Dividing Fractions

Use the "keep, change, flip" method to divide fractions

The "Keep, Change, Flip" Method

To divide fractions:

$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$

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

The reciprocal is the fraction flipped upside down:

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!

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

Calculate: $\frac{1}{2} \div \frac{1}{4}$

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Solution:

Keep, Change, Flip: $\frac{1}{2} \div \frac{1}{4} = \frac{1}{2} \times \frac{4}{1} = \frac{4}{2} = 2$

Answer: 2

Calculate: $\frac{3}{5} \div \frac{2}{3}$

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Solution:

Keep, Change, Flip: $\frac{3}{5} \div \frac{2}{3} = \frac{3}{5} \times \frac{3}{2}$

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

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

You have $\frac{3}{4}$ of a pizza. You want to divide it equally among 3 people. What fraction does each person get?

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Solution:

Divide: $\frac{3}{4} \div 3$

Turn 3 into a fraction: $\frac{3}{4} \div \frac{3}{1}$

Keep, Change, Flip: $\frac{3}{4} \times \frac{1}{3} = \frac{3}{12} = \frac{1}{4}$

Answer: Each person gets $\frac{1}{4}$ of the pizza

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