Decompose Unit Fractions using Area Models

Videos, solutions, and examples to help Grade 4 students learn how to decompose unit fractions using area models to show equivalence.

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

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

Download Grade 4, Module 5, Lesson 5 Worksheets

 

Lesson 5 Concept Development
Problem 1: Draw an area model to illustrate that 1/5 is equal to 2/10.
Problem 2: Decompose 1/3 as 4/12 represented in an area model and as the sum and product of unit fractions.
Problem 3: Model 1/2 = 5/10 and represent the decomposition as the sum and product of unit fractions.

• Show Step-by-step Solutions

Lesson 5 Problem Set

1. Draw horizontal lines to decompose each rectangle into the number of rows as indicated. Use the model to give the shaded area as both a sum of unit fractions and as a multiplication sentence.
   a. 2 rows
   b. 2 rows
   c. 4 rows
2. Draw area models to show the decompositions represented by the number sentences below. Represent the decomposition as a sum of unit fractions and as a multiplication sentence.
   a. 1/2 = 3/6
   b. 1/2 = 4/8
   c. 1/2 = 5/10
   d. 1/3 = 2/6
   e. 1/3 = 4/12
   f. 1/3 = 3/12
3. Explain why 1/12 + 1/12 + 1/12 is the same as 1/4.

• Show Step-by-step Solutions

Lesson 5 Homework

1. Draw horizontal lines to decompose each rectangle into the number of rows as indicated. Use the model to give the shaded area as both a sum of unit fractions and as a multiplication sentence.
   a. 3 rows
   b. 2 rows
   c. 4 rows
2. Draw area models to show the decompositions represented by the number sentences below. Represent the decomposition as a sum of unit fractions and as a multiplication sentence. a. 1/3 = 2/6
   b. 1/3 = 3/9
   c. 1/3 = 4/12
   d. 1/3 = 5/15
   e. 1/5 = 2/10
   f. 1/5 = 3/15
3. Explain why 1/12 + 1/12 + 1/12 + 1/12 is the same as 1/3.

• Show Step-by-step Solutions

• Show Step-by-step Solutions

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.