Learn on PengiPengi Math (Grade 4)Chapter 6: Understanding Fractions

Lesson 2: Understanding and Generating Equivalent Fractions

In this Grade 4 Pengi Math lesson from Chapter 6, students learn to define and generate equivalent fractions using area models and number lines. They explore why a/b equals (n × a)/(n × b) through visual decomposition, and practice creating equivalent fractions by multiplying or dividing the numerator and denominator by the same common factor. By the end of the lesson, students can confidently identify and produce equivalent fractions using multiple strategies.

Section 1

Defining Equivalent Fractions

Property

Two fractions, ab\frac{a}{b} and cd\frac{c}{d}, are equivalent if they represent the same value, area, or length. This is only true if both fractions refer to the same size whole.

Examples

Section 2

Generating Equivalent Fractions by Multiplication

Property

To generate an equivalent fraction, multiply the numerator and the denominator by the same whole number (n>1n > 1).

ab=a×nb×n\frac{a}{b} = \frac{a \times n}{b \times n}

Examples

Section 3

Visualizing Equivalent Fractions with Area Models

Property

To find an equivalent fraction, multiply the numerator and the denominator by the same whole number, nn, where n>1n > 1.
This process corresponds to visually decomposing each part of an area model into nn smaller, equal parts.

ab=a×nb×n\frac{a}{b} = \frac{a \times n}{b \times n}

Examples

Section 4

Identifying Equivalent Fractions on a Number Line

Property

If two fractions ab\frac{a}{b} and cd\frac{c}{d} represent the same point on a number line, then they are equivalent: ab=cd\frac{a}{b} = \frac{c}{d}.

Examples

Book overview

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Chapter 6: Understanding Fractions

  1. Lesson 1

    Lesson 1: The Unit Fraction Concept

  2. Lesson 2Current

    Lesson 2: Understanding and Generating Equivalent Fractions

  3. Lesson 3

    Lesson 3: Strategies for Comparing Fractions

  4. Lesson 4

    Lesson 4: Decomposition, Mixed Numbers, and Improper Fractions

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Defining Equivalent Fractions

Property

Two fractions, ab\frac{a}{b} and cd\frac{c}{d}, are equivalent if they represent the same value, area, or length. This is only true if both fractions refer to the same size whole.

Examples

Section 2

Generating Equivalent Fractions by Multiplication

Property

To generate an equivalent fraction, multiply the numerator and the denominator by the same whole number (n>1n > 1).

ab=a×nb×n\frac{a}{b} = \frac{a \times n}{b \times n}

Examples

Section 3

Visualizing Equivalent Fractions with Area Models

Property

To find an equivalent fraction, multiply the numerator and the denominator by the same whole number, nn, where n>1n > 1.
This process corresponds to visually decomposing each part of an area model into nn smaller, equal parts.

ab=a×nb×n\frac{a}{b} = \frac{a \times n}{b \times n}

Examples

Section 4

Identifying Equivalent Fractions on a Number Line

Property

If two fractions ab\frac{a}{b} and cd\frac{c}{d} represent the same point on a number line, then they are equivalent: ab=cd\frac{a}{b} = \frac{c}{d}.

Examples

Book overview

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

Continue this chapter

Chapter 6: Understanding Fractions

  1. Lesson 1

    Lesson 1: The Unit Fraction Concept

  2. Lesson 2Current

    Lesson 2: Understanding and Generating Equivalent Fractions

  3. Lesson 3

    Lesson 3: Strategies for Comparing Fractions

  4. Lesson 4

    Lesson 4: Decomposition, Mixed Numbers, and Improper Fractions