Learn on PengiBig Ideas Math, Course 2Chapter 2: Rational Numbers

Lesson 3: Subtracting Rational Numbers

In this Grade 7 lesson from Big Ideas Math Course 2, students learn to subtract rational numbers — including fractions, mixed numbers, and decimals — by applying the same sign rules used for subtracting integers, such as adding the opposite. Activities use number lines to visualize differences and explore how absolute value relates to distance between two rational numbers. Students also apply subtraction of rational numbers to real-life financial literacy problems involving positive and negative decimal amounts.

Section 1

Subtract Fractions with Common Denominators

Property

If aa, bb, and cc are numbers where c≠0c \neq 0, then

ac−bc=a−bc\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}

To subtract fractions with the same denominator, subtract the numerators and place the result over the common denominator.

Examples

Section 2

Procedure: Subtracting Fractions with Unlike Denominators

Property

To subtract fractions with different denominators, first find the least common denominator (LCD). The LCD is the least common multiple (LCM) of the denominators.
Then, convert each fraction into an equivalent fraction with the LCD.
Finally, subtract the numerators and place the result over the common denominator.

Examples

Section 3

Subtract Decimal Numbers

Property

How to subtract decimals:
Step 1. Write the numbers vertically so the decimal points line up.
Step 2. Use zeros as place holders, as needed.
Step 3. Subtract the numbers as if they were whole numbers. Then place the decimal in the answer under the decimal points in the given numbers.

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Subtract Fractions with Common Denominators

Property

If aa, bb, and cc are numbers where c≠0c \neq 0, then

ac−bc=a−bc\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}

To subtract fractions with the same denominator, subtract the numerators and place the result over the common denominator.

Examples

Section 2

Procedure: Subtracting Fractions with Unlike Denominators

Property

To subtract fractions with different denominators, first find the least common denominator (LCD). The LCD is the least common multiple (LCM) of the denominators.
Then, convert each fraction into an equivalent fraction with the LCD.
Finally, subtract the numerators and place the result over the common denominator.

Examples

Section 3

Subtract Decimal Numbers

Property

How to subtract decimals:
Step 1. Write the numbers vertically so the decimal points line up.
Step 2. Use zeros as place holders, as needed.
Step 3. Subtract the numbers as if they were whole numbers. Then place the decimal in the answer under the decimal points in the given numbers.

Examples