Learn on PengienVision, Mathematics, Grade 4Chapter 9: Understand Addition and Subtraction of Fractions

Lesson 2: Decompose Fractions

Property.

Section 1

Representing Fraction Decomposition with Visual Models

Property

The decomposition of a fraction into a sum of unit fractions can be represented by three connected models: a visual tape diagram, a schematic number bond, and a symbolic addition sentence.
All three models represent the same core equation:

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

Examples

Section 2

Decomposing Mixed Numbers into Wholes and a Fraction Part

Property

A mixed number $A \frac{b}{c}$ is visually represented by $A$ wholes, where each whole is equivalent to $\frac{c}{c}$ , plus the fractional part $\frac{b}{c}$ .

Examples

Section 3

Decompose a Fraction into a Sum of Fractions

Property

A fraction $\frac{a}{b}$ can be decomposed into a sum of smaller fractions with the same denominator, such as $\frac{a}{b} = \frac{x}{b} + \frac{y}{b}$ , where $x + y = a$ .

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Representing Fraction Decomposition with Visual Models

Property

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

Examples

Section 2

Decomposing Mixed Numbers into Wholes and a Fraction Part

Property

A mixed number $A \frac{b}{c}$ is visually represented by $A$ wholes, where each whole is equivalent to $\frac{c}{c}$ , plus the fractional part $\frac{b}{c}$ .

Examples

Section 3

Decompose a Fraction into a Sum of Fractions

Property

A fraction $\frac{a}{b}$ can be decomposed into a sum of smaller fractions with the same denominator, such as $\frac{a}{b} = \frac{x}{b} + \frac{y}{b}$ , where $x + y = a$ .

Examples

Overview

Lesson overview

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

Overview

Section 1

Representing Fraction Decomposition with Visual Models

Property

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

Examples

Section 2

Decomposing Mixed Numbers into Wholes and a Fraction Part

Property

A mixed number $A \frac{b}{c}$ is visually represented by $A$ wholes, where each whole is equivalent to $\frac{c}{c}$ , plus the fractional part $\frac{b}{c}$ .

Examples

Section 3

Decompose a Fraction into a Sum of Fractions

Property

A fraction $\frac{a}{b}$ can be decomposed into a sum of smaller fractions with the same denominator, such as $\frac{a}{b} = \frac{x}{b} + \frac{y}{b}$ , where $x + y = a$ .