Sections:

# Dividing Fractions

In this section, we continue to learn about fractions. Our next step is to learn about Dividing fractions. How do we divide one fraction by another? In order to divide fractions, we must first learn about taking the reciprocal of a number. To find the reciprocal of a number, we swap the numerator and the denominator.
Find the Reciprocal of the following: $$\frac{2}{7}$$ -To find the reciprocal, we swap the numerator and denominator
-2 will become the denominator
-7 will become the numerator
Our reciprocal is: $$\frac{7}{2}$$ When we divide fractions, we convert the problem into the multiplication of the first fraction by the reciprocal of the second.
Dividing Fractions:
1. Simplify each fraction involved in the division
2. Leave the dividend or left fraction unchanged
3. Setup the multiplication of the dividend by the reciprocal of the divisor
4. Cross cancel and find the product
Example 1: Find each quotient $$\frac{3}{4}\div \frac{9}{2}$$ -Each fraction is simplified
-Multiply the dividend by the reciprocal of the divisor $$\frac{3}{4}\cdot \frac{2}{9}$$ $$\require{cancel}\frac{\cancel{3}}{\cancel{2}\cdot 2}\cdot \frac{\cancel{2}}{\cancel{3}\cdot 3}$$ Result: $$\frac{1}{6}$$ $$\frac{3}{4}\div \frac{9}{2}=\frac{1}{6}$$