How to multiply fractions

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ACT Math › How to multiply fractions

Questions 1 - 4

Simplfiy the following expression;

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

$\frac{1}{6}$

$\frac{1}{2}$

$\frac{3}{4}$

$\frac{5}{6}$

Explanation

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.

Simplify the following into one fraction

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

$\frac{20}{7}$

$\frac{15}{35}$

$\frac{2}{5}$

$\frac{5}{6}$

$\frac{50}{42}$

Explanation

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

$\frac{20}{7}$

Evaluate –3–2 * 2–3.

$\frac{1}{72}$

$-\frac{1}{72}$

$-\frac{3}{2}$

Explanation

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.

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