Example: $\frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4} = \frac{10}{12} = \frac{5}{6}$

What is a Reciprocal?

The reciprocal is the fraction flipped upside down:

• Reciprocal of $\frac{3}{4}$ is $\frac{4}{3}$
• Reciprocal of $5 = \frac{5}{1}$ is $\frac{1}{5}$

Why Does This Work?

Dividing by a fraction is the same as multiplying by its reciprocal: $6 \div 2 = 3$ $6 \times \frac{1}{2} = 3$

Same idea with fractions!

Dividing by a Whole Number

Turn the whole number into a fraction first: $\frac{3}{4} \div 2 = \frac{3}{4} \div \frac{2}{1} = \frac{3}{4} \times \frac{1}{2} = \frac{3}{8}$

Multiply: $\frac{3 \times 3}{5 \times 2} = \frac{9}{10}$

Answer: $\frac{9}{10}$