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

Lesson 1: 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 by folding paper strips and drawing tape diagrams to represent the parts. The lesson builds understanding of fraction equivalence by writing addition sentences such as 1 = 1/3 + 1/3 + 1/3 and decomposing fractions like 5/6 into unit fractions. Students also explore how non-standard shapes like diagonal cuts can still represent equal fractional parts with the same area.

Section 1

Composing Fractions with Unit Fractions

Property

Any fraction ab\frac{a}{b} is the sum of 'a' unit fractions of size 1b\frac{1}{b}.

ab=1b+1b+⋯+1b⏟a times\frac{a}{b} = \underbrace{\frac{1}{b} + \frac{1}{b} + \dots + \frac{1}{b}}_{a \text{ times}}

Section 2

Representing Fraction Decomposition with Visual Models

Property

The decomposition of a fraction into a sum of unit fractions can be represented by three connected models: a visual tape diagram, a schematic number bond, and a symbolic addition sentence.
All three models represent the same core equation:

ab=1b+1b+⋯+1b⏟a times\frac{a}{b} = \underbrace{\frac{1}{b} + \frac{1}{b} + \dots + \frac{1}{b}}_{a \text{ times}}

Examples

Section 3

Decompose a Fraction into a Sum of Fractions

Property

A fraction ab\frac{a}{b} can be decomposed into a sum of smaller fractions with the same denominator, such as ab=xb+yb\frac{a}{b} = \frac{x}{b} + \frac{y}{b}, where x+y=ax + y = a.

Examples

Book overview

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Chapter 21: Decomposition and Fraction Equivalence

  1. Lesson 1Current

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

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  2. Lesson 2

    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

Composing Fractions with Unit Fractions

Property

Any fraction ab\frac{a}{b} is the sum of 'a' unit fractions of size 1b\frac{1}{b}.

ab=1b+1b+⋯+1b⏟a times\frac{a}{b} = \underbrace{\frac{1}{b} + \frac{1}{b} + \dots + \frac{1}{b}}_{a \text{ times}}

Section 2

Representing Fraction Decomposition with Visual Models

Property

The decomposition of a fraction into a sum of unit fractions can be represented by three connected models: a visual tape diagram, a schematic number bond, and a symbolic addition sentence.
All three models represent the same core equation:

ab=1b+1b+⋯+1b⏟a times\frac{a}{b} = \underbrace{\frac{1}{b} + \frac{1}{b} + \dots + \frac{1}{b}}_{a \text{ times}}

Examples

Section 3

Decompose a Fraction into a Sum of Fractions

Property

A fraction ab\frac{a}{b} can be decomposed into a sum of smaller fractions with the same denominator, such as ab=xb+yb\frac{a}{b} = \frac{x}{b} + \frac{y}{b}, where x+y=ax + y = a.

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 1Current

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

    LearnPractice
  2. Lesson 2

    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