Fraction Equivalence

Equivalent Fraction Word Problems

By Olivia Kilbride

Multiple Choice

QUICK REVIEW:

Which of the following fractions is equivalent to $$\frac{1}{2}$$  ?

Equivalent Fractions are fractions that represent the same part of a whole. Equivalent fractions may be represented through different numbers, but are the same size.

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Equivalent Fractions

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These pizzas are a good example of equivalent fractions. They may be cut into a different amount of slices, but you still eat half of the pizza if you eat 3 slices out of 6, or 4 slices out of 8. The pieces themselves are smaller individually, but these fractions represent the same part of the whole pizza.

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One way we can find equivalent fractions is by multiplying both the numerator (top number) and denominator (bottom number) ​by the same number, in this case two. 2/3, 4/6, and 8/12 are all equivalent because they represent the same part of the whole.

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Because division and multiplication are related, we can also divide these numbers to find equivalent fractions if the numbers in the fraction have common factors. In this case, if we divide these fractions by two, we can see that in its simplest form these fractions all come out to 8/12.​

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Multiple Choice

Which is NOT equivalent to $$\frac{2}{3}$$  ?

W​ord Problems

Word Problems do not have to be intimidating! There are strategies we can use to make these problems more manageable! The first step should always be to read the word problem twice. The first time, we read to get an understanding of the problem. The second time we read with our problem solving strategy in mind. We can follow our C.O.I.N.S problem solving strategy to get to the key points of our word problems!

C.O.I.N.S. Problem Solving Strategy​

​C Comprehend. What is the question asking? Underline the question

O Observe. Circle the numbers that we need to solve the problem.

I Illustrate. Draw a picture or diagram that can help us visualize the problem.

N Number. Write out an equation or number sentence that will help solve the problem.

S​ Solve. Solve the problem and write your answer in a complete sentence.

Joey and Kyle are trying to see who ate more pizza at the pizza party. Joey ate 3/6 slices of a pepperoni pizza. Kyle ate 4/8 slices of a cheese pizza. Kyle thinks he ate more pizza than Joey because he had 4 slices and Joey only had 3. Joey thinks he ate more pizza than Kyle because his slices were larger. Their friend Tony thinks that Joey and Kyle ate the same amount of pizza. Which friend is correct?

Draw

Underline the question and Circle the important numbers.

I circled 3/6 and 4/8 ​because those represent how many slices of pizza the friends ate. I did not circle 4 and 3 because those numbers are already part of the fractions. Each friend has a claim, and the question is which one of the friends is correct?

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Draw

The next step in C.O.I.N.S. is illustrate. Draw a picture that will help you answer the question.

This is one way this problem can be represented with a picture

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Draw

Show your work! What do we know about 4/8 and 3/6? Are they equivalent?

We are not done yet! Our question was asking us which friend was correct! We have to make sure we answer our word problems fully!

Multiple Choice

Which friend is correct?

• Joey. Joey ate 3/6 of the pizza and 3/6 is more than 4/8.

• Kyle. Kyle ate 4/8 of the pizza and 4 pieces is more than 3 pieces.

• Tony. Tony says that Joey and Kyle ate the same amount of pizza.

Your turn!

Try these two word problems about equivalent fractions on your own following the same strategy!

Kelsey had 12 homework problems and she completed 8/12 questions. Olivia had only ​6 homework problems and she completed 3/6 questions. Who completed more of their homework?

Draw

Circle the Numbers we need to solve the problem and underline the question.

Draw

Draw a diagram that will help you solve the problem.

Draw

Show your work! What do we know about 8/12 and 3/6? Are they equivalent?

Multiple Choice

Who completed more of their homework?

• Olivia

• Kelsey

Abby ate 2/6 of her birthday cake. Chris ate 1/3 of his birthday cake. Who ate more cake?

Draw

circle the numbers we need to solve the problem and underline the question.

Draw

Draw a picture that can help you solve the problem.

Draw

Show your work! What do we know about 2/6 and 1/3? Are they equivalent?

Multiple Choice

Who ate more cake?

• They ate the same amount of cake.

• Abby

• Chris

Open Ended

Bonus Question! Can you come up with a word problem that relates to equivalent fractions?