homework 7 2 equivalent fractions answers

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Eureka Math Grade 7 Module 2 Lesson 13 Answer Key

Engage ny eureka math 7th grade module 2 lesson 13 answer key, eureka math grade 7 module 2 lesson 13 example answer key.

Example 1. Representations of Rational Numbers in the Real World Following the Opening Exercise and class discussion, describe why we need to know how to represent rational numbers in different ways. Answer: Different situations in the real world require different representations of rational numbers. Because of common usage in life outside of the classroom, we may automatically know that a quarter of a dollar is the same as 25 cents, or a quarter, but for people who are used to measuring money in only decimals, a quarter of a dollar might not make much sense.

Example 2. Using Place Values to Write (Terminating) Decimals as Equivalent Fractions a. What is the value of the number 2.25? How can this number be written as a fraction or mixed number? Answer: Two and twenty-five hundredths or 2\(\frac{25}{100}\)

→ How do we rewrite this fraction (or any fraction) in its simplest form? → If a factor is common to both the numerator and denominator of a fraction, the fraction can be simplified, resulting in a fraction whose numerator and denominator only have a common factor of 1 (the numerator and denominator are relatively prime).

b. Rewrite the fraction in its simplest form showing all steps that you use. Answer: Answer: \(\frac{25}{100}\) = \(\frac{25}{4×25}\) = \(\frac{1}{4}\) → 2\(\frac{25}{100}\) = 2\(\frac{1}{4}\)

c. What is the value of the number 2.025? How can this number be written as a mixed number? Answer: Two and twenty-five thousandths, or 2\(\frac{25}{1,000}\)

d. Rewrite the fraction in its simplest form showing all steps that you use. Answer: \(\frac{25}{1,000}\) = \(\frac{25}{(100×10)}\) \(\frac{25}{4×25×10}\) = \(\frac{1}{40}\) → 2\(\frac{25}{1,000}\) = 2\(\frac{1}{40}\)

Example 3. Converting Fractions to Decimals—Fractions with Denominators Having Factors of only 2 or 5 a. What are decimals? Answer: Decimals specify points on the number line by repeatedly subdividing intervals into tenths. If a unit is divided into ten equal-sized pieces, one piece would be one-tenth of that unit.

b. Use the meaning of decimal to relate decimal place values. Answer: Each place value in a decimal is \(\frac{1}{10}\) of the value of the place to its left. This means that the denominators of the fractions that represent each decimal place value must be powers of ten.

c. Write the number \(\frac{3}{100}\) as a decimal. Describe your process. Answer: The decimal form is 0.03. The fraction includes a power of ten, 100, as its denominator. The value of the second decimal place is \(\frac{1}{100}\), so \(\frac{3}{100}\) in decimal form is 0.03.

→ How could we obtain an equivalent fraction to \(\frac{3}{20}\) with a power of ten in the denominator? → If there was another factor of 5 in the denominator, then we would have an equal number of 2’s and 5’s resulting in a power of ten. If we multiply the fraction by \(\frac{5}{5}\) (or 1), we get an equivalent fraction with a power of ten in its denominator.

d. Write the number \(\frac{3}{20}\) as a decimal. Describe your process. Answer: The fractional form is \(\frac{3}{20}\) = \(\frac{3}{2^{2} \times 5}\). The denominator lacks a factor of 5 to be a power of ten. To arrive at the decimal form, I multiply the fractional form by \(\frac{5}{5}\) to arrive at \(\frac{3}{2^{2} \times 5}\) × \(\frac{5}{5}\) = \(\frac{3 \times 5}{2^{2} \times 5^{2}}\) = \(\frac{15}{100}\), and \(\frac{15}{100}\) = 0.15.

e. Write the number \(\frac{10}{25}\) as a decimal. Describe your process. Answer: The fractional form is \(\frac{10}{25}\) = \(\frac{2×5}{5×5}\) ; and, since \(\frac{5}{5}\) = 1, then \(\frac{2×5}{5×5}\) = \(\frac{2}{5}\). The denominator lacks a factor of 2 to be a power of ten. To arrive at the decimal form, I multiply the fractional form by \(\frac{2}{2}\) to arrive at \(\frac{2}{5}\) × \(\frac{2}{2}\) = \(\frac{4}{10}\), and \(\frac{4}{10}\) = 0.4.

