Adding Mixed Numbers

In this section, we learn about adding mixed numbers, subtracting mixed numbers, multiplying mixed numbers, and dividing mixed numbers. We will learn two different techniques and apply them to two different scenarios:

1. Working with the mixed numbers and fractions separately
2. Converting the mixed numbers into improper fractions

Adding Mixed Numbers:
It is generally faster to work with mixed numbers when it comes to adding mixed numbers or subtracting mixed numbers. For these problems, we add or subtract the fraction parts first, followed by the whole number parts.
Example 1: Find each sum $$3 \frac{1}{5}+ \hspace{.25em}2 \frac{2}{5}$$ • add the fractions first $$\frac{1}{5}+ \frac{2}{5}=\frac{3}{5}$$ • add the whole numbers: 3 + 2 = 5 $$3 \frac{1}{5}+ \hspace{.25em}2 \frac{2}{5}=5 \frac{3}{5}$$ Multiplying Mixed Numbers:
For our second technique, we will show that it is faster to convert the mixed numbers into improper fractions when we are multiplying or dividing. In this case, when we have finished we can convert the answer into a mixed number if required.
Example 1: Find each product $$1 \frac{2}{7}\cdot \hspace{.25em}4 \frac{4}{7}$$ • Convert each to an improper fraction $$1 \frac{2}{7}=\frac{9}{7}$$ $$4 \frac{4}{7}=\frac{32}{7}$$ • Multiply the improper fractions $$\frac{9}{7}\cdot \frac{32}{7}=\frac{288}{49}=5 \frac{43}{49}$$