Multiplying Fractions

Learn to multiply fractions and whole numbers by fractions

Multiplying Two Fractions

Three simple steps:

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

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

Turn the whole number into a fraction (put it over 1):

Example: $5 \times \frac{2}{3}$

$5 \times \frac{2}{3} = \frac{5}{1} \times \frac{2}{3} = \frac{10}{3} = 3\frac{1}{3}$

Multiplying by a fraction means "taking a part of" something:

You can cross-cancel to make math easier:

$\frac{4}{5} \times \frac{5}{8} = \frac{4 \times \cancel{5}}{\cancel{5} \times 8} = \frac{4}{8} = \frac{1}{2}$

Calculate: $\frac{1}{3} \times \frac{2}{5}$

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Solution:

Multiply numerators and denominators: $\frac{1 \times 2}{3 \times 5} = \frac{2}{15}$

Already in simplest form.

Answer: $\frac{2}{15}$

What is $\frac{1}{2}$ of 18?

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Solution:

"Of" means multiply: $\frac{1}{2} \times 18 = \frac{1}{2} \times \frac{18}{1} = \frac{18}{2} = 9$

Answer: 9

A recipe needs $\frac{3}{4}$ cup of sugar. If you want to make $\frac{2}{3}$ of the recipe, how much sugar do you need?

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Solution:

Multiply the fractions: $\frac{2}{3} \times \frac{3}{4} = \frac{2 \times 3}{3 \times 4} = \frac{6}{12}$

Simplify (divide by 6): $\frac{6}{12} = \frac{1}{2}$

Answer: $\frac{1}{2}$ cup of sugar

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