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

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

In this Grade 4 Eureka Math lesson from Chapter 21, students learn to decompose fractions into sums of smaller unit fractions using tape diagrams. Students practice expressing fractions like 2/3 and 3/4 as repeated addition sentences and multiplication expressions involving unit fractions. The lesson builds fraction equivalence skills by connecting visual tape diagram models to symbolic notation.

Section 1

Decomposing a Fraction into a Sum of Unit Fractions

Property

A fraction ab\frac{a}{b} can be expressed as the sum of its unit fractions, 1b\frac{1}{b}, added 'a' times.
This can also be written as the product of the numerator 'a' and the unit fraction 1b\frac{1}{b}.

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

Examples

Section 2

Modeling Equivalent Non-Unit Fractions

Property

To find an equivalent fraction for a non-unit fraction, decompose each part of its tape diagram into an equal number of smaller parts. This multiplies both the numerator (shaded parts) and the denominator (total parts) by the same number, creating an equivalent fraction. This is represented by the equation:

ab=n×an×b\frac{a}{b} = \frac{n \times a}{n \times b}

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.

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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.

    LearnPractice
  4. Lesson 4Current

    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

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Decomposing a Fraction into a Sum of Unit Fractions

Property

A fraction ab\frac{a}{b} can be expressed as the sum of its unit fractions, 1b\frac{1}{b}, added 'a' times.
This can also be written as the product of the numerator 'a' and the unit fraction 1b\frac{1}{b}.

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

Examples

Section 2

Modeling Equivalent Non-Unit Fractions

Property

To find an equivalent fraction for a non-unit fraction, decompose each part of its tape diagram into an equal number of smaller parts. This multiplies both the numerator (shaded parts) and the denominator (total parts) by the same number, creating an equivalent fraction. This is represented by the equation:

ab=n×an×b\frac{a}{b} = \frac{n \times a}{n \times b}

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.

    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 4Current

    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