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

Lesson 2: 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, students learn to represent the multiplication of n times a/b as (n × a)/b by applying the associative property to fraction multiplication. Using visual models such as tape diagrams and number lines, students practice rewriting repeated addition of fractions as multiplication sentences and simplifying expressions like 5 × 5/6 = 25/6. This lesson from Chapter 27 builds fluency with multiplying whole numbers by fractions and converting improper fractions to mixed numbers.

Section 1

Multiplying a Whole Number by a Fraction

Property

To multiply a whole number ( $n$ ) by a fraction ( $\frac{a}{b}$ ), multiply the whole number by the numerator ( $a$ ) and keep the denominator ( $b$ ) the same.

n \times \frac{a}{b} = \frac{n \times a}{b}

Examples

Section 2

Using Multiplication to Find a Total in a Multi-Step Problem

Property

To solve a multi-step word problem, break the problem down into smaller parts.
First, write a number sentence to find a total amount using fraction multiplication.
Then, use that result in a second step, such as addition or subtraction, to find the final answer.

Examples

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Chapter 27: Repeated Addition of Fractions as Multiplication

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Lesson 1
Lesson 1: Represent the multiplication of n times a/b as (n x a)/b using the associative property and visual models.
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Lesson 2Current
Lesson 2: Represent the multiplication of n times a/b as (n x a)/b using the associative property and visual models.
Learn Practice
Lesson 3
Lesson 3: Find the product of a whole number and a mixed number using the distributive property.
Learn Practice
Lesson 4
Lesson 4: Find the product of a whole number and a mixed number using the distributive property.
Learn Practice
Lesson 5
Lesson 5: Solve multiplicative comparison word problems involving fractions.
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Lesson 6
Lesson 6: Solve word problems involving the multiplication of a whole number and a fraction including those involving line plots.
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Lesson overview

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Section 1

Multiplying a Whole Number by a Fraction

Property

To multiply a whole number ( $n$ ) by a fraction ( $\frac{a}{b}$ ), multiply the whole number by the numerator ( $a$ ) and keep the denominator ( $b$ ) the same.

n \times \frac{a}{b} = \frac{n \times a}{b}

Examples

Section 2

Using Multiplication to Find a Total in a Multi-Step Problem

Property

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

Back to Eureka Math, Grade 4

Lesson 1
Lesson 1: Represent the multiplication of n times a/b as (n x a)/b using the associative property and visual models.
Learn Practice
Lesson 2Current
Lesson 2: Represent the multiplication of n times a/b as (n x a)/b using the associative property and visual models.
Learn Practice
Lesson 3
Lesson 3: Find the product of a whole number and a mixed number using the distributive property.
Learn Practice
Lesson 4
Lesson 4: Find the product of a whole number and a mixed number using the distributive property.
Learn Practice
Lesson 5
Lesson 5: Solve multiplicative comparison word problems involving fractions.
Learn Practice
Lesson 6
Lesson 6: Solve word problems involving the multiplication of a whole number and a fraction including those involving line plots.
Learn Practice

Overview

Lesson overview

Review the lesson summary and core properties without leaving the current page.

Overview

Section 1

Multiplying a Whole Number by a Fraction

Property

To multiply a whole number ( $n$ ) by a fraction ( $\frac{a}{b}$ ), multiply the whole number by the numerator ( $a$ ) and keep the denominator ( $b$ ) the same.

n \times \frac{a}{b} = \frac{n \times a}{b}

Examples

Section 2

Using Multiplication to Find a Total in a Multi-Step Problem

Property

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

Back to Eureka Math, Grade 4

Lesson 1
Lesson 1: Represent the multiplication of n times a/b as (n x a)/b using the associative property and visual models.
Learn Practice
Lesson 2Current
Lesson 2: Represent the multiplication of n times a/b as (n x a)/b using the associative property and visual models.
Learn Practice
Lesson 3
Lesson 3: Find the product of a whole number and a mixed number using the distributive property.
Learn Practice
Lesson 4
Lesson 4: Find the product of a whole number and a mixed number using the distributive property.
Learn Practice
Lesson 5
Lesson 5: Solve multiplicative comparison word problems involving fractions.
Learn Practice
Lesson 6
Lesson 6: Solve word problems involving the multiplication of a whole number and a fraction including those involving line plots.
Learn Practice

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

Property

Examples

Property

Examples

Chapter 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.

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

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

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

Lesson 5: Solve multiplicative comparison word problems involving fractions.

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

Lesson overview

Property

Examples

Property

Examples

Chapter 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.

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

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

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

Lesson 5: Solve multiplicative comparison word problems involving fractions.

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

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

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

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

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

Lesson 5: Solve multiplicative comparison word problems involving fractions.

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