Learn on PengiIllustrative Mathematics, Grade 5Chapter 3: Multiplying and Dividing Fractions

Lesson 2: Multiply Unit Fractions

In this Grade 5 Illustrative Mathematics lesson from Chapter 3: Multiplying and Dividing Fractions, students learn to multiply unit fractions by applying the concept that multiplying by a unit fraction is the same as finding a fractional part of a quantity. Students use visual models and equations to develop fluency with expressions such as 1/2 × 1/3, building foundational understanding of fraction multiplication.

Section 1

Writing Expressions from Area Models

Property

An area model divided into aa horizontal parts (rows) and bb vertical parts (columns) represents the multiplication of two unit fractions, 1a×1b\frac{1}{a} \times \frac{1}{b}. The product is 1a×b\frac{1}{a \times b}.

Examples

Section 2

Commutative Property with Unit Fractions

Property

The commutative property of multiplication states that changing the order of the fractions does not change the product. For any two unit fractions:

1a×1b=1b×1a\frac{1}{a} \times \frac{1}{b} = \frac{1}{b} \times \frac{1}{a}

Examples

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Writing Expressions from Area Models

Property

An area model divided into aa horizontal parts (rows) and bb vertical parts (columns) represents the multiplication of two unit fractions, 1a×1b\frac{1}{a} \times \frac{1}{b}. The product is 1a×b\frac{1}{a \times b}.

Examples

Section 2

Commutative Property with Unit Fractions

Property

The commutative property of multiplication states that changing the order of the fractions does not change the product. For any two unit fractions:

1a×1b=1b×1a\frac{1}{a} \times \frac{1}{b} = \frac{1}{b} \times \frac{1}{a}

Examples