Learn on PengiIllustrative Mathematics, Grade 5Chapter 6: Place Value Patterns and Decimal Operations

Lesson 8: Put It All Together: Add and Subtract Fractions

In this Grade 5 Illustrative Mathematics lesson from Chapter 6, students apply and consolidate their skills for adding and subtracting fractions, including fractions with unlike denominators. The lesson brings together key strategies from the chapter to solve multi-step problems involving fraction addition and subtraction. Students practice selecting efficient methods and checking the reasonableness of their answers in real-world and mathematical contexts.

Section 1

The 'Like Units' Rule for Adding and Subtracting Fractions

Property

To add numbers, they must represent the same kind of unit.
For fractions, this means they must have a common denominator.
We can only add fractions once they are in the form $\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}$ .
If denominators are different, we must first find equivalent fractions that share a common denominator.

Examples

Section 2

Visualizing Equivalent Fractions with Area Models

Property

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

\frac{a}{b} = \frac{a \times n}{b \times n}

Examples

Section 3

Finding a Common Denominator When One is a Multiple of the Other

Property

If one denominator, $d_2$ , is a multiple of another denominator, $d_1$ , then the larger denominator, $d_2$ , can be used as a common denominator.

Examples

Section 4

Step 1: Find the Lowest Common Denominator (LCD)

Property

The lowest common denominator (LCD) for two fractions is the smallest number that both denominators divide into evenly.
Finding the LCD is the same as finding the lowest common multiple (LCM) of their denominators.

To find the LCD, you can list multiples of the larger number until you find one that is also a multiple of the smaller number.

Examples

For $\frac{1}{6}$ and $\frac{3}{8}$ , we list multiples of 8: 8, 16, 24. Since 6 divides into 24, the LCD is 24.

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

The 'Like Units' Rule for Adding and Subtracting Fractions

Property

Examples

Section 2

Visualizing Equivalent Fractions with Area Models

Property

\frac{a}{b} = \frac{a \times n}{b \times n}

Examples

Section 3

Finding a Common Denominator When One is a Multiple of the Other

Property

If one denominator, $d_2$ , is a multiple of another denominator, $d_1$ , then the larger denominator, $d_2$ , can be used as a common denominator.

Examples

Section 4

Step 1: Find the Lowest Common Denominator (LCD)

Property

To find the LCD, you can list multiples of the larger number until you find one that is also a multiple of the smaller number.

Examples

For $\frac{1}{6}$ and $\frac{3}{8}$ , we list multiples of 8: 8, 16, 24. Since 6 divides into 24, the LCD is 24.

Overview

Lesson overview

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

Overview

Section 1

The 'Like Units' Rule for Adding and Subtracting Fractions

Property

Examples

Section 2

Visualizing Equivalent Fractions with Area Models

Property

\frac{a}{b} = \frac{a \times n}{b \times n}

Examples

Section 3

Finding a Common Denominator When One is a Multiple of the Other

Property

If one denominator, $d_2$ , is a multiple of another denominator, $d_1$ , then the larger denominator, $d_2$ , can be used as a common denominator.

Examples

Section 4

Step 1: Find the Lowest Common Denominator (LCD)

Property

To find the LCD, you can list multiples of the larger number until you find one that is also a multiple of the smaller number.

Examples

For $\frac{1}{6}$ and $\frac{3}{8}$ , we list multiples of 8: 8, 16, 24. Since 6 divides into 24, the LCD is 24.