fraction Worksheets
Math explained in easy language, plus puzzles, games, quizzes, videos and worksheets. For K-12 kids, teachers and parents. Fraction Worksheets ... Fractions - Addition. Worksheet. Example. Fractions (Same Denominator) 15 + 25. Unit Fractions. 13 + 19. Easy Proper Fractions. 38 + 27. Harder Proper Fractions. 712 + 1525. Easy Mixed Fractions.
Adding and Subtracting Fraction Word Problems
Adding and Subtracting Fraction Word Problems. Subject: Mathematics. Age range: 7-11. Resource type: Worksheet/Activity. File previews. docx, 18.11 KB. Here are some word-based questions for solving problems involving the addition and subtraction of fractions. Feedback greatly appreciated!
3rd Grade Math Worksheets
These third grade math worksheets are perfect to help students understand, learn, and become comfortable using mathematics skills. The printable activities target advanced multi-digit addition and subtraction as well as multiplication, division, fractions, and place value. STW offers free worksheets in all of these 3rd grade topic areas.
Addition Lesson: Strategies, Techniques, and Practical ...
From calculating totals while shopping to solving complex mathematical problems, addition is a skill that is frequently used. In this lesson, we will explore various addition strategies, techniques, and tips to help you solve addition problems efficiently and accurately. ... How Do You Add Fractions? Adding fractions involves several steps to ...
What Do 2nd Graders Learn in Math
9 Important Second-Grade Math Topics and Skills 1. Mental Addition and Subtraction. In 2nd grade, one of the key math skills your child will develop is mental addition and subtraction. This involves solving basic math problems in their head without needing a pencil and paper.
Basic Math
Solution: Subtract the fractions using the same denominator: 2 5 − 1 8 = 16 40 − 5 40 = 11 40 Answer: 11 40 Problem 5) The boss wants 1 4 of the employees to work on Saturday morning and 1 6 of the employees to work on Saturday afternoon.
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Solution. This word problem requires addition of fractions. Choosing a common denominator of 4, we get. 1/2 + 3/4 = 2/4 + 3/4 = 5/4. So, John walked a total of 5/4 miles. Example #2: Mary is preparing a final exam. She study 3/2 hours on Friday, 6/4 hours on Saturday, and 2/3 hours on Sunday. How many hours she studied over the weekend.
Like & unlike denominators. Below are our grade 5 math word problem worksheet on adding and subtracting fractions. The problems include both like and unlike denominators, and may include more than two terms. Worksheet #1 Worksheet #2 Worksheet #3 Worksheet #4. Worksheet #5 Worksheet #6.
A wealth of real-life scenarios that involve addition of fractions with whole numbers and addition of two like fractions, two unlike fractions, and two mixed numbers, our pdf worksheets are indispensable for grade 3, grade 4, grade 5, and grade 6 students. The free fraction addition word problems worksheet is worth a try!
Fraction addition worksheets: grades 6-7. In grades 6 and 7, students simply practice addition with fractions that have larger denominators than in grade 5. Add two fractions, select (easier) denominators within 2-25. View in browser Create PDF. Add three fractions, select (easier) denominators within 2-25.
To add fractions with different denominators, you need to find a common denominator. A common denominator is a number that both denominators can divide into evenly. You can solve problems involving adding fractions for either scenario by applying the following 3-step process: Step One: Identify whether the denominators are the same or different.
Answer: The carpenter needs to cut four and seven-twelfths feet of wood. Summary: In this lesson we learned how to solve word problems involving addition and subtraction of fractions and mixed numbers. We used the following skills to solve these problems: Add fractions with like denominators. Subtract fractions with like denominators.
Adding Fractions. A fraction like 3 4 says we have 3 out of the 4 parts the whole is divided into. To add fractions there are Three Simple Steps: Step 1: Make sure the bottom numbers (the denominators) are the same. Step 2: Add the top numbers (the numerators), put that answer over the denominator. Step 3: Simplify the fraction (if possible)
If you are looking to add fractions which have the same denominator, take a look at our sheets below. Sheet 1: the easiest sheet, no simplifying or converting needed. Sheet 2: Fractions need adding then simplifying. Sheet 3: fractions need simplifying and/or converting from an improper fraction into a mixed number.
Whenever you are adding or subtracting fractions, the key is having both fractions having common denominators. If both fractions share a common denominator, you can simply add/subtract the numerators together, keep the denominator as is, and simplify the result if possible. For example, we could solve the problem: 1/4 + 2/4 as follows:
Here's an example of adding fractions with like denominators, using the three steps from earlier. Find the sum of 3 / 5 + 1 / 5. Solution: The denominators are already the same, so we can skip step 1. Let's add the numerators. 3 + 1 = 4, so the sum of our numerators is 4. The denominator is still 5, so our result is 4 / 5.
