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

Lesson 6: Subtract Fractions: Multiple Strategies

In this Grade 5 lesson from Illustrative Mathematics Chapter 6, students learn how to find common denominators for fractions with unlike denominators, including cases where multiplying the two denominators gives a valid common denominator. Students practice adding and subtracting fractions such as three-fourths plus seven-eighths and three-fourths minus two-fifths by converting to equivalent fractions with a shared denominator. The lesson addresses standard 5.NF.A.1 and encourages students to choose the common denominator that makes the most sense for each problem.

Section 1

Model Fraction Subtraction

Property

Subtracting fractions with common denominators is like adding fractions.

Examples

To model $\frac{6}{8} - \frac{1}{8}$ , start with six $\frac{1}{8}$ pieces and remove one. You will have five $\frac{1}{8}$ pieces left, so the answer is $\frac{5}{8}$ .
Imagine you have $\frac{4}{5}$ of a cup of juice. If you drink $\frac{2}{5}$ of a cup, you have $\frac{4-2}{5} = \frac{2}{5}$ of a cup remaining.
Using fraction circles for $\frac{7}{8} - \frac{3}{8}$ , start with seven $\frac{1}{8}$ pieces. Take away three $\frac{1}{8}$ pieces. You are left with four $\frac{1}{8}$ pieces, or $\frac{4}{8}$ .

Explanation

Modeling subtraction shows you are starting with a certain number of equal-sized pieces (the first numerator) and removing some of them (the second numerator). The result is the number of pieces that are left.

Section 2

Subtracting Fractions from Mixed Numbers

Property

To subtract a fraction from a mixed number with the same denominator, first convert the mixed number into an improper fraction.
Then, subtract the numerators.

A \frac{b}{c} - \frac{d}{c} = \frac{(A \times c) + b}{c} - \frac{d}{c} = \frac{((A \times c) + b) - d}{c}

Examples

Section 3

Procedure: Subtracting Mixed Numbers with Regrouping

Property

To subtract mixed numbers when the top fraction is smaller than the bottom fraction:

Regroup: Take one from the whole number part of the first mixed number. Add that one to its fraction part by converting it to a fraction with the common denominator (e.g., $1 = \frac{n}{n}$ ).
Subtract Fractions: Subtract the fraction parts.
Subtract Whole Numbers: Subtract the whole number parts.
Simplify: Write the final answer in simplest form.

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Model Fraction Subtraction

Property

Subtracting fractions with common denominators is like adding fractions.

Examples

To model $\frac{6}{8} - \frac{1}{8}$ , start with six $\frac{1}{8}$ pieces and remove one. You will have five $\frac{1}{8}$ pieces left, so the answer is $\frac{5}{8}$ .
Imagine you have $\frac{4}{5}$ of a cup of juice. If you drink $\frac{2}{5}$ of a cup, you have $\frac{4-2}{5} = \frac{2}{5}$ of a cup remaining.
Using fraction circles for $\frac{7}{8} - \frac{3}{8}$ , start with seven $\frac{1}{8}$ pieces. Take away three $\frac{1}{8}$ pieces. You are left with four $\frac{1}{8}$ pieces, or $\frac{4}{8}$ .

Explanation

Section 2

Subtracting Fractions from Mixed Numbers

Property

To subtract a fraction from a mixed number with the same denominator, first convert the mixed number into an improper fraction.
Then, subtract the numerators.

A \frac{b}{c} - \frac{d}{c} = \frac{(A \times c) + b}{c} - \frac{d}{c} = \frac{((A \times c) + b) - d}{c}

Examples

Section 3

Procedure: Subtracting Mixed Numbers with Regrouping

Property

To subtract mixed numbers when the top fraction is smaller than the bottom fraction:

Regroup: Take one from the whole number part of the first mixed number. Add that one to its fraction part by converting it to a fraction with the common denominator (e.g., $1 = \frac{n}{n}$ ).
Subtract Fractions: Subtract the fraction parts.
Subtract Whole Numbers: Subtract the whole number parts.
Simplify: Write the final answer in simplest form.

Examples

Overview

Lesson overview

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

Overview

Section 1

Model Fraction Subtraction

Property

Subtracting fractions with common denominators is like adding fractions.

Examples

To model $\frac{6}{8} - \frac{1}{8}$ , start with six $\frac{1}{8}$ pieces and remove one. You will have five $\frac{1}{8}$ pieces left, so the answer is $\frac{5}{8}$ .
Imagine you have $\frac{4}{5}$ of a cup of juice. If you drink $\frac{2}{5}$ of a cup, you have $\frac{4-2}{5} = \frac{2}{5}$ of a cup remaining.
Using fraction circles for $\frac{7}{8} - \frac{3}{8}$ , start with seven $\frac{1}{8}$ pieces. Take away three $\frac{1}{8}$ pieces. You are left with four $\frac{1}{8}$ pieces, or $\frac{4}{8}$ .

Explanation

Section 2

Subtracting Fractions from Mixed Numbers

Property

To subtract a fraction from a mixed number with the same denominator, first convert the mixed number into an improper fraction.
Then, subtract the numerators.

A \frac{b}{c} - \frac{d}{c} = \frac{(A \times c) + b}{c} - \frac{d}{c} = \frac{((A \times c) + b) - d}{c}

Examples

Section 3

Procedure: Subtracting Mixed Numbers with Regrouping

Property

To subtract mixed numbers when the top fraction is smaller than the bottom fraction:

Regroup: Take one from the whole number part of the first mixed number. Add that one to its fraction part by converting it to a fraction with the common denominator (e.g., $1 = \frac{n}{n}$ ).
Subtract Fractions: Subtract the fraction parts.
Subtract Whole Numbers: Subtract the whole number parts.
Simplify: Write the final answer in simplest form.