f. Write the number \(\frac{8}{40}\) as a decimal. Describe your process. Answer: The fractional form is \(\frac{8}{40}\) = \(\frac{2^{3}}{2^{3} \times 5}\). There are factors of 2 in the numerator and denominator that will cancel. If I leave one factor of two in the denominator, it will be 10 (a power of ten). \(\frac{2^{3}}{2^{3} \times 5}\) = \(\frac{2^{2} \times 2}{2^{2} \times 2 \times 5}\) = \(\frac{2}{2 \times 5}\) = \(\frac{2}{10}\) = 0.2

Eureka Math Grade 7 Module 2 Lesson 13 Exercise Answer Key

Exercise 1. Use place value to convert each terminating decimal to a fraction. Then rewrite each fraction in its simplest form. a. 0.218 Answer: \(\frac{218}{1,000}\) = \(\frac{109×2}{500×2}\) = \(\frac{109}{100}\) → 0.218 = \(\frac{109}{500}\)

b. 0.16 Answer: \(\frac{16}{100}\) = \(\frac{4×4}{4×25}\) = \(\frac{4}{25}\) → 0.16 = \(\frac{4}{25}\)

c. 2.72 Answer: \(\frac{72}{100}\) = \(\frac{4×18}{4×25}\) = \(\frac{18}{25}\) → 2.72 = 2\(\frac{18}{25}\)

d. 0.0005 Answer: \(\frac{5}{10,000}\) = \(\frac{5×1}{5×2,000}\) = \(\frac{1}{2,000}\) → 0.0005 = \(\frac{1}{2,000}\)

Exercise 2. Convert each fraction to a decimal using an equivalent fraction. a. \(\frac{3}{16}\) = Answer: \(\frac{3}{16}\) = \(\frac{3}{2×4}\) → \(\frac{3 \times 5^{4}}{2^{4} \times 5^{4}}\) = \(\frac{1,875}{10,000}\) → \(\frac{1875}{10,000}\) = 0.1875

b. \(\frac{7}{5}\)= \(\frac{7}{5}\) → \(\frac{7×2}{5×2}\) = \(\frac{14}{10}\) → \(\frac{14}{10}\) = 1 \(\frac{4}{10}\) = 1.4

c. \(\frac{11}{32}\)= \(\frac{11}{32}\) = \(\frac{11}{2^{5}}\) → \(\frac{11 \times 5^{5}}{2^{5} \times 5^{5}}\) = \(\frac{34,375}{100,000}\) → \(\frac{34375}{100,000}\) = 0.34375

d. \(\frac{35}{50}\)= \(\frac{35}{50}\) = \(\frac{5 \times 7}{5^{2} \times 2}\) → \(\frac{7}{5×2}\) = \(\frac{7}{10}\) → \(\frac{7}{10}\) = 0.7

Eureka Math Grade 7 Module 2 Lesson 13 Problem Set Answer Key

Question 1. Convert each terminating decimal to a fraction in its simplest form. a. 0.4 Answer: 0.4 = \(\frac{2}{5}\)

b. 0.16 Answer: 0.16 = \(\frac{4}{25}\)

c. 0.625 Answer: 0.625 = \(\frac{5}{8}\)

d. 0.08 Answer: 0.08 = \(\frac{2}{25}\)

e. 0.012 Answer: 0.012 = \(\frac{3}{250}\)

Question 2. Convert each fraction or mixed number to a decimal using an equivalent fraction. a. \(\frac{4}{5}\) Answer: \(\frac{4}{5}\) = 0.8

b. \(\frac{3}{40}\) Answer: \(\frac{3}{40}\) = 0.075

c. \(\frac{8}{200}\) Answer: \(\frac{8}{200}\) = 0.04

d. 3\(\frac{5}{16}\) Answer: 3 \(\frac{5}{16}\) = 3.3125

Question 3. Tanja is converting a fraction into a decimal by finding an equivalent fraction that has a power of 10 in the denominator. Sara looks at the last step in Tanja’s work (shown below) and says that she cannot go any further. Is Sara correct? If she is, explain why. If Sara is incorrect, complete the remaining steps. \(\frac{72}{480}\) = \(\frac{2^{3} \cdot 3^{2}}{2^{5} \cdot 3 \cdot 5}\) Answer: Tanja can finish the conversion since there is a factor pair of 3’s in the numerator and denominator that can be divided out with a quotient of 1. Remaining Steps: \(\frac{72}{480}\) = \(\frac{2^{3} \cdot 3^{2}}{2^{5} \cdot 3 \cdot 5}\) = \(\frac{3}{2^{2} \cdot 5}\)(\(\frac{5}{5}\)) = \(\frac{3 \cdot 5}{2^{2} \cdot 5^{2}}\) = \(\frac{15}{100}\) Answer:0.5

