Learn on PengiEureka Math, Grade 4Chapter 25: Extending Fraction Equivalence to Fractions Greater Than 1

Lesson 2: Add and multiply unit fractions to build fractions greater than 1 using visual models.

In this Grade 4 Eureka Math lesson from Chapter 25, students learn to add and multiply unit fractions to build fractions greater than 1, using visual models such as number lines and number bonds to connect improper fractions and mixed numbers. The lesson develops fluency with equivalent fractions by counting by fractional units like sixths and fifths, and reinforces how whole numbers relate to fractions with the same denominator. Students also practice subtracting fractions from whole numbers, strengthening their understanding of fraction equivalence across values greater than 1.

Section 1

Multiplying a Whole Number by a Unit Fraction

Property

Multiplying a whole number, nn, by a unit fraction, 1d\frac{1}{d}, is equivalent to repeated addition.
This relationship is generalized by the rule:

n×1d=1d+1d+⋯+1d⏟n times=ndn \times \frac{1}{d} = \underbrace{\frac{1}{d} + \frac{1}{d} + \dots + \frac{1}{d}}_{n \text{ times}} = \frac{n}{d}

Examples

Section 2

Expressing Products as Mixed Numbers

Property

To convert an improper fraction nd\frac{n}{d} (the product of n×1dn \times \frac{1}{d}) to a mixed number, divide the numerator nn by the denominator dd. The quotient qq is the whole number part, and the remainder rr is the new numerator.

nd=qrd\frac{n}{d} = q\frac{r}{d}

Examples

Book overview

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Chapter 25: Extending Fraction Equivalence to Fractions Greater Than 1

  1. Lesson 1

    Lesson 1: Add a fraction less than 1 to, or subtract a fraction less than 1 from, a whole number using decomposition and visual models.

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  2. Lesson 2Current

    Lesson 2: Add and multiply unit fractions to build fractions greater than 1 using visual models.

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  3. Lesson 3

    Lesson 3: Decompose and compose fractions greater than 1 to express them in various forms.

    LearnPractice
  4. Lesson 4

    Lesson 4: Decompose and compose fractions greater than 1 to express them in various forms.

    LearnPractice
  5. Lesson 5

    Lesson 5: Compare fractions greater than 1 by reasoning using benchmark fractions.

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  6. Lesson 6

    Lesson 6: Compare fractions greater than 1 by creating common numerators or denominators.

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  7. Lesson 7

    Lesson 7: Solve word problems with line plots.

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Lesson overview

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Section 1

Multiplying a Whole Number by a Unit Fraction

Property

Multiplying a whole number, nn, by a unit fraction, 1d\frac{1}{d}, is equivalent to repeated addition.
This relationship is generalized by the rule:

n×1d=1d+1d+⋯+1d⏟n times=ndn \times \frac{1}{d} = \underbrace{\frac{1}{d} + \frac{1}{d} + \dots + \frac{1}{d}}_{n \text{ times}} = \frac{n}{d}

Examples

Section 2

Expressing Products as Mixed Numbers

Property

To convert an improper fraction nd\frac{n}{d} (the product of n×1dn \times \frac{1}{d}) to a mixed number, divide the numerator nn by the denominator dd. The quotient qq is the whole number part, and the remainder rr is the new numerator.

nd=qrd\frac{n}{d} = q\frac{r}{d}

Examples

Book overview

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

Continue this chapter

Chapter 25: Extending Fraction Equivalence to Fractions Greater Than 1

  1. Lesson 1

    Lesson 1: Add a fraction less than 1 to, or subtract a fraction less than 1 from, a whole number using decomposition and visual models.

    LearnPractice
  2. Lesson 2Current

    Lesson 2: Add and multiply unit fractions to build fractions greater than 1 using visual models.

    LearnPractice
  3. Lesson 3

    Lesson 3: Decompose and compose fractions greater than 1 to express them in various forms.

    LearnPractice
  4. Lesson 4

    Lesson 4: Decompose and compose fractions greater than 1 to express them in various forms.

    LearnPractice
  5. Lesson 5

    Lesson 5: Compare fractions greater than 1 by reasoning using benchmark fractions.

    LearnPractice
  6. Lesson 6

    Lesson 6: Compare fractions greater than 1 by creating common numerators or denominators.

    LearnPractice
  7. Lesson 7

    Lesson 7: Solve word problems with line plots.

    LearnPractice