Lesson 4: Add Mixed Numbers with Unlike Denominators

Property

To add mixed numbers with unlike denominators, first find a common denominator and rewrite the fractions.
Then, add the whole numbers and add the newly rewritten fractions.

Examples

Property

When adding mixed numbers, first add the whole numbers and then add the fractions.
If the sum of the fractions is an improper fraction (greater than or equal to 1), convert it to a mixed number and add it to the sum of the whole numbers.

If $\frac{b+e}{d} \geq 1$, regroup.

Examples

• $2\frac{3}{4} + 1\frac{3}{4} = (2+1) + (\frac{3}{4} + \frac{3}{4}) = 3 + \frac{6}{4} = 3 + 1\frac{2}{4} = 4\frac{2}{4}$
• $5\frac{2}{3} + 2\frac{2}{3} = (5+2) + (\frac{2}{3} + \frac{2}{3}) = 7 + \frac{4}{3} = 7 + 1\frac{1}{3} = 8\frac{1}{3}$

Explanation

This skill builds on adding like units. You first combine the whole numbers and then the fractions separately. When the sum of the fractions is an improper fraction, you must regroup. To do this, you convert the improper fraction into a mixed number and then add this new whole number to your original sum of whole numbers.