Decompose Fractions into Sums of Unit Fractions

Examples, solutions, and videos to help Grade 4 students learn how to decompose fractions into sums of smaller unit fractions using tape diagrams.

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

New York State Common Core Grade 4, Module 5, Lesson 3

Worksheets for Grade 4

Lesson 4 Concept Development
Problem 1: Use tape diagrams to represent the decomposition of 1/3 as the sum of unit fractions.
Problem 2: Use tape diagrams to represent the decomposition of 1/5 and 2/5 as the sum of smaller unit fractions.
Problem 3: Draw a tape diagram and use addition to show that 2/6 is the sum of 4 twelfths.

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Lesson 4 Problem Set 1

1. The total length of each tape diagram represents 1 whole. Decompose the shaded unit fractions as the sum of smaller unit fractions in at least two different ways.
   a to d
2. The total length of each tape diagram represents 1 whole. Decompose the shaded fractions as the sum of smaller unit fractions in at least two different ways.
   a and b
3. Draw and label tape diagrams to prove the following statements.
   a. 2/5 = 4/10
   b. 2/6 = 4/12
   c. 3/4 = 6/8
   d. 3/4 = 9/12
4. Show that 1/2 is equivalent to 4/8 using a tape diagram and a number sentence.
5. Show that 2/3 is equivalent to 6/9 using a tape diagram and a number sentence.
6. Show that 4/6 is equivalent to 8/12 using a tape diagram and a number sentence.

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Lesson 4 Homework

1. The total length of each tape diagram represents 1 whole. Decompose the shaded unit fractions as the sum of smaller unit fractions in at least two different ways.
   a and b
2. The total length of each tape diagram represents 1 whole. Decompose the shaded fractions as the sum of smaller unit fractions in at least two different ways.
   a to c
3. Draw and label tape diagrams to prove the following statements.
   a. 2/5 = 4/10
   b. 3/6 = 6/12
   c. 2/6 = 6/18
   d. 3/4 = 12/16
4. Show that 1/2 is equivalent to 6/12 using a tape diagram and a number sentence.
   
5. Show that 2/3 is equivalent to 8/12 using a tape diagram and a number sentence.
   
6. Show that 4/5 is equivalent to 12/15 using a tape diagram and a number sentence.
   

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