Learn on PengienVision, Mathematics, Grade 4Chapter 10: Extend Multiplication Concepts to Fractions

Lesson 3: Multiply a Fraction by a Whole Number: Use Symbols

Property.

Section 1

Justifying the Rule with the Associative Property

Property

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

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

Examples

Section 2

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

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Justifying the Rule with the Associative Property

Property

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

Examples

Section 2

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

Overview

Lesson overview

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

Overview

Section 1

Justifying the Rule with the Associative Property

Property

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

Examples

Section 2

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}