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How to Add Fractions

Adding fractions is a fundamental skill in mathematics that plays a crucial role in various aspects of everyday life and advanced mathematical concepts. Understanding how to add fractions helps in dealing with situations involving parts of a whole, such as cooking, budgeting, and even time management.

Why Learning How to Add Fractions Is Important

Maybe math isn’t your favorite subject, but learning how to add fractions is important:

• Practical Applications : In cooking, fractions measure ingredients. In budgeting, fractions help in understanding portions of money spent or saved.
• Foundation for Advanced Mathematics : Knowledge of fractions is essential for understanding more complex mathematical concepts like algebra, calculus, and statistics.
• Developing Problem-Solving Skills : Learning how to add fractions enhances logical thinking and problem-solving abilities.

Steps for Adding Fractions

Probably the first step is understanding the parts of a fraction. The top portion (above the line) is the numerator. This is the part of the fraction where the actual addition occurs. The bottom portion of the fraction (below the line) is the denominator. You make the denominator the same (if it isn’t already) and then add up the numerators. After you have an answer, simplify the fraction.

• Just add the numerators while keeping the denominator the same.
• Simplify the fraction if possible.
• Find a common denominator by finding the least common multiple (LCM) of the denominators. The easiest way of doing this is multiplying both the numerator and denominator of each fraction by the denominator of the other fraction.
• Once both fractions have the same denominator, add the numerators of these equivalent fractions.
• Simplify the resulting fraction if possible.

Examples of How to Add Fractions

Adding fractions with the same denominator.

This is the easiest case, since all you do is add up the numerators.

The process is the same when working with negative numbers , but pay attention to the signs.

Adding Fractions With Different Denominators

Remember, make the denominators the same and then add the numerators. In this example, the denominators are 3 and 5. Multiplying both the numerator and denominator of each fraction by the denominator of the other fraction yields the LCM, which is 15 in this case.

Here is an example of adding fraction with different denominators involving negative numbers:

Adding Improper Fractions

Improper fractions are fractions where the numerator is larger than or equal to the denominator. The process of adding improper fractions is the same as adding proper fractions. After adding, if the result is an improper fraction, convert it into a mixed fraction. A mixed fraction is one which has a whole number together with a fraction. For example, 7/3 is an improper fraction, while 2⅓ is the equivalent mixed fraction.

Adding Mixed Fractions

Adding mixed fractions involves a few more steps compared to adding simple fractions. A mixed fraction is a combination of a whole number and a fraction. To add mixed fractions, you either convert them to improper fractions first and then add, or add the whole numbers and fractions separately.

• Multiply the whole number by the denominator of the fraction.
• Add this to the numerator of the fraction.
• Place this over the original denominator.
• Find a common denominator if necessary.
• Add the numerators, keeping the denominator the same.
• Divide the numerator by the denominator to get the whole number part.
• The remainder becomes the numerator of the fractional part.

Add 2⅓ and 1⅔​.

• Convert to improper fractions.
• Add the improper fractions.
• Simplify the result.

If the denominators are different, find the LCM and make them the same before the addition step.

• Perry, Owen; Perry, Joyce (1981). “Chapter 2: Common fractions”. Mathematics I . Palgrave Macmillan UK. pp. 13–25. doi: 10.1007/978-1-349-05230-1_2
• Schoenborn, Barry; Simkins, Bradley (2010). “8. Fun with Fractions”. Technical Math For Dummies . Hoboken: Wiley Publishing Inc. ISBN 978-0-470-59874-0.
• Schwartzman, Steven (1994). The Words of Mathematics: An Etymological Dictionary of Mathematical Terms Used in English . Mathematical Association of America. ISBN 978-0-88385-511-9.

Related Posts

Adding Fractions

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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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)

Step 1 . The bottom numbers (the denominators) are already the same. Go straight to step 2.

Step 2 . Add the top numbers and put the answer over the same denominator:

1 4 + 1 4 = 1 + 1 4 = 2 4

Step 3 . Simplify the fraction:

In picture form it looks like this:

... and do you see how 2 4 is simpler as 1 2 ? (see Equivalent Fractions .)

