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}

Lesson overview

Expand to review the lesson summary and core properties.

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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}