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ACT Math : How to divide fractions

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Example Questions

Example Question #1 : How To Divide Fractions

$\dpi{100} \small \frac{1}{3}\div \frac{3}{5} =$ $\displaystyle \dpi{100} \small \frac{1}{3}\div \frac{3}{5} =$

Possible Answers:

$\dpi{100} \small \frac{2}{3}$ $\displaystyle \dpi{100} \small \frac{2}{3}$

$\dpi{100} \small \frac{1}{5}$ $\displaystyle \dpi{100} \small \frac{1}{5}$

$\dpi{100} \small \frac{3}{8}$ $\displaystyle \dpi{100} \small \frac{3}{8}$

$\dpi{100} \small \frac{2}{5}$ $\displaystyle \dpi{100} \small \frac{2}{5}$

$\dpi{100} \small \frac{5}{9}$ $\displaystyle \dpi{100} \small \frac{5}{9}$

Correct answer:

$\dpi{100} \small \frac{5}{9}$ $\displaystyle \dpi{100} \small \frac{5}{9}$

Explanation:

Cross multiply or multiply using the reciprocal of the second fraction.

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Example Question #2 : How To Divide Fractions

Simplify the following expression:

$\frac{2}{3}\div\frac{5}{6}$ $\displaystyle \frac{2}{3}\div\frac{5}{6}$

Possible Answers:

$\frac{1}{5}$ $\displaystyle \frac{1}{5}$

$\frac{7}{9}$ $\displaystyle \frac{7}{9}$

$\frac{5}{9}$ $\displaystyle \frac{5}{9}$

$\frac{4}{5}$ $\displaystyle \frac{4}{5}$

Correct answer:

$\frac{4}{5}$ $\displaystyle \frac{4}{5}$

Explanation:

$\frac{2}{3}\div\frac{5}{6}=\frac{2}{3}\times\frac{6}{5}=\frac{12}{15}=\frac{4}{5}$ $\displaystyle \frac{2}{3}\div\frac{5}{6}=\frac{2}{3}\times\frac{6}{5}=\frac{12}{15}=\frac{4}{5}$

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Example Question #3 : How To Divide Fractions

Evaluate the following:

$7\frac{1}{3}\div6\frac{2}{3}$ $\displaystyle 7\frac{1}{3}\div6\frac{2}{3}$

Possible Answers:

$6\frac{1}{10}$ $\displaystyle 6\frac{1}{10}$

$1\frac{1}{10}$ $\displaystyle 1\frac{1}{10}$

$1\frac{6}{10}$ $\displaystyle 1\frac{6}{10}$

$\frac{65}{60}$ $\displaystyle \frac{65}{60}$

$1\frac{1}{3}$ $\displaystyle 1\frac{1}{3}$

Correct answer:

$1\frac{1}{10}$ $\displaystyle 1\frac{1}{10}$

Explanation:

Start by converting 7¹/₃to 22/3, and 6 ²/₃to 20/3. We then multiply 22/3 by the reciprocal of 20/3, 3/20, and you get 66/60. This simplifies to 1¹/₁₀.

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Example Question #481 : Arithmetic

Solve.

$\small \frac{2}{5}\div \frac{1}{25}=$ $\displaystyle \small \frac{2}{5}\div \frac{1}{25}=$

Possible Answers:

$\displaystyle 10$

$\small \frac{27}{5}$ $\displaystyle \small \frac{27}{5}$

$\small \frac{2}{5}$ $\displaystyle \small \frac{2}{5}$

$\small \frac{1}{2}$ $\displaystyle \small \frac{1}{2}$

$\small \frac{1}{15}$ $\displaystyle \small \frac{1}{15}$

Correct answer:

$\displaystyle 10$

Explanation:

Remember, to divide a number by a fraction, multiply the number by the reciprocal of the fraction. In this case, $\small \small \frac{2}{5}\div \frac{1}{25}=\frac{2}{5}\times \frac{25}{1}=\frac{50}{5}=10$ $\displaystyle \small \small \frac{2}{5}\div \frac{1}{25}=\frac{2}{5}\times \frac{25}{1}=\frac{50}{5}=10$

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ACT Math : How to divide fractions

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : How To Divide Fractions

Example Question #2 : How To Divide Fractions

Example Question #3 : How To Divide Fractions

Example Question #481 : Arithmetic

All ACT Math Resources

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