Learn on PengiPengi Math (Grade 4)Chapter 7: Fraction Operations

Lesson 1: Addition and Subtraction of Fractions with Like Denominators

In this Grade 4 lesson from Pengi Math Chapter 7, students learn to add and subtract fractions with like denominators by understanding joining and separating parts of a whole. Using tape diagrams, number bonds, area models, and number lines, they decompose fractions into unit fractions and apply these skills to solve word problems. An extension activity introduces adding fractions with related denominators, such as halves and fourths, by identifying common units.

Section 1

Rule for Adding Fractions with Like Denominators

Property

To add fractions with like denominators, add the numerators and keep the denominator the same.
This can be represented on a number line as combining lengths from a starting point.

ac+bc=a+bc\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}

Examples

Section 2

Rule for Subtracting Fractions with Like Denominators

Property

To subtract fractions with the same denominator, subtract the numerators and keep the denominator the same.

acbc=abc\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}

Examples

  • 5828=528=38\frac{5}{8} - \frac{2}{8} = \frac{5-2}{8} = \frac{3}{8}
  • 1112412=11412=712\frac{11}{12} - \frac{4}{12} = \frac{11-4}{12} = \frac{7}{12}

Explanation

When subtracting fractions that have the same denominator, you only need to perform the subtraction on the numerators. The denominator represents the size of the fractional parts, which remains constant during the operation. This rule is the counterpart to adding fractions with like denominators, where you simply add the numerators.

Section 3

Model Subtracting a Fraction from One on a Number Line

Property

To subtract a fraction from one whole, first rename 1 as a fraction with the same denominator as the fraction being subtracted.
Then, subtract the numerators.

1ab=bbab=bab1 - \frac{a}{b} = \frac{b}{b} - \frac{a}{b} = \frac{b-a}{b}

Examples

Section 4

Solving Word Problems with Like Fractions

Property

To solve a word problem involving fractions, first identify the given fractions and determine the necessary operation.
Use keywords in the problem to decide whether to add or subtract.

Examples

Book overview

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

Continue this chapter

Chapter 7: Fraction Operations

  1. Lesson 1Current

    Lesson 1: Addition and Subtraction of Fractions with Like Denominators

  2. Lesson 2

    Lesson 2: Adding Mixed Numbers

  3. Lesson 3

    Lesson 3: Subtracting Mixed Numbers

  4. Lesson 4

    Lesson 4: Multiplying Fractions by Whole Numbers and Applications

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Rule for Adding Fractions with Like Denominators

Property

To add fractions with like denominators, add the numerators and keep the denominator the same.
This can be represented on a number line as combining lengths from a starting point.

ac+bc=a+bc\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}

Examples

Section 2

Rule for Subtracting Fractions with Like Denominators

Property

To subtract fractions with the same denominator, subtract the numerators and keep the denominator the same.

acbc=abc\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}

Examples

  • 5828=528=38\frac{5}{8} - \frac{2}{8} = \frac{5-2}{8} = \frac{3}{8}
  • 1112412=11412=712\frac{11}{12} - \frac{4}{12} = \frac{11-4}{12} = \frac{7}{12}

Explanation

When subtracting fractions that have the same denominator, you only need to perform the subtraction on the numerators. The denominator represents the size of the fractional parts, which remains constant during the operation. This rule is the counterpart to adding fractions with like denominators, where you simply add the numerators.

Section 3

Model Subtracting a Fraction from One on a Number Line

Property

To subtract a fraction from one whole, first rename 1 as a fraction with the same denominator as the fraction being subtracted.
Then, subtract the numerators.

1ab=bbab=bab1 - \frac{a}{b} = \frac{b}{b} - \frac{a}{b} = \frac{b-a}{b}

Examples

Section 4

Solving Word Problems with Like Fractions

Property

To solve a word problem involving fractions, first identify the given fractions and determine the necessary operation.
Use keywords in the problem to decide whether to add or subtract.

Examples

Book overview

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

Continue this chapter

Chapter 7: Fraction Operations

  1. Lesson 1Current

    Lesson 1: Addition and Subtraction of Fractions with Like Denominators

  2. Lesson 2

    Lesson 2: Adding Mixed Numbers

  3. Lesson 3

    Lesson 3: Subtracting Mixed Numbers

  4. Lesson 4

    Lesson 4: Multiplying Fractions by Whole Numbers and Applications