Learn on PengienVision, Mathematics, Grade 5Chapter 9: Apply Understanding of Division to Divide Fractions

Lesson 5: Divide Unit Fractions by Non-Zero Whole Numbers

In this Grade 5 lesson from enVision Mathematics Chapter 9, students learn how to divide a unit fraction by a non-zero whole number, such as solving 1/2 ÷ 3 using area models and number lines. The lesson builds understanding of how dividing a unit fraction by a whole number produces a smaller quotient, connecting this idea to multiplying by a unit fraction. Students apply this skill through real-world problems involving equal sharing of fractional amounts.

Section 1

Model Fraction Division with Tape Diagrams

Property

A tape diagram models fraction division by visually representing the dividend and the divisor.

Whole Number ÷ Unit Fraction ( $a \div \frac{1}{b}$ ): Draw $a$ wholes and partition each whole into $b$ equal parts. The total number of parts is the quotient.
Unit Fraction ÷ Whole Number ( $\frac{1}{b} \div a$ ): Draw one whole, represent the fraction $\frac{1}{b}$ , and then partition that fractional part into $a$ equal pieces. The size of one new piece relative to the whole is the quotient.

Examples

Section 2

Using a Number Line to Divide a Unit Fraction

Property

To divide a unit fraction $\frac{1}{b}$ by a whole number $c$ , partition the segment from $0$ to $\frac{1}{b}$ on a number line into $c$ equal parts. The length of one new part is the quotient.

\frac{1}{b} \div c = \frac{1}{b \times c}

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Model Fraction Division with Tape Diagrams

Property

A tape diagram models fraction division by visually representing the dividend and the divisor.

Whole Number ÷ Unit Fraction ( $a \div \frac{1}{b}$ ): Draw $a$ wholes and partition each whole into $b$ equal parts. The total number of parts is the quotient.
Unit Fraction ÷ Whole Number ( $\frac{1}{b} \div a$ ): Draw one whole, represent the fraction $\frac{1}{b}$ , and then partition that fractional part into $a$ equal pieces. The size of one new piece relative to the whole is the quotient.

Examples

Section 2

Using a Number Line to Divide a Unit Fraction

Property

To divide a unit fraction $\frac{1}{b}$ by a whole number $c$ , partition the segment from $0$ to $\frac{1}{b}$ on a number line into $c$ equal parts. The length of one new part is the quotient.

\frac{1}{b} \div c = \frac{1}{b \times c}

Examples

Overview

Lesson overview

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

Overview

Section 1

Model Fraction Division with Tape Diagrams

Property

A tape diagram models fraction division by visually representing the dividend and the divisor.

Whole Number ÷ Unit Fraction ( $a \div \frac{1}{b}$ ): Draw $a$ wholes and partition each whole into $b$ equal parts. The total number of parts is the quotient.
Unit Fraction ÷ Whole Number ( $\frac{1}{b} \div a$ ): Draw one whole, represent the fraction $\frac{1}{b}$ , and then partition that fractional part into $a$ equal pieces. The size of one new piece relative to the whole is the quotient.

Examples

Section 2

Using a Number Line to Divide a Unit Fraction

Property

To divide a unit fraction $\frac{1}{b}$ by a whole number $c$ , partition the segment from $0$ to $\frac{1}{b}$ on a number line into $c$ equal parts. The length of one new part is the quotient.

\frac{1}{b} \div c = \frac{1}{b \times c}