Step 1 : The bottom numbers are different. See how the slices are different sizes?

We need to make them the same before we can continue, because we can't add them like that.

The number "6" is twice as big as "3", so to make the bottom numbers the same we can multiply the top and bottom of the first fraction by 2 , like this:

Important: you multiply both top and bottom by the same amount, to keep the value of the fraction the same

Now the fractions have the same bottom number ("6"), and our question looks like this:

The bottom numbers are now the same, so we can go to step 2.

Step 2 : Add the top numbers and put them over the same denominator:

2 6 + 1 6 = 2 + 1 6 = 3 6

Step 3 : Simplify the fraction:

In picture form the whole answer looks like this:

With Pen and Paper

And here is how to do it with a pen and paper (press the play button):

A Rhyme To Help You Remember

♫ "If adding or subtracting is your aim, The bottom numbers must be the same! ♫ "Change the bottom using multiply or divide, But the same to the top must be applied, ♫ "And don't forget to simplify, Before its time to say good bye"

Again, the bottom numbers are different (the slices are different sizes)!

But let us try dividing them into smaller sizes that will each be the same :

The first fraction: by multiplying the top and bottom by 5 we ended up with 5 15 :

The second fraction: by multiplying the top and bottom by 3 we ended up with 3 15 :

The bottom numbers are now the same, so we can go ahead and add the top numbers:

The result is already as simple as it can be, so that is the answer: 

1 3 + 1 5 = 8 15

Making the Denominators the Same

In the previous example how did we know to cut them into 1 / 15 ths to make the denominators the same? We simply multiplied the two denominators together (3 × 5 = 15).

Read about the two main ways to make the denominators the same here:

• Common Denominator Method , or the
• Least Common Denominator Method

They both work, use which one you prefer!

Example: Cupcakes

You want to make and sell cupcakes:

• A friend can supply the ingredients, if you give them 1 / 3 of sales
• And a market stall costs 1 / 4 of sales

How much is that altogether?

We need to add 1 / 3 and 1 / 4

First make the bottom numbers (the denominators) the same.

Multiply top and bottom of 1 / 3 by 4 :

And multiply top and bottom of 1 / 4 by 3 :

Now do the calculations:

Answer: 7 12 of sales go in ingredients and market costs.

Adding Mixed Fractions

We have a special (more advanced) page on Adding Mixed Fractions .

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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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• How to Add Fractions support
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Adding Fractions with Like Denominators Quiz

• Adding Fractions (with Unlike Denominators) Worksheets
• Adding Fractions (with Unlike Denominators) Quiz
• More related Math resources

How to Add Fraction s

Here you will find support pages and our adding fraction calculator to help you to learn about how to add fractions.

Formula for adding two fractions

\[{a \over b} + {c \over d} = {ad + bc \over bd} \]

• How do you Add Fractions support page

• Adding Fractions Calculator

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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Adding Fractions

The addition of fractions is a little different from the normal addition of numbers since a fraction has a numerator and a denominator which is separated by a bar. The addition of fractions can be easily done if the denominators are equal. While like fractions have common denominators, unlike fractions are converted to like fractions to make addition easier. Let us explore more about adding fractions , and how to add two fractions in this article.

How to Add Fractions?

Fractions are part of a whole. Before moving to the addition of fractions, let us quickly revise what are fractions. Fractions are made up of two parts, the numerator and the denominator. A general representation of a fraction is a/b, where 'a' is the numerator, 'b' is the denominator, and 'b' cannot be zero. For example, 2/3, 14/5, 6/7, 28/9, and 21/43. Just like other numbers, we can perform the arithmetic operations of addition , subtraction , multiplication , and division on fractions. The addition of fractions means finding the sum of two or more fractions. Now, let us learn the basic steps of the addition of fractions with the help of the following example.

Example: Add 1/4 + 2/4

Solution: Let us add these fractions using the following steps.

