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

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

In this Grade 4 Eureka Math lesson from Chapter 21, students learn to decompose fractions as a sum of unit fractions using tape diagrams and number bonds. Working with fractions such as thirds, fourths, and eighths, students practice writing repeated addition sentences and breaking apart fractions like 3/4 and 7/8 into multiple equivalent expressions. The lesson builds fraction equivalence concepts by showing how the same fraction can be decomposed in different ways while maintaining the same value.

Section 1

Decomposing the Whole (1) into Unit Fractions

Property

The number 1 can be expressed as a fraction nn\frac{n}{n} and decomposed into a sum of nn unit fractions.

1=nn=1n+1n+⋯+1n⏟n times1 = \frac{n}{n} = \underbrace{\frac{1}{n} + \frac{1}{n} + \dots + \frac{1}{n}}_{n \text{ times}}

Examples

Section 2

Decompose an Improper Fraction into a Whole Number and a Fraction

Property

For an improper fraction ab\frac{a}{b} where a>ba > b, it can be decomposed by separating one whole:

ab=bb+a−bb=1+a−bb\frac{a}{b} = \frac{b}{b} + \frac{a-b}{b} = 1 + \frac{a-b}{b}

Examples

Section 3

Decompose an Improper Fraction Using a Tape Diagram

Property

An improper fraction ab\frac{a}{b} where a>ba > b represents a quantity greater than one whole. Using a tape diagram, it can be decomposed into a sum of fractions, most commonly by separating the wholes from the fractional part.

ab=bb+a−bb=1+a−bb\frac{a}{b} = \frac{b}{b} + \frac{a-b}{b} = 1 + \frac{a-b}{b}

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.

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  2. Lesson 2Current

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

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  3. Lesson 3

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

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  4. Lesson 4

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

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  5. Lesson 5

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

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  6. Lesson 6

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

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Lesson overview

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Section 1

Decomposing the Whole (1) into Unit Fractions

Property

The number 1 can be expressed as a fraction nn\frac{n}{n} and decomposed into a sum of nn unit fractions.

1=nn=1n+1n+⋯+1n⏟n times1 = \frac{n}{n} = \underbrace{\frac{1}{n} + \frac{1}{n} + \dots + \frac{1}{n}}_{n \text{ times}}

Examples

Section 2

Decompose an Improper Fraction into a Whole Number and a Fraction

Property

For an improper fraction ab\frac{a}{b} where a>ba > b, it can be decomposed by separating one whole:

ab=bb+a−bb=1+a−bb\frac{a}{b} = \frac{b}{b} + \frac{a-b}{b} = 1 + \frac{a-b}{b}

Examples

Section 3

Decompose an Improper Fraction Using a Tape Diagram

Property

An improper fraction ab\frac{a}{b} where a>ba > b represents a quantity greater than one whole. Using a tape diagram, it can be decomposed into a sum of fractions, most commonly by separating the wholes from the fractional part.

ab=bb+a−bb=1+a−bb\frac{a}{b} = \frac{b}{b} + \frac{a-b}{b} = 1 + \frac{a-b}{b}

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.

    LearnPractice
  2. Lesson 2Current

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

    LearnPractice
  3. Lesson 3

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

    LearnPractice
  4. Lesson 4

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

    LearnPractice
  5. Lesson 5

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

    LearnPractice
  6. Lesson 6

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

    LearnPractice