Learn on PengiYoshiwara Core MathChapter 4: Calculation

Lesson 4.2: Multiplying and Dividing Fractions

In this Grade 8 lesson from Yoshiwara Core Math, students learn how to multiply and divide fractions by multiplying numerators together and denominators together, and by applying the concept of taking a fractional part of a quantity or another fraction. The lesson covers multiplying by unit fractions, multiplying by non-unit fractions such as two-thirds, and interpreting division by a fraction using visual models like rectangles and pie diagrams. Students practice applying these skills to real-world problems involving mixed numbers and improper fractions.

Section 1

📘 Multiplying and Dividing Fractions

New Concept

This lesson demystifies multiplying and dividing fractions. You'll learn that multiplication is like taking a 'fraction of' a number, while division asks 'how many fractional parts fit inside another?' We'll master the rules for both operations.

What’s next

Next, we'll explore these concepts through worked examples and interactive practice cards to build your skills.

Section 2

Taking a Fractional Part

Property

To take $\frac{1}{3}$ of something, we can multiply by $\frac{1}{3}$ . The same idea works if we want to take $\frac{1}{4}$ of something, or $\frac{1}{5}$ of something, or so on.

To multiply two fractions together:

Multiply the numerators together.
Multiply the denominators together.

\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}

Examples

How many feet are in $\frac{1}{3}$ of a yard? Since there are 3 feet in 1 yard, we calculate $\frac{1}{3} \times \frac{3}{1} = \frac{3}{3} = 1$ foot.

Section 3

Multiplying by a Fraction

Property

Taking $\frac{2}{3}$ of something means to divide the quantity into 3 equal parts, and then take 2 of them. This is the same as multiplying by $\frac{2}{3}$ .

To multiply two fractions:

Multiply the numerators together.
Multiply the denominators together.

\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}

Examples

What is $\frac{3}{4}$ of 24? We can calculate this by multiplying: $\frac{3}{4} \times \frac{24}{1} = \frac{3 \times 24}{4 \times 1} = \frac{72}{4} = 18$ .

Section 4

Dividing by a Fraction

Property

To divide a number by a fraction, multiply the number by the reciprocal of the fraction.

The reciprocal of a fraction is found by interchanging the numerator and the denominator. The reciprocal of $\frac{a}{b}$ is $\frac{b}{a}$ .

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

Examples

How many $\frac{1}{4}$ -cup scoops of sugar are in a 2-cup bag? This is $2 \div \frac{1}{4}$ . We calculate $2 \times \frac{4}{1} = 8$ . There are 8 scoops.

Section 5

More Dividing by Fractions

Property

To divide a number by a fraction, multiply the number by the reciprocal of the fraction. For example, to divide by $\frac{2}{3}$ , you multiply by its reciprocal, $\frac{3}{2}$ .

First, convert any mixed numbers to improper fractions. Then, apply the rule:

a \div \frac{b}{c} = a \times \frac{c}{b}

Examples

How many $\frac{3}{4}$ -foot lengths of rope can be cut from a 6-foot rope? We calculate $6 \div \frac{3}{4} = 6 \times \frac{4}{3} = \frac{24}{3} = 8$ lengths.

Book overview

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Chapter 4: Calculation

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Lesson 1
Lesson 4.1: Adding and Subtracting Fractions
Learn Practice
Lesson 2Current
Lesson 4.2: Multiplying and Dividing Fractions
Learn Practice
Lesson 3
Lesson 4.3: Roots and Radicals
Learn Practice
Lesson 4
Lesson 4.4: Negative Numbers
Learn Practice
Lesson 5
Lesson 4.5: Order of Operations
Learn Practice

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

📘 Multiplying and Dividing Fractions

New Concept

What’s next

Next, we'll explore these concepts through worked examples and interactive practice cards to build your skills.

Section 2

Taking a Fractional Part

Property

To take $\frac{1}{3}$ of something, we can multiply by $\frac{1}{3}$ . The same idea works if we want to take $\frac{1}{4}$ of something, or $\frac{1}{5}$ of something, or so on.

To multiply two fractions together:

Multiply the numerators together.
Multiply the denominators together.

\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}

Examples

How many feet are in $\frac{1}{3}$ of a yard? Since there are 3 feet in 1 yard, we calculate $\frac{1}{3} \times \frac{3}{1} = \frac{3}{3} = 1$ foot.

Section 3

Multiplying by a Fraction

Property

Taking $\frac{2}{3}$ of something means to divide the quantity into 3 equal parts, and then take 2 of them. This is the same as multiplying by $\frac{2}{3}$ .

To multiply two fractions:

Multiply the numerators together.
Multiply the denominators together.

\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}

Examples

What is $\frac{3}{4}$ of 24? We can calculate this by multiplying: $\frac{3}{4} \times \frac{24}{1} = \frac{3 \times 24}{4 \times 1} = \frac{72}{4} = 18$ .

Section 4

Dividing by a Fraction

Property

To divide a number by a fraction, multiply the number by the reciprocal of the fraction.

The reciprocal of a fraction is found by interchanging the numerator and the denominator. The reciprocal of $\frac{a}{b}$ is $\frac{b}{a}$ .

