Lesson 6: Subtract Fractions: Multiple Strategies

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.

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.

Examples

Property

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

1. 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., $1 = \frac{n}{n}$).
2. Subtract Fractions: Subtract the fraction parts.
3. Subtract Whole Numbers: Subtract the whole number parts.
4. Simplify: Write the final answer in simplest form.

Examples