Learn on PengienVision, Mathematics, Grade 5Chapter 8: Apply Understanding of Multiplication to Multiply Fractions

Lesson 4: Use Models to Multiply Two Fractions

In this Grade 5 lesson from enVision Mathematics Chapter 8, students learn how to multiply two fractions using area models, grids, and number lines, such as finding that one-third times one-fourth equals one-twelfth by identifying the overlap in a shaded grid. Students explore multiplying fractions with both unit fractions and non-unit fractions, applying the concept that multiplying two fractions produces a product smaller than either factor. Practice problems connect fraction multiplication to real-world contexts and build toward solving equations with unknown factors.

Section 1

Introduction: A Fraction of a Fraction

Property

Finding a fraction of another fraction means you are taking a part of an existing part. For example, taking one-half of a one-half piece results in a one-fourth piece of the original whole.

12 of 12=14\frac{1}{2} \text{ of } \frac{1}{2} = \frac{1}{4}

Section 2

Visual Models for Fraction Multiplication

Property

Use rectangular area models to visualize and calculate fraction multiplication.
Divide a rectangle into equal parts to represent each fraction, then find the overlapping region to determine the product.
This visual approach shows that multiplying fractions means finding a fractional part of a fractional part.

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Introduction: A Fraction of a Fraction

Property

Finding a fraction of another fraction means you are taking a part of an existing part. For example, taking one-half of a one-half piece results in a one-fourth piece of the original whole.

12 of 12=14\frac{1}{2} \text{ of } \frac{1}{2} = \frac{1}{4}

Section 2

Visual Models for Fraction Multiplication

Property

Use rectangular area models to visualize and calculate fraction multiplication.
Divide a rectangle into equal parts to represent each fraction, then find the overlapping region to determine the product.
This visual approach shows that multiplying fractions means finding a fractional part of a fractional part.

Examples