Multiplying and Dividing Fractions

Master multiplication and division with fractions and mixed numbers

Multiplying and Dividing Fractions

Multiplying Fractions

Steps:

Multiply numerators
Multiply denominators
Simplify

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

Example: $\frac{2}{3} \times \frac{4}{5} = \frac{8}{15}$

With Mixed Numbers

Convert to improper fractions first!

$2\frac{1}{3} \times 1\frac{1}{2} = \frac{7}{3} \times \frac{3}{2} = \frac{21}{6} = \frac{7}{2} = 3\frac{1}{2}$

Dividing Fractions

Rule: Multiply by the reciprocal (flip the second fraction)

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

Example: $\frac{3}{4} \div \frac{2}{5} = \frac{3}{4} \times \frac{5}{2} = \frac{15}{8} = 1\frac{7}{8}$

Reciprocal

The reciprocal of a fraction is obtained by flipping it:

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

📚 Practice Problems

1Problem 1easy

❓ Question:

Calculate: $\frac{3}{5} \times \frac{2}{7}$

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Solution:

Multiply numerators and denominators: $\frac{3 \times 2}{5 \times 7} = \frac{6}{35}$

Already in simplest form.

Answer: $\frac{6}{35}$

2Problem 2medium

❓ Question:

Calculate: $\frac{5}{6} \div \frac{2}{3}$

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Solution:

Multiply by the reciprocal: $\frac{5}{6} \div \frac{2}{3} = \frac{5}{6} \times \frac{3}{2}$

$= \frac{5 \times 3}{6 \times 2} = \frac{15}{12}$

Simplify (divide by 3): $\frac{15}{12} = \frac{5}{4} = 1\frac{1}{4}$

Answer: $1\frac{1}{4}$

3Problem 3hard

❓ Question:

A recipe calls for $2\frac{2}{3}$ cups of flour. If you want to make $\frac{3}{4}$ of the recipe, how much flour do you need?

💡 Show Solution

Solution:

Multiply: $2\frac{2}{3} \times \frac{3}{4}$

Convert to improper fraction: $2\frac{2}{3} = \frac{8}{3}$

Multiply: $\frac{8}{3} \times \frac{3}{4} = \frac{24}{12} = 2$

Answer: 2 cups of flour

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