Lesson 7: Use Models to Add Mixed Numbers

Property

To add mixed numbers like $W_1 \frac{a}{b}$ and $W_2 \frac{c}{d}$, add the whole numbers and the fractions separately. Find a common denominator to add the fractions:

Examples

• To solve $1 \frac{1}{2} + 2 \frac{1}{3}$ using models, you would combine one whole and a half with two wholes and a third. First, add the whole numbers: $1 + 2 = 3$. Then, add the fractions by finding a common denominator: $\frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6}$. The final sum is $3 \frac{5}{6}$.
• To solve $2 \frac{3}{4} + 1 \frac{1}{2}$, you would combine two wholes and three-fourths with one whole and a half. Add the whole numbers: $2 + 1 = 3$. Add the fractions: $\frac{3}{4} + \frac{1}{2} = \frac{3}{4} + \frac{2}{4} = \frac{5}{4}$. Since $\frac{5}{4}$ is an improper fraction, regroup it as $1 \frac{1}{4}$. The final sum is $3 + 1 \frac{1}{4} = 4 \frac{1}{4}$.

Explanation

When adding mixed numbers with unlike denominators, you can use models to visualize the process. First, combine the whole number parts. Then, focus on the fractional parts. To add fractions with different denominators, you must find a common denominator before you can combine them. If the resulting fraction is improper, regroup it into a whole number and a fraction before finding the final sum.