How to multiply fractions - ACT Math

Card 0 of 4

Question

Simplfiy the following expression;

$\frac{2}{3}\times\frac{6}{8}\times\frac{4}{12}$

Answer

Multiply the numerators 2 x 6 x 4 = 48. Then multiply the denominators 3 x 8 x 12 = 288. The answer is 48/288. To simplify, divide both numerator and denominator by 48 to get 1/6.

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Question

Evaluate –3–2 * 2–3.

Answer

Because the exponents are negative, we can convert –3–2 to 1/9 and 2–3 to 1/8. We then multiply straight across the top and the bottom, giving you 1/72.

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Question

What value of $s$ makes the equation $\frac{7}{s}=\frac{8}{10}$ true?

Answer

We can simply cross multiply to obtain $70=8s$ and divide by 8 to solve for $s$ .

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Question

Simplify the following into one fraction

$\frac{2}{7}\cdot\frac{12}{5}\cdot\frac{25}{6}$

Answer

To multiply fractions you multiply the entire numerator and the entire denominator together. However, before we do that we can cancel anything from the denominator with anything in the numerator.

Six cancels with 12

$\frac{2}{7}\cdot\frac{\textbf{12}}{5}\cdot\frac{25}{\textbf{6}}=\frac{2}{7}\cdot\frac{2}{5}\cdot25$

5 cancels with 25

$\frac{2}{7}\cdot\frac{2}{\textbf5}\cdot\textbf{25}=\frac{2}{7}\cdot2\cdot5$

multiply it all out and get

$\frac{20}{7}$

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