Lesson 9: Use Models to Subtract Mixed Numbers

Property

When subtracting mixed numbers like $A\frac{b}{c} - D\frac{e}{f}$ where the fractional part of the first number is smaller than the second ($\frac{b}{c} < \frac{e}{f}$), you must regroup. After finding a common denominator, rename one whole from the first number as a fraction and add it to its fractional part.

Examples

• To solve $3\frac{1}{4} - 1\frac{1}{2}$, first find a common denominator: $3\frac{1}{4} - 1\frac{2}{4}$. Since $\frac{1}{4} < \frac{2}{4}$, regroup $3\frac{1}{4}$ into $2\frac{5}{4}$. The model changes from 3 wholes and 1 quarter to 2 wholes and 5 quarters. Then, subtract $1\frac{2}{4}$ to get $1\frac{3}{4}$.
• To solve $4\frac{1}{3} - 2\frac{5}{6}$, find a common denominator: $4\frac{2}{6} - 2\frac{5}{6}$. Since $\frac{2}{6} < \frac{5}{6}$, regroup $4\frac{2}{6}$ into $3\frac{8}{6}$. The model shows 4 wholes and 2 sixths becoming 3 wholes and 8 sixths. Subtracting $2\frac{5}{6}$ leaves $1\frac{3}{6}$, which simplifies to $1\frac{1}{2}$.

Explanation

This skill involves using visual models, like fraction bars or circles, to subtract mixed numbers with unlike denominators. When the fraction you are subtracting is larger than the fraction you have, you need to regroup. This is similar to borrowing in whole number subtraction. To do this, you "break apart" one of the whole numbers into its fractional equivalent and add it to the existing fraction before subtracting.