• Step 1: Check if the denominators are the same. (Here, the denominators are the same, so we move to the next step)
• Step 2: Add the numerators and place the sum over the common denominator . This means (1 + 2)/4 = 3/4
• Step 3: Simplify the fraction to its lowest form, if needed. Here, it is not needed. So, the sum of the given fractions is, 1/4 + 2/4 = 3/4

There are different types of fractions in Mathematics. While adding fractions we need to check whether they are like fractions or unlike fractions. Like fractions are a group of fractions with a common denominator, while unlike fractions are a group of fractions having different denominators. While learning about the addition of fractions, we might come across the following scenarios.

• Addition of fractions with same denominators: 3/4 + 1/4
• Addition of fractions with different denominators: 3/5 + 1/2
• Addition of fractions with whole numbers: 1/2 + 2
• Adding fractions with variables: 3/5y + 1/4y

Now, let us learn more about the above cases in detail.

Adding Fractions with Like Denominators

Adding fractions with the same denominators is done by writing the sum of the numerators over the common denominator. Let us understand how to add fractions with the same denominator with the help of an example.

Example: Add the fractions 2/4 + 1/4

Solution: We can see that the denominators of the given fractions are the same. These fractions are called like fractions .

The addition of like fractions can be done by adding the numerators of the given fractions and retaining the common denominator. In this case, we keep the denominator as 4, and we add the numerators. This can be expressed as 2/4 + 1/4 = (2 +1)/4 = 3/4. This gives the sum as 3/4.

Adding Fractions with Unlike Denominators

We just learned how to add fractions with like denominators. Now let us understand how to do the addition of fractions with different or unlike denominators. When the denominators are different, the fractions are called unlike fractions. In such fractions, the first step is to convert them to like fractions so that the denominators become common. This is done by finding the Least Common Multiple (LCM) of the denominators. Let us understand this with the help of the following example.

Example: Add the fractions 1/3 and 3/5.

Solution: We will use the following steps to add these fractions.

• Step 1: Since the denominators in the given fractions are different, we find the LCM of 3 and 5 to make them the same. LCM of 3 and 5 = 15.
• Step 2: Now, multiply 1/3 with 5/5, (1/3) × (5/5) = 5/15, and 3/5 with 3/3, (3/5) × (3/3) = 9/15, which will convert them to like fractions with the same denominators.
• Step 3: Now, the denominators are the same, so we simply add the numerators and write the sum over the common denominator. The new fractions with common denominators are 5/15 and 9/15. So, 5/15 + 9/15 = (5 + 9)/15 = 14/15.

Adding Fractions with Whole Numbers

An easy way to add a whole number and a proper fraction is to combine and express them as a mixed fraction . For example, 5 + 1/2 can be combined and expressed as 5½ = 11/2. Similarly, 3 + 1/7 = \(3\frac{1}{7} \) = 22/7. However, there is another method for adding fractions with whole numbers. Let us understand that with the help of the following example.

Example: Add 3 + 4/5

Solution: Let us add these numbers using the following steps:

• Step 1: In this method, we change the whole number to its fraction form by writing 1 as its denominator. Here, 3 is the whole number and this can be written as 3/1
• Step 2: Now, 3/1 can be added to 4/5, that is, 3/1 + 4/5. We will add these by making the denominators the same because they are unlike fractions. This implies, (3/1) + (4/5) = (3/1) × (5/5) + (4/5) × (1/1) = 15/5 + 4/5 = 19/5 = \(3\frac{4}{5} \)

Adding Fractions with Variables

Now that we have seen the addition of fractions with like and unlike fractions, we can extend the same concept for adding fractions with variables. Let us understand this with the help of the following example.

Example: Add y/5 + 2y/5 where 'y' is the variable.

Solution: Let us add these fractions using the following steps:

• Step 1: The given fractions, y/5 + 2y/5 are like fractions since they have the same denominator and we can see that 'y' is common.
• Step 2: We can take the common factor out and rewrite it as: y/5 + 2y/5 = (1/5 + 2/5)y = 3y/5
• Step 3: Therefore, the sum of y/5 + 2y/5 = 3y/5

Now, let us learn how to add unlike fractions using the following example.

Example: Add y/2 + y/3

Solution: Let us add the fractions using the following steps.

