Lesson 4.6: Add and Subtract Mixed Numbers

New Concept

This lesson shows how to add and subtract mixed numbers. You will learn to work with both common and different denominators, and master regrouping (borrowing) to solve any problem you encounter.

What’s next

Next, you'll explore interactive models for these operations. Then, test your understanding with guided practice cards and build confidence by solving challenge problems.

Property

Add mixed numbers with a common denominator.

Step 1. Add the whole numbers.

Step 2. Add the fractions.

Property

Subtract mixed numbers with common denominators.

Step 1. Rewrite the problem in vertical form.

Step 2. Compare the two fractions. If the top fraction is smaller than the bottom fraction, in the top mixed number, take one whole and add it to the fraction part, making a mixed number with an improper fraction.

Property

To add or subtract mixed numbers with different denominators, we first convert the fractions to equivalent fractions with the LCD. Then we can follow all the steps we used above for adding or subtracting fractions with like denominators.

Examples

• Add $3\frac{1}{3} + 4\frac{1}{2}$. The LCD of 3 and 2 is 6. The problem becomes $3\frac{2}{6} + 4\frac{4}{6}$. Add the wholes $3+4=7$ and fractions $\frac{2}{6}+\frac{4}{6}=\frac{6}{6}=1$. The sum is $7+1=8$.

• Subtract $8\frac{1}{4} - 3\frac{5}{6}$. The LCD of 4 and 6 is 12. This is $8\frac{3}{12} - 3\frac{10}{12}$. Borrow 1 from 8 to get $7\frac{15}{12}$. Now, $7\frac{15}{12} - 3\frac{10}{12} = 4\frac{5}{12}$.

Property

Subtract mixed numbers with common denominators as improper fractions.

Step 1. Rewrite the mixed numbers as improper fractions.

Step 2. Subtract the numerators.