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

Examples

How many $\frac{1}{4}$ -cup scoops of sugar are in a 2-cup bag? This is $2 \div \frac{1}{4}$ . We calculate $2 \times \frac{4}{1} = 8$ . There are 8 scoops.

Section 5

More Dividing by Fractions

Property

To divide a number by a fraction, multiply the number by the reciprocal of the fraction. For example, to divide by $\frac{2}{3}$ , you multiply by its reciprocal, $\frac{3}{2}$ .

First, convert any mixed numbers to improper fractions. Then, apply the rule:

a \div \frac{b}{c} = a \times \frac{c}{b}

Examples

How many $\frac{3}{4}$ -foot lengths of rope can be cut from a 6-foot rope? We calculate $6 \div \frac{3}{4} = 6 \times \frac{4}{3} = \frac{24}{3} = 8$ lengths.

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 4: Calculation

Back to Yoshiwara Core Math

Lesson 1
Lesson 4.1: Adding and Subtracting Fractions
Learn Practice
Lesson 2Current
Lesson 4.2: Multiplying and Dividing Fractions
Learn Practice
Lesson 3
Lesson 4.3: Roots and Radicals
Learn Practice
Lesson 4
Lesson 4.4: Negative Numbers
Learn Practice
Lesson 5
Lesson 4.5: Order of Operations
Learn Practice

Overview

Lesson overview

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

Overview

Section 1

📘 Multiplying and Dividing Fractions

New Concept

What’s next

Next, we'll explore these concepts through worked examples and interactive practice cards to build your skills.

Section 2

Taking a Fractional Part

Property

To take $\frac{1}{3}$ of something, we can multiply by $\frac{1}{3}$ . The same idea works if we want to take $\frac{1}{4}$ of something, or $\frac{1}{5}$ of something, or so on.

To multiply two fractions together:

Multiply the numerators together.
Multiply the denominators together.

\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}

Examples

How many feet are in $\frac{1}{3}$ of a yard? Since there are 3 feet in 1 yard, we calculate $\frac{1}{3} \times \frac{3}{1} = \frac{3}{3} = 1$ foot.

Section 3

Multiplying by a Fraction

Property

Taking $\frac{2}{3}$ of something means to divide the quantity into 3 equal parts, and then take 2 of them. This is the same as multiplying by $\frac{2}{3}$ .

To multiply two fractions:

Multiply the numerators together.
Multiply the denominators together.

\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}

Examples

What is $\frac{3}{4}$ of 24? We can calculate this by multiplying: $\frac{3}{4} \times \frac{24}{1} = \frac{3 \times 24}{4 \times 1} = \frac{72}{4} = 18$ .

Section 4

Dividing by a Fraction

Property

To divide a number by a fraction, multiply the number by the reciprocal of the fraction.

The reciprocal of a fraction is found by interchanging the numerator and the denominator. The reciprocal of $\frac{a}{b}$ is $\frac{b}{a}$ .

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

Examples

How many $\frac{1}{4}$ -cup scoops of sugar are in a 2-cup bag? This is $2 \div \frac{1}{4}$ . We calculate $2 \times \frac{4}{1} = 8$ . There are 8 scoops.

Section 5

More Dividing by Fractions

Property

To divide a number by a fraction, multiply the number by the reciprocal of the fraction. For example, to divide by $\frac{2}{3}$ , you multiply by its reciprocal, $\frac{3}{2}$ .

First, convert any mixed numbers to improper fractions. Then, apply the rule:

a \div \frac{b}{c} = a \times \frac{c}{b}

Examples

How many $\frac{3}{4}$ -foot lengths of rope can be cut from a 6-foot rope? We calculate $6 \div \frac{3}{4} = 6 \times \frac{4}{3} = \frac{24}{3} = 8$ lengths.

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 4: Calculation

Back to Yoshiwara Core Math

Lesson 1
Lesson 4.1: Adding and Subtracting Fractions
Learn Practice
Lesson 2Current
Lesson 4.2: Multiplying and Dividing Fractions
Learn Practice
Lesson 3
Lesson 4.3: Roots and Radicals
Learn Practice
Lesson 4
Lesson 4.4: Negative Numbers
Learn Practice
Lesson 5
Lesson 4.5: Order of Operations
Learn Practice

Lesson 4.2: Multiplying and Dividing Fractions

New Concept

What’s next

Property

Examples

Property

Examples

Property

Examples

Property

Examples

Chapter 4: Calculation

Lesson 4.1: Adding and Subtracting Fractions

Lesson 4.2: Multiplying and Dividing Fractions

Lesson 4.3: Roots and Radicals

Lesson 4.4: Negative Numbers

Lesson 4.5: Order of Operations

Lesson overview

New Concept

What’s next

Property

Examples

Property

Examples

Property

Examples

Property

Examples

Chapter 4: Calculation

Lesson 4.1: Adding and Subtracting Fractions

Lesson 4.2: Multiplying and Dividing Fractions

Lesson 4.3: Roots and Radicals

Lesson 4.4: Negative Numbers

Lesson 4.5: Order of Operations

Lesson 4.1: Adding and Subtracting Fractions

Lesson 4.2: Multiplying and Dividing Fractions

Lesson 4.3: Roots and Radicals

Lesson 4.4: Negative Numbers

Lesson 4.5: Order of Operations