• Step 1: Since the given fractions, y/2 + y/3 are unlike fractions, we will take the LCM of the denominators and convert them into like fractions.
• Step 4: Next, we need to take the common variable out and rewrite it as follows: LCM (2, 3) = 6; y/2 = (y/2) × (3/3) = 3y/6 and y/3 = (y/3 × (2/2) = 2y/6
• Step 5: We got two fractions with common denominators, (3y/6) + (2y/6) = (3y + 2y)/6 = 5y/6. Therefore, the sum of y/2 + y/3 = 5y/6

It should be noted that in some cases, when we have different variables, like 'x' and 'y', they are treated as unlike terms and cannot be simplified further, for example, x/2 + y/3

Tips and Tricks on Addition of Fractions

The following points are helpful and should be remembered while working with the addition of fractions:

• For unlike fractions, we do not add the numerators and denominators directly. 1/5 + 2/3 ≠ 3/8
• To add unlike fractions, first, convert the given fractions to like fractions by taking the LCM of the denominators.
• Add the numerators and retain the common denominator to get the sum of the fractions.

☛ Related Topics

• Subtraction of Fractions
• Multiplying Fractions
• Division of Fractions
• Like Fractions and Unlike Fractions
• Adding Fractions Calculator

Addition of Fractions Examples

Example 1: Add the following fractions: 1/7 and 3/7

The given fractions are like fractions. For the addition of like fractions, we add the numerators and retain the common denominator. This means, 1/7 + 3/7 = (1 + 3)/7 = 4/7

Example 2: Add the following fractions: 2/5 and 2/3

The given fractions are unlike fractions. For adding fractions with different denominators, we have to find the LCM of the denominators and convert 2/5 and 2/3 to fractions with a common denominator. LCM of 3 and 5 is 15. 2/5 + 2/3 = (2/5 × 3/3) + (2/3 × 5/5)

= 6/15 + 10/15

= (6 + 10)/15

= \(1 \dfrac{1}{15}\)

Therefore, the sum is \(1 \dfrac{1}{15}\)

Example 3: How to add a whole number and a fraction: 3 + 1/3?

This question is based on adding fractions with whole numbers. The whole number 3 can be written in the form of a fraction as 3/1. Now,

3 + 1/3 = 3/1 + 1/3

= (3/1 × 3/3) + 1/3

= 9/3 + 1/3

= (9 + 1)/3

= \(3 \frac{1}{3} \)

Therefore, the sum is \(3\frac{1}{3}\)

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Practice Questions on Adding Fractions

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FAQs on Addition of Fractions

The process of addition of fractions is a little different from normal addition of whole numbers. The first step in adding fractions is to check if the denominators of the given fractions are the same. Then we use the following procedure to add them.

• If the fractions have common denominators then we can easily add the numerators and keep the same denominator to get the sum. For example, 2/4 + 1/4 = (2 + 1)/4 = 3/4
• If the denominators are different, we make the denominators equal by converting them to equivalent fractions by finding the LCM of the denominators. Then the addition can be done. For example, 1/2 + 2/3 = (1/2 × 3/3) + (2/3 × 2/2) = 3/6 + 4/6 = (3 + 4)/6 = 7/6 = \(1 \dfrac{1}{6}\)

What is the Rule for Adding Fractions?

The basic rule for the addition of fractions is to make the denominators of the fractions the same. If the fractions have the same denominator we can simply add the numerators keeping the same denominator. However, if the denominators are different, we need to convert them to like fractions with the same denominators. This is done by writing their equivalent fractions by taking the LCM of the denominators. Once they are converted to like fractions, the fractions can be added easily because we just need to work with the numerators while we keep the same denominator.

How to Add Fractions with Whole Numbers?

To add a fraction with a whole number, we first convert the whole number into a fraction. For example, if we need to add 3 and 1/2, the whole number 3 can be easily converted into a fraction like 3/1 and added to the other fraction. Let us see how this works. (3/1) + (1/2) = (3/1) × (2/2) + (1/2) = 6/2 + 1/2 = 7/2 = 3½. Another way to add fractions and whole numbers is to simply combine and express them as mixed fractions. For example, 6 + 1/2 can be combined and written as \(6 \dfrac{1}{2}\)

How to Add Fractions with Different Denominators?

