Lesson 8: Add Mixed Numbers

Property

To convert a mixed number to an improper fraction:

1. Multiply the whole number by the denominator.
2. Add the numerator to the product found in Step 1.
3. Write the final sum over the original denominator.

Examples

• To convert $3 \frac{1}{4}$: First, multiply $3 \times 4 = 12$. Then, add the numerator, $12 + 1 = 13$. The improper fraction is $\frac{13}{4}$.
• To convert $5 \frac{2}{3}$: First, multiply $5 \times 3 = 15$. Then, add the numerator, $15 + 2 = 17$. The improper fraction is $\frac{17}{3}$.
• To convert $7 \frac{3}{5}$: First, multiply $7 \times 5 = 35$. Then, add the numerator, $35 + 3 = 38$. The improper fraction is $\frac{38}{5}$.

Explanation

To change $2 \frac{1}{4}$ into just fourths, you break down the wholes. Two wholes are eight-fourths ($2 \times 4$). Add the extra one-fourth, and you have nine-fourths in total, which is written as $\frac{9}{4}$.

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.

Property

To add mixed numbers by converting to improper fractions, use the following process:

Examples