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

Lesson overview

Expand to review the lesson summary and core properties.

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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}