Learn on PengiEureka Math, Grade 4Chapter 27: Repeated Addition of Fractions as Multiplication

Lesson 1: Represent the multiplication of n times a/b as (n x a)/b using the associative property and visual models.

In this Grade 4 Eureka Math lesson from Chapter 27, students learn to represent the multiplication of a whole number times a fraction, such as n times a/b, as (n x a)/b by applying the associative property. Using visual models and real-world contexts, students explore how a fractional unit like "fourths" or "fifths" behaves just like any other unit in a multiplication expression. The lesson builds directly on students' prior work with equivalent fractions, mixed numbers, and fraction addition.

Section 1

Justifying the Rule with the Associative Property

Property

To multiply a whole number nn by a fraction ab\frac{a}{b}, you can decompose the fraction, apply the associative property, and then multiply the whole number by the numerator.
This demonstrates the rule n×ab=n×abn \times \frac{a}{b} = \frac{n \times a}{b}.

n×ab=n×(a×1b)=(n×a)×1b=n×abn \times \frac{a}{b} = n \times (a \times \frac{1}{b}) = (n \times a) \times \frac{1}{b} = \frac{n \times a}{b}

Examples

Book overview

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

Continue this chapter

Chapter 27: Repeated Addition of Fractions as Multiplication

  1. Lesson 1Current

    Lesson 1: Represent the multiplication of n times a/b as (n x a)/b using the associative property and visual models.

    LearnPractice
  2. Lesson 2

    Lesson 2: Represent the multiplication of n times a/b as (n x a)/b using the associative property and visual models.

    LearnPractice
  3. Lesson 3

    Lesson 3: Find the product of a whole number and a mixed number using the distributive property.

    LearnPractice
  4. Lesson 4

    Lesson 4: Find the product of a whole number and a mixed number using the distributive property.

    LearnPractice
  5. Lesson 5

    Lesson 5: Solve multiplicative comparison word problems involving fractions.

    LearnPractice
  6. Lesson 6

    Lesson 6: Solve word problems involving the multiplication of a whole number and a fraction including those involving line plots.

    LearnPractice

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Justifying the Rule with the Associative Property

Property

To multiply a whole number nn by a fraction ab\frac{a}{b}, you can decompose the fraction, apply the associative property, and then multiply the whole number by the numerator.
This demonstrates the rule n×ab=n×abn \times \frac{a}{b} = \frac{n \times a}{b}.

n×ab=n×(a×1b)=(n×a)×1b=n×abn \times \frac{a}{b} = n \times (a \times \frac{1}{b}) = (n \times a) \times \frac{1}{b} = \frac{n \times a}{b}

Examples

Book overview

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

Continue this chapter

Chapter 27: Repeated Addition of Fractions as Multiplication

  1. Lesson 1Current

    Lesson 1: Represent the multiplication of n times a/b as (n x a)/b using the associative property and visual models.

    LearnPractice
  2. Lesson 2

    Lesson 2: Represent the multiplication of n times a/b as (n x a)/b using the associative property and visual models.

    LearnPractice
  3. Lesson 3

    Lesson 3: Find the product of a whole number and a mixed number using the distributive property.

    LearnPractice
  4. Lesson 4

    Lesson 4: Find the product of a whole number and a mixed number using the distributive property.

    LearnPractice
  5. Lesson 5

    Lesson 5: Solve multiplicative comparison word problems involving fractions.

    LearnPractice
  6. Lesson 6

    Lesson 6: Solve word problems involving the multiplication of a whole number and a fraction including those involving line plots.

    LearnPractice