Eureka Math Grade 7 Module 2 Lesson 13 Exit Ticket Answer Key

Question 1. Write 3.0035 as a fraction. Explain your process. Answer: The right-most decimal place is the ten-thousandths place, so the number in fractional form would be 3\(\frac{35}{10,000}\). There are common factors of 5 in the numerator and denominator, and dividing both by these results in the fraction 3\(\frac{7}{2,000}\).

Question 2. This week is just one of 40 weeks that you spend in the classroom this school year. Convert the fraction \(\frac{1}{40}\) to decimal form. Answer: \(\frac{1}{40}\) = \(\frac{1}{2^{3} \times 5}\)×\(\frac{5^{2}}{5^{2}}\) = \(\frac{5^{2}}{2^{3} \times 5^{3}}\) = \(\frac{25}{1,000}\) = 0.025

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Course: 4th grade   >   Unit 7

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Equivalent fractions without visual models

The following worksheets are similar to the ones above, but using larger numbers in the denominators and numerators.

With this worksheet generator, you can make worksheets for equivalent fractions. The worksheet can include problems with visual models (pie images) or not. There are five problem types to choose from:

• Two fractions are given with 2 empty pie images to color in (e.g. 3/5 = 6/10).
• There are 2 pie images that are already colored; the student writes both fractions.
• Two pie images are given, one colored in, one not; the student writes both fractions.
• There are 2 pie images to color, one fraction is given, one not (e.g. 4/5 =     /     )
• Problems without any visual model; the student writes the missing numerator or denominator in one of the fractions (e.g. 2/3 =     /12).

You can choose to include or not include mixed numbers and improper fractions. You can control the minimum and maximum values for the numerator and the denominator. However, for the problems with visual models, the maximum denominator is limited to 16.

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Equivalent Fractions Worksheets

Every nook and cranny of our pdf equivalent fractions worksheets is stuffed with practice that helps children ease into fractions equivalence! As concepts like operations with fractions and comparing or ordering them are all built around equivalence of fractions, a deeper insight into the topic will alleviate the learning stress of students in grade 3, grade 4, and grade 5. The printable resources include determining whether a fraction is equivalent or not, identifying equivalent fractions, generating equivalent fractions, and answering Who-Am-I riddles and patterns. Try some of our free equivalent fraction worksheets now!

» Equivalent Fractions on a Number Line

» Equivalent Fractions | Visual Models

Equivalent or Not Equivalent?

Is 4/6 equivalent to 2/3? Yes, it is. Find similar pairs of fractions in these pdf worksheets on equivalent fractions, ascertain whether they are equivalent or not, and write a '=' or '≠' symbol in between accordingly.

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Finding Equivalent Fractions Step-by-Step

Are your 3rd grade and 4th grade children aware of the steps in finding an equivalent fraction? Let them know that both multiplication and division are the bread and butter of equivalent fractions.

Missing Parts of Fractions | Standard

Missing here is either the numerator or denominator of a fraction, equivalent to another. Find out the factor that makes it equivalent to the given fraction, and fill in the missing part.

Missing Parts of Fractions | Variables

A variable is given in place of the missing parts of an equivalent-fraction sentence. There's a shortcut to solving these problems. All you need to do is cross-multiply the fractions and find the missing value.

Missing Parts of Multiple Equivalent Fractions

Pound it into 4th grade and 5th grade students' heads that a fraction can have an infinite number of equivalent fractions, and task them with finding the missing parts of more than five equivalents for a fraction.

Identifying and Generating Equivalent Fractions

Scoop up our printable equivalent fractions worksheets, ideal for grade 3 and grade 4, with practice exercises on identifying equivalent fractions in part A and generating three equivalents for a fraction in part B.

