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

Lesson overview

Expand to review the lesson summary and core properties.

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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