The fractions with different denominators can be added by making the denominators common. This is done by multiplying the numerator and denominator of each of the fractions with a suitable number such that all the fractions become like fractions. To add the fractions 3/5 + 4/3, we need to multiply both the fractions with a number that makes the denominators equal. For this, we need the LCM of the denominators, which is 15 in this case. The numerator and denominator of the first fraction 3/5 have to be multiplied by 3, and the numerator and denominator of the second fraction 4/3 have to be multiplied by 5. Hence, we have (3/5 × 3/3) + (4/3 × 5/5) = (9/15) + (20/15) = (9 + 20)/15 = 29/15 = \(1 \dfrac{14}{15}\)

How to Add 3 Fractions with Different Denominators?

The addition of three fractions is the same as the addition of two fractions with different denominators . First of all, we need the LCM of all three denominators. Accordingly, the denominators of all the three fractions are made common by multiplying the numerator and denominator of each of the fractions with a suitable number so that they are converted to like fractions. Now, once the denominators are common, the numerators are added to get the sum of the fraction. Let us understand this with the help of this addition problem: 2/3 + 4/5 + 1/6. The LCM of 3, 5, and 6 is 30. Now, we will multiply each fraction with the suitable number to make their denominators common: (2/3 × 10/10) + (4/5 × 6/6) + (1/6 × 5/5) = (20/30) + (24/30) + (5/30) = (20 + 24 + 5)/30 = 49/30 = \(1 \dfrac{19}{30}\)

What is the Identity Element For the Addition of Fractions?

The identity element for addition is 0, which means, for any real number 'a', a + 0 = a. Similarly, for the addition of fractions, the identity element is 0. For a fraction of the form a/b, we have a/b + 0 = 0 + a/b = a/b. The use of the identity element for addition does not change the value of the fraction .

What is Subtraction and Addition of Fractions?

In the subtraction and addition of fractions, first, the denominators of the fractions should be made equal. If the denominators are the same, we can simply add or subtract the fractions easily. However, if the fractions have different denominators, then the process starts with the LCM (Least Common Multiple) of the denominators. Then, the fractions are multiplied with a suitable number which makes all the denominators equal. Finally, the numerators are added or subtracted as per the question and the new denominator remains the same.

How to Add Fractions with the Same Denominators?

In order to add fractions with the same denominators, we can simply add the numerators and keep the denominator the same. For example, let us add 3/7 + 2/7. Since the fractions have the same denominators, we just need to add the numerators. So, this will be 3/7 + 2/7 = (3 + 2)/7 = 5/7

How to Add Improper Fractions?

In order to add improper fractions, we use the same rules of adding fractions. For example, let us add 8/3 + 7/3. Since the fractions have the same denominators , we just need to add the numerators. So, this will be 8/3 + 7/3 = (8 + 7)/3 = 15/3 = 5

How to Add Mixed Fractions Step by Step?

Adding mixed numbers follows the same rules of adding fractions. The only extra step is to convert the mixed fractions to improper fractions. Let us understand this with an example. Let us add \(6 \dfrac{1}{2}\) + \(3 \dfrac{3}{4}\) using the following steps.

• Step 1: To add \(6 \dfrac{1}{2}\) + \(3 \dfrac{3}{4}\), let us convert these mixed fractions to improper fractions. This will be 13/2 + 15/4
• Step 2: Now, we will use the basic rules of addition. Here, the denominators are different, so we will convert these to their equivalent fractions so that their denominators become the same.
• Step 3: The LCM of 2 and 4 is 4. Now, we will multiply each fraction with the suitable number to make their denominators common: (13/2 × 2/2) + (15/4 × 1/1) = (26/4) + (15/4) = (26 + 15)/4 = 41/4 = \(1 0\dfrac{1}{4}\)

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Fractions- Add fractions within 1- Year 5

Subject: Mathematics

Age range: 7-11

Resource type: Lesson (complete)

Last updated

19 February 2020

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This is a whole lesson based on the Year 5 Fraction objective of 'Add fractions within 1’. This resource includes the teacher input ( learning journey), independent worksheet and a depth activity to deepen the children’s understanding of the concept being learned.