Get children excitedly enthusing over this set of riddles! Pore over the sentences, frame the equivalent-fraction statement, and figure out the fraction that replaces "I" in each and every riddle.

Circling the Equivalent Fractions

Buff up your practice with our pdf equivalent fractions worksheets, which require grade 4 and grade 5 children to circle three to four fractions out of a set of five that are equivalent to a given fraction.

Equivalent Fractions Patterns

As fun and frolic as they are, patterns are not fully devoid of challenge! Seize this compilation of printable worksheets, analyze the patterns the fractions follow, and fill in the blanks with the appropriate fraction.

Equivalent Fractions on a Number Line

Did you know that equivalent fractions represent the same point on a number line? Work out our printable worksheets and learn such intriguing facts by plotting equivalent fractions on number lines.

(15 Worksheets)

Equivalent Fractions - Visual Models

Jam-packed with visual models like fraction pies, pizzas, 2d shapes split equally, area models, and tape diagrams, this pdf practice set will help children chase away all their doubts in fraction equivalence.

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Equivalent Fractions Worksheets

Maths Worksheets / Equivalent Fractions Worksheets

As most older students and adults know, equivalent fractions are fractions that have different numerators and denominators that reduce to the same fraction in their simplest form. This may sound straightforward to those who excelled in maths in school, but students start learning about equivalent fractions at a very young age and they can pose a serious challenge. Teaching students who have a hard time understanding fractions can be equally difficult for those who don’t have dedicated training or access to classroom resources. Teachers who are looking for easily accessible and affordable classroom resources, parents who want to play an active role in their students’ educations and tutors hired to facilitate the learning process can all benefit from professionally designed worksheets and other resources. With equivalent fractions worksheets ks3, students can get the help they need to understand these fractions and solve questions relating to simplification, subtraction, multiplication, and division of equivalent fractions with ease.

Equivalent Fractions (A)

Equivalent Fractions (B)

Equivalent Fractions (C)

Fractions Equivalent to One Half

Fractions Equivalent to One Quarter

Fractions Equivalent to One Third

Introducing the Fraction Wall

Using a Fraction Wall – Equivalent Fractions

Why Equivalent Fractions are Important

Worksheets for teachers.

Most teachers use and equivalent fractions worksheet in the classroom.

Many also assign equivalent fractions worksheets as homework. The idea behind assigning these worksheets is that as students complete similar calculations repeatedly they will begin to develop a more comprehensive understanding of the concepts being expressed.

Just like textbooks, a downloadable worksheet can be used to ease the burden on teachers of coming up with classroom activities and learning strategies, allowing them to focus more energy on making sure every student learns the material. They can begin with simple worksheets that allow students to practice basic fractions calculations such as addition and subtraction, then move on to multiplying and dividing fractions. Once they’ve reached the point where all of the students have a decent understanding of these basics, they’ll be ready to move on to equivalent fractions – worksheet problems can help.

Although lectures and reading play a large role in any classroom learning experience, only repetitive hands-on experience will cement these abstract concepts in students’ minds. Worksheets can facilitate this repetitive, hands-on learning process both in the classroom and at home.

Worksheets for Parents

Teachers aren’t the only adults who can benefit from downloading the occasional equivalent fractions worksheet ks3 as an educational device.

Personal tutors and concerned parents can also benefit from using these important tools. Learning doesn’t have to stop when kids leave the school grounds.

While most parents want to help their children succeed in the classroom, few have the time or even the kind of knowledge to come up with their own sample problems. That shouldn’t mean that they can’t offer their kids extra help at home if they’re having trouble keeping up in the classroom. Downloadable worksheets allow even busy parents to offer their kids the resources they need to succeed.

Parents who home-school their children are always looking for new ways to take advantage of the wealth of educational resources available online. Fractions worksheets offer them an easy way of doing just that. The fact that all of Cazoom Maths’ worksheets come with separate answer sheets so that parents can check their children’s work makes this particular resource even more helpful for parents of home-schooled children. With these advanced worksheets, there’s no need for parents to be concerned that their home-schooled children aren’t keeping up with their peers since they’ll be able to check students’ progress every step of the way.

Worksheets for Tutors

Older students who mentor their younger peers or professional tutors hired to provide extra assistance to students in their homes can also take advantage of downloadable worksheets.

