Learn on PengiEureka Math, Grade 4Chapter 21: Decomposition and Fraction Equivalence

Lesson 5: Decompose unit fractions using area models to show equivalence.

In this Grade 4 Eureka Math lesson from Chapter 21, students learn to decompose unit fractions using area models to demonstrate fraction equivalence, for example showing that one-half equals three-sixths or that two-thirds equals six-ninths. Students practice breaking apart unit fractions into smaller equal parts and writing the results as addition sentences and multiplication equations. The lesson builds directly on prior work with tape diagrams and prepares students to recognize and generate equivalent fractions using visual models.

Section 1

Representing Decomposed Unit Fractions as Sums and Products

Property

When a unit fraction 1b\frac{1}{b} is decomposed into an equivalent fraction nd\frac{n}{d}, the equivalence can be expressed in two ways:

  1. As a sum of unit fractions: 1b=1d+1d+\frac{1}{b} = \frac{1}{d} + \frac{1}{d} + \dots
  2. As a product of a whole number and a unit fraction: 1b=n×1d\frac{1}{b} = n \times \frac{1}{d}

Examples

Book overview

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Chapter 21: Decomposition and Fraction Equivalence

  1. Lesson 1

    Lesson 1: Decompose fractions as a sum of unit fractions using tape diagrams.

  2. Lesson 2

    Lesson 2: Decompose fractions as a sum of unit fractions using tape diagrams.

  3. Lesson 3

    Lesson 3: Decompose non-unit fractions and represent them as a whole number times a unit fraction using tape diagrams.

  4. Lesson 4

    Lesson 4: Decompose fractions into sums of smaller unit fractions using tape diagrams.

  5. Lesson 5Current

    Lesson 5: Decompose unit fractions using area models to show equivalence.

  6. Lesson 6

    Lesson 6: Decompose fractions using area models to show equivalence.

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Representing Decomposed Unit Fractions as Sums and Products

Property

When a unit fraction 1b\frac{1}{b} is decomposed into an equivalent fraction nd\frac{n}{d}, the equivalence can be expressed in two ways:

  1. As a sum of unit fractions: 1b=1d+1d+\frac{1}{b} = \frac{1}{d} + \frac{1}{d} + \dots
  2. As a product of a whole number and a unit fraction: 1b=n×1d\frac{1}{b} = n \times \frac{1}{d}

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 21: Decomposition and Fraction Equivalence

  1. Lesson 1

    Lesson 1: Decompose fractions as a sum of unit fractions using tape diagrams.

  2. Lesson 2

    Lesson 2: Decompose fractions as a sum of unit fractions using tape diagrams.

  3. Lesson 3

    Lesson 3: Decompose non-unit fractions and represent them as a whole number times a unit fraction using tape diagrams.

  4. Lesson 4

    Lesson 4: Decompose fractions into sums of smaller unit fractions using tape diagrams.

  5. Lesson 5Current

    Lesson 5: Decompose unit fractions using area models to show equivalence.

  6. Lesson 6

    Lesson 6: Decompose fractions using area models to show equivalence.