The questions have been inspired and adapted from the White Rose Small Steps Guidance and Teaching for Mastery documents. This document is useful for teachers who have adapted Maths Mastery and need guidance in the approach or those who are looking for variation in fluency, reasoning and problem solving or simply those who don’t want to plan it themselves but want high quality resources and quality first teaching. =)

All of the documents that are uploaded as an Activinspire file are interactive and all of the concrete/pictorial manipulative can be used, moved and manipulated.

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Thank you for taking the time to review my resources. =) I hope this helps you with your teaching and if it does please could you be kind enough to leave some positive feedback. =)

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Having Paid £3 for this resource which looks lovely none of the numbers come up on my Active inspire which is why I purchased it for the interactivity - I think it's the font used because every slide that looks like it has the wavy font on from the images here does not appear to have anything on the slideshow it just says calculate at the top with nothing underneath. Very disappointed as I bought to save time

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Add Fractions within 1 Year 5 Fractions Step 8 Resource Pack

Step 8: Add Fractions within 1 Year 5 Spring Block 2 Resources

Add Fractions within 1 Year 5 Resource Pack includes a teaching PowerPoint and differentiated varied fluency and reasoning and problem solving resources for Spring Block 2.

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What's included in the pack?

This pack includes:

• Add Fractions within 1 Year 5 Teaching PowerPoint.
• Add Fractions within 1 Year 5 Varied Fluency with answers.
• Add Fractions within 1 Year 5 Reasoning and Problem Solving with answers.

National Curriculum Objectives

Mathematics Year 5: (5F4)  Add and subtract fractions with the same denominator and denominators that are multiples of the same number

Differentiation For Year 5 Add Fractions within 1:

Varied Fluency Developing Questions to support adding fractions where the denominator is double or half of the starting fraction. Models and pictorial representations used. Expected Questions to support adding fractions where the denominators are direct multiples of each other. Models and pictorial representations used. Greater Depth Questions to support adding fractions where the denominators are not all direct multiples of each other. Answers to be recorded using knowledge of equivalent fractions.

Reasoning and Problem Solving Questions 1, 4 and 7 (Problem Solving) Developing Identify the calculation from the model shown. Denominators are all double or half of the starting fraction. Expected Identify the calculation from the model shown. Denominators are all direct multiples of each another. Greater Depth Identify the calculation from the model shown. Denominators are not all direct multiples of each other. Answers to be recorded using knowledge of equivalent fractions.

Questions 2, 5 and 8 (Reasoning) Developing Explain whether the fraction calculation is true or false. Denominators are all double or half of the starting fraction. Expected Explain whether the fraction calculation is true or false. Denominators are all direct multiples of each another. Greater Depth Explain whether the fraction calculation is true or false. Denominators are not all direct multiples of each other.

Questions 3, 6 and 9 (Problem Solving) Developing Solve the word problem. Denominators are all double or half of the starting fraction. Expected Solve the word problem. Denominators are all direct multiples of each another. Greater Depth Solve the word problem. Denominators are not all direct multiples of each other.

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Most Used Actions

• reduce\:fraction\:\frac{4}{8}
• \frac{1}{2}+\frac{1}{4}+\frac{3}{4}
• \frac{1}{2}\cdot\frac{8}{7}
• \frac{-\frac{1}{5}}{\frac{7}{4}}
• descending\:order\:\frac{1}{2},\:\frac{3}{6},\:\frac{7}{2}
• decimal\:to\:fraction\:0.35
• What is a mixed number?
• A mixed number is a combination of a whole number and a fraction.
• How can I compare two fractions?
• To compare two fractions, first find a common denominator, then compare the numerators.Alternatively, compare the fractions by converting them to decimals.
• How do you add or subtract fractions with different denominators?
• To add or subtract fractions with different denominators, convert the fractions to have a common denominator. Then you can add or subtract the numerators of the fractions, leaving the denominator unchanged.

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