Once they’ve signed up or an unlimited account, they can download as many resources as they want directly to their computers.

Tutors can also print off as many copies of these worksheets as they want so those who have multiple clients can use the same materials time and again without worrying about constantly updating them. The files can also be saved, so those who prefer to sign up for a one-month membership instead of an unlimited account can download as many as 60 resources then continue using them throughout their time as tutors.

Worksheets for Students

Enterprising students who are committed to making the most of their education can ask their parents how they can access downloadable fractions worksheets, themselves.

Since answer sheets are also available online, they can complete as many extra worksheets as they want then check the answers for themselves. New resources are added constantly so there’s no reason to be concerned that students will run out of material to review and students can access the site from home, school, or even their friends’ houses.

Tips for Parents Who Don't Love Maths

Let’s face it: maths isn’t every adult’s strong suit any more than it is every child’s. That shouldn’t mean parents who never developed a love of maths can’t instill positive feelings about this important subject in their kids or that they can’t play an active role in their kids’ learning processes.

If you’re nervous about your mathematical abilities, try not to share those feelings with your children. Instead, make a point of reviewing basic ideas prior to helping kids with homework and simply download the answers to worksheets and correct them out of the child’s view.

When helping children with homework, make a point of asking for explanations rather than offering them. Letting students explain what they have learned in their own words is one of the best ways for parents to ensure that their kids really understand the material and get an idea of what they need help with. Those who feel that attempting to help with maths homework is completely hopeless can always hire tutors for children who are struggling.

How to Tell it's Time to Hire a Tutor?

Before hiring a tutor, parents who want to remain involved in their young students’ lives may want to sign up for a Cazoom Maths account so they can access the same learning materials available to teachers. It’s worth taking the time to review equivalent fractions as soon as children begin requesting help with fractions worksheets or homework assignments. If the information on the worksheets remains inaccessible even after parents have reviewed the answers and the additional resources available online, it might be time to consider a tutor.

Children who attend public school or private schools typically bring home report cards. Even parents who are terrible at maths will be able to evaluate their children’s progress by checking on their grades periodically. Those who hire other, older students to mentor their children in maths can even provide their kids’ tutors with the same resources described above. This will help tutors, parents and students stay on the same page. It will also allow tutors to spend more time teaching and less time working out the answers themselves because they’ll have access to answer sheets the parents have provided.

Tips for Teaching Equivalent Fractions at Home

Teachers, tutors and parents can use other teaching techniques in conjunction with worksheets to facilitate learning. Some parents use food to teach equivalent fractions, dividing oranges or even chocolate bars in different ways and then sharing them with their children. Teachers often use fraction tiles, number lines, or pattern blocks that offer students a visual representation of how different fractions are equivalent.

These lessons allow children to learn through observation instead of relying on explanations of abstract ideas alone, but they can’t replace ongoing practice when it comes to cementing the ideas in students’ minds. Only repetition can ensure that children will remember the lessons they have learned when it’s time to take their tests. With repetitive practice, there’s really no replacing printable worksheets.

Make Fractions Fun with Visual Learning Devices

The best way for any adult to help a young student is to make the process more fun. When they are assigned an equivalent fractions worksheet, students are more likely to enjoy the learning process, which will encourage them to engage actively with the material. Although lectures and classroom exercises can be helpful, many young children find taking a visual approach to learning maths is more fun and more rewarding.

Fractions worksheets often come with helpful diagrams, which can make learning even easier. Children can begin with fractions that are equivalent to one-half, one-quarter or one-third by learning how to use shading grids and using them as a visual aid for understanding equivalency. Once the basic concept of equivalency has been established in a student’s mind, he or she will have the tools required to move on to harder worksheets and solve more challenging problems.

Teach Practical Applications

Just about every parent, teacher, tutor or adult who regularly meets school-aged kids has been posed the age-old question, “but why do I have to learn maths?” These adults know that an understanding of basic maths, including fractions, will come in handy later in life, but it can be hard to explain how abstract concepts like equivalency are relevant to children’s lives. The best worksheets should offer students the chance to see some of the practical applications of equivalent fractions.

Examples include telling time as an equivalent fraction of one hour and worksheets that present fractions of amounts. These kinds of real-world applications let students see how the material they are being taught can be used in their everyday lives, offering context that can inspire them to devote more time and energy to thoroughly learning these lessons.

