Dividing Fractions

When you need to divide a fraction by a whole number, first convert that whole number into a fraction with a denominator of 1. Then, multiply by the reciprocal (flip the second fraction upside down).

For example: $\frac{2}{3} \div 4 = \frac{2}{3} \div \frac{4}{1} = \frac{2}{3} \times \frac{1}{4} = \frac{2}{12} = \frac{1}{6}$

A reciprocal is what you get when you switch the numerator and denominator in a fraction. The reciprocal of $\frac{3}{4}$ is $\frac{4}{3}$. When you multiply a fraction by its reciprocal, you always get 1!

Dividing a whole number by a fraction works the same way. For example: $5 \div \frac{2}{3} = 5 \times \frac{3}{2} = \frac{15}{2} = 7.5$

🔍 Remember This! The key to dividing with fractions is "keep, change, flip" - keep the first number, change division to multiplication, and flip the second number!

Another example: $8 \div \frac{5}{6} = 8 \times \frac{6}{5} = \frac{48}{5} = 9.6$