Fraction Equivalence Using Area Model

Examples, solutions, and videos to help Grade 4 students learn how to use the area model and multiplication to show the equivalence of two fractions.

Common Core Standards: 4.NF.1, 4.NF.3b

New York State common Core Grade 4 Module 5, Lesson 8

Worksheets for Grade 4

Lesson 8 Concept Development

Problem 1: Determine that multiplying both the numerator and denominator by n results in an equivalent fraction.
Problem 2: Determine that two fractions are equivalent using an area model and a number sentence.
Problem 3: Write a number sentence using multiplication to show the equivalence of two fractions. Draw the corresponding area model.

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Lesson 8 Problem Set 1

Each rectangle represents 1 whole.

1. The shaded fractions have been decomposed into smaller units. Express the equivalent fractions in a number sentence using multiplication.
   
   
2. Decompose the shaded fractions into smaller units, as given below. Express the equivalent fractions in a number sentence using multiplication.
   a. Decompose into tenths.
   b. Decompose into fifteenths.
   
   
3. Draw area models to prove that the following number sentences are true.
   a. 2/5 = 4/10
   b. 2/3 = 8/12
   c. 3/6 = 6/12
   d. 4/6 = 8/12
   
   
4. Use multiplication to rename each fraction below.
   a. 3/4
   b. 4/5
   c. 7/6
   d. 12/7
   
   
5. Determine which of the following are true number sentences. Correct those that are false by changing the right-hand side of the number sentence.
   a. 4/3 = 8/9
   b. 5/4 = 10/8
   c. 4/5 = 12/10
   d. 4/6 = 12/8

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Lesson 8 Homework

Each rectangle represents 1 whole.

1. The shaded fractions have been decomposed into smaller units. Express the equivalent fractions in a number sentence using multiplication.
   
   
2. Decompose the shaded fractions into smaller units, as given below. Express the equivalent fractions in a number sentence using multiplication.
   a. Decompose into tenths.
   b. Decompose into fifteenths.
   
   
3. Draw area models to prove that the following number sentences are true.
   a. 1/3 = 2/6
   b. 2/5 = 4/10
   c. 5/7 = 10/24
   d. 3/6 = 9/18
   
   
4. Use multiplication to rename each fraction below.
   a. 2/3
   b. 5/6
   c. 6/5
   d. 10/8
   
   
5. Determine which of the following are true number sentences. Correct those that are false by changing the right-hand side of the number sentence.
   a. 2/3 = 4/9
   b. 5/6 = 10/12
   c. 3/5 = 6/15
   d. 7/4 = 21/12

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