Access Additional Resources

Parents and teachers can benefit from additional online resources that can be used in conjunction with downloadable worksheets. These include diagrams, blank fraction shading grids, fraction comparisons, division help sheets, and more.

Teachers can use these resources to develop more-effective lesson plans that cater to their students’ levels of understanding. Parents can use them as a refresher course before they sit down to help their children with homework assignments.

Given the reasonable price and easy accessibility of the online worksheets available through Cazoom Maths, there’s no reason that any child should be left without the additional help he or she needs to understand even abstract mathematical concepts. Parents who want to home-school their kids or just stay involved in their children’s educations as they attend public schools will find these resources equally helpful.

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Equivalent Fractions

Subject: Mathematics

Age range: 11-14

Resource type: Worksheet/Activity

Last updated

11 December 2017

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Math Expressions Grade 3 Unit 7 Lesson 7 Answer Key Equivalent Fractions

Solve the questions in Math Expressions Grade 3 Homework and Remembering Answer Key Unit 7 Lesson 7 Answer Key Equivalent Fractions to attempt the exam with higher confidence. https://mathexpressionsanswerkey.com/math-expressions-grade-3-unit-7-lesson-7-answer-key/

Math Expressions Common Core Grade 3 Unit 7 Lesson 7 Answer Key Equivalent Fractions

Math Expressions Grade 3 Unit 7 Lesson 7 Homework

Use your number lines. Write an equivalence chain.

Unit 7 Equivalent Fractions Answer Key Grade 3 Math Expressions Question 2. With fractions that equal \(\frac{1}{2}\) Answer: \(\frac{1}{2}\) = \(\frac{2}{4}\).

Explanation: The fractions that equal \(\frac{1}{2}\) is \(\frac{1}{2}\) = \(\frac{2}{4}\).

Math Expressions Grade 3 Answer Key Equivalent Fractions Question 3. With fractions that equal \(\frac{3}{4}\) Answer: \(\frac{3}{4}\) = \(\frac{6}{8}\).

Explanation: The fractions that equal \(\frac{3}{4}\) is \(\frac{3}{4}\) = \(\frac{6}{8}\).

Grade 3 Unit 7 Answer Key Equivalent Fractions Lesson 7 Question 4. With fractions that equal \(\frac{6}{6}\) Answer: \(\frac{6}{6}\) = \(\frac{12}{12}\).

Explanation: The fractions that equal \(\frac{6}{6}\) is \(\frac{6}{6}\) = \(\frac{12}{12}\).

Math Expressions Grade 3 Unit 7 Lesson 7 Remembering

Solve each problem. Label your answers. Show your work.

Equivalent Fractions Grade 3 Unit 7 Lesson 7 Answer Key Math Expressions Question 1. Mrs. Garcia has 15 pencils in a cup. 7 students take a pencil from the cup to use in class. Mrs. Garcia puts 3 more pencils in the cup. How many pencils are in the cup now? Answer: The number of pencils are in the cup are 11 pencils.

Explanation: Given that Mrs. Garcia has 15 pencils in a cup and 7 students take a pencil from the cup to use in class, so the number of pencils will be 15 – 7 which is 8 pencils. And Mrs. Garcia puts 3 more pencils in the cup, so the total number of pencils will be 8+3 which is 11 pencils.

Question 2. Matthew buys 13 baseball cards. His dad buys him 5 more. Then Matthew gives his brother 6 cards. How many cards does Matthew have now? Answer: The number of cards does Matthew have now is 12 cards.

Explanation: Given that Matthew buys 13 baseball cards and his dad buys him 5 more, so the total number baseball cards are 13 + 5 which is 18 baseball cards. Then Matthew gives his brother 6 cards, so the number of cards does Matthew have now is 18 – 6 which is 12 cards.

Decompose the figure into rectangles. Then find the area of the figure.

Use your fraction strips for Exercise 4. Fill in the blanks.

Explanation: There are two sixths in one third.

Explanation: The different fractions that are equivalent to \(\frac{1}{2}\) is \(\frac{1}{2}\) = \(\frac{2}{4}\), \(\frac{1}{2}\) = \(\frac{3}{6}\), \(\frac{1}{2}\) = \(\frac{4}{8}\).

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