Problem nº 1. Problem nº 2. Problem nº 3. Solution to Problem nº 1. This is an example of a problem involving the addition of a whole number and a fraction. The simplest way to show the number of cookies I ate is to write it as a mixed number. And the data given in the word problem gives us the result: 9 biscuits and 5 / 6 of a biscuit = 9 ...
Add the 3 numerators together to get a sum of 9 (3 + 2 + 4 = 9). 3. Put the new numerator on top and leave the denominator as is. Take the sum of the numerators and place it on the top of the fraction. When you add like fractions, you don't add the denominators together.
The Corbettmaths Practice Questions on Adding Fractions. Welcome; Videos and Worksheets; Primary; 5-a-day. 5-a-day GCSE 9-1; 5-a-day Primary; 5-a-day Further Maths; More. ... Addition, Adding. Practice Questions. Previous: Solving Quadratics Practice Questions. Next: Dividing Fractions Practice Questions. GCSE Revision Cards. 5-a-day Workbooks ...
Solved Examples. Let us solve some problems based on adding fractions. Q. 1: Add 1/2 and 7/2. Solution: Given fractions: 1/2 and 7/2 Since the denominators are the same, hence we can just add the numerators here, keeping the denominator as it is.
Evaluate 5th grade and 6th grade students' skills in adding mixed numbers with different denominators in this part of the fraction addition word problems worksheets. Convert to mixed numbers with the same denominators, and press on! Grab Worksheet 1. Try our free fraction addition word problems worksheets, replete with refreshing real-world ...
Step Two: Add the numerators together and keep the denominator. Now we have a new expression where both fractions share a common denominator: 1/4 + 1/2 → 2/8 + 4/8. Next, we have to add the numerators together and keep the denominator as follows: 2/8 + 4/8 = (2+4)/8 = 6/8. Step Three: Simplify the result if possible.
Here are the steps to add fractions with the same denominator: Step 1: Add the numerators of the given fractions. Step 2: Keep the denominator the same. Step 3: Simplify. a c + b c = a + b c … c ≠ 0. Example 1: Find 1 4 + 2 4. 1 4 + 2 4 = 1 + 2 4 = 3 4. We can visualize this addition using a bar model:
Word problem worksheets: Addition & subtraction of fractions. Below are three versions of our grade 4 math worksheet on adding and subtracting fractions and mixed numbers. All fractions have like denominators. Some problems will include irrelevant data so that students have to read and understand the questions, rather than simply recognizing a pattern to the solutions.
Now that we know how to write addition problems with fractions, let's practice solving a few. If you can add whole numbers, you're ready to add fractions. Click through the slideshow to learn how to add fractions. Let's continue with our previous example and add these fractions: 3/5 of cup of oil and 1/5 of a cup of oil.
5th grade adding and subtracting fractions worksheets, including adding like fractions, adding mixed numbers, completing whole numbers, adding unlike fractions and mixed numbers, and subtracting like and unlike fractions and mixed numbers. No login required.
Include Word Problems Worksheet Answer Page. Now you are ready to create your Word Problems Worksheet by pressing the Create Button. If You Experience Display Problems with Your Math Worksheet. Click here for More Word Problems Worksheets. This Fractions Word Problems worksheet will produce problems involving adding two fractions.
Math explained in easy language, plus puzzles, games, quizzes, videos and worksheets. For K-12 kids, teachers and parents. Fraction Worksheets ... Fractions - Addition. Worksheet. Example. Fractions (Same Denominator) 15 + 25. Unit Fractions. 13 + 19. Easy Proper Fractions. 38 + 27. Harder Proper Fractions. 712 + 1525. Easy Mixed Fractions.
Adding and Subtracting Fraction Word Problems. Subject: Mathematics. Age range: 7-11. Resource type: Worksheet/Activity. File previews. docx, 18.11 KB. Here are some word-based questions for solving problems involving the addition and subtraction of fractions. Feedback greatly appreciated!
These third grade math worksheets are perfect to help students understand, learn, and become comfortable using mathematics skills. The printable activities target advanced multi-digit addition and subtraction as well as multiplication, division, fractions, and place value. STW offers free worksheets in all of these 3rd grade topic areas.
From calculating totals while shopping to solving complex mathematical problems, addition is a skill that is frequently used. In this lesson, we will explore various addition strategies, techniques, and tips to help you solve addition problems efficiently and accurately. ... How Do You Add Fractions? Adding fractions involves several steps to ...
9 Important Second-Grade Math Topics and Skills 1. Mental Addition and Subtraction. In 2nd grade, one of the key math skills your child will develop is mental addition and subtraction. This involves solving basic math problems in their head without needing a pencil and paper.
Solution: Subtract the fractions using the same denominator: 2 5 − 1 8 = 16 40 − 5 40 = 11 40 Answer: 11 40 Problem 5) The boss wants 1 4 of the employees to work on Saturday morning and 1 6 of the employees to work on Saturday afternoon.