Learn on PengiEureka Math, Grade 4Chapter 24: Fraction Addition and Subtraction

Lesson 5: Use visual models to add two fractions with related units using the denominators 2, 3, 4, 5, 6, 8, 10, and 12.

In this Grade 4 Eureka Math lesson from Chapter 24, students use visual models to add two fractions with related denominators, focusing on denominators 2, 3, 4, 5, 6, 8, 10, and 12 where one denominator is a factor of the other. Students build on their prior work with equivalent fractions to understand that units must be the same before adding, converting fractions to like units before finding sums. This lesson prepares students for adding decimals in later modules and for working with unrelated denominators in Grade 5.

Section 1

Add Fractions with Related Denominators Using Tape Diagrams

Property

To add fractions with related denominators (where one denominator is a multiple of the other), use a tape diagram to decompose the fraction with the larger units.
Partition its parts into smaller, equivalent units to match the denominator of the other fraction, creating like units for addition.

Examples

Section 2

Add Fractions with Related Denominators on a Number Line

Property

To add fractions on a number line, partition the line into the smaller unit (larger denominator) to create common units.
Model the first fraction with a jump from 0.
From that point, model the second fraction with another jump to find the sum.

Examples

Section 3

Adding Fractions with Related Denominators

Property

To add fractions with related denominators, such as ab+cd\frac{a}{b} + \frac{c}{d} where dd is a multiple of bb, find a number nn so that b×n=db \times n = d.
Then, convert ab\frac{a}{b} to an equivalent fraction and add:

ab+cd=a×nb×n+cd=(a×n)+cd\frac{a}{b} + \frac{c}{d} = \frac{a \times n}{b \times n} + \frac{c}{d} = \frac{(a \times n) + c}{d}

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Add Fractions with Related Denominators Using Tape Diagrams

Property

To add fractions with related denominators (where one denominator is a multiple of the other), use a tape diagram to decompose the fraction with the larger units.
Partition its parts into smaller, equivalent units to match the denominator of the other fraction, creating like units for addition.

Examples

Section 2

Add Fractions with Related Denominators on a Number Line

Property

To add fractions on a number line, partition the line into the smaller unit (larger denominator) to create common units.
Model the first fraction with a jump from 0.
From that point, model the second fraction with another jump to find the sum.

Examples

Section 3

Adding Fractions with Related Denominators

Property

To add fractions with related denominators, such as ab+cd\frac{a}{b} + \frac{c}{d} where dd is a multiple of bb, find a number nn so that b×n=db \times n = d.
Then, convert ab\frac{a}{b} to an equivalent fraction and add:

ab+cd=a×nb×n+cd=(a×n)+cd\frac{a}{b} + \frac{c}{d} = \frac{a \times n}{b \times n} + \frac{c}{d} = \frac{(a \times n) + c}{d}

Examples