Learn on PengiIllustrative Mathematics, Grade 5Chapter 2: Fractions as Quotients and Fraction Multiplication

Lesson 10: Multiply More Fractions

In this Grade 5 lesson from Illustrative Mathematics Chapter 2, students multiply whole numbers and mixed numbers by applying properties of operations such as the distributive property to decompose and find products. Students practice expressions like 12 × 9⅔ and 3⅝ × 18, using fraction decomposition to break calculations into manageable parts. The lesson builds fluency with multiplying fractions greater than 1 written as mixed numbers, connecting to real-world contexts involving area.

Section 1

Calculate the area of a rectangle by multiplying its side lengths

Property

The area of a rectangle can be found by multiplying its two side lengths (length and width). The formula is:

Area = length \times width

Examples

Section 2

Decomposing a Fraction into a Sum of Unit Fractions

Property

A fraction $\frac{a}{b}$ can be expressed as the sum of its unit fractions, $\frac{1}{b}$ , added 'a' times.
This can also be written as the product of the numerator 'a' and the unit fraction $\frac{1}{b}$ .

\frac{a}{b} = \underbrace{\frac{1}{b} + \frac{1}{b} + \dots + \frac{1}{b}}_{\text{a times}} = a \times \frac{1}{b}

Examples

Section 3

Calculate Total Area from a Fraction Model

Property

To find the total area from a model representing a whole number $W$ times a fraction $\frac{a}{b}$ , multiply the whole number by the numerator and keep the denominator.

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

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Calculate the area of a rectangle by multiplying its side lengths

Property

The area of a rectangle can be found by multiplying its two side lengths (length and width). The formula is:

Area = length \times width

Examples

Section 2

Decomposing a Fraction into a Sum of Unit Fractions

Property

\frac{a}{b} = \underbrace{\frac{1}{b} + \frac{1}{b} + \dots + \frac{1}{b}}_{\text{a times}} = a \times \frac{1}{b}

Examples

Section 3

Calculate Total Area from a Fraction Model

Property

To find the total area from a model representing a whole number $W$ times a fraction $\frac{a}{b}$ , multiply the whole number by the numerator and keep the denominator.

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

Examples

Overview

Lesson overview

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

Overview

Section 1

Calculate the area of a rectangle by multiplying its side lengths

Property

The area of a rectangle can be found by multiplying its two side lengths (length and width). The formula is:

Area = length \times width

Examples

Section 2

Decomposing a Fraction into a Sum of Unit Fractions

Property

\frac{a}{b} = \underbrace{\frac{1}{b} + \frac{1}{b} + \dots + \frac{1}{b}}_{\text{a times}} = a \times \frac{1}{b}

Examples

Section 3

Calculate Total Area from a Fraction Model

Property

To find the total area from a model representing a whole number $W$ times a fraction $\frac{a}{b}$ , multiply the whole number by the numerator and keep the denominator.

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