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ACT Math : ACT Math

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Example Questions

Example Question #3 : How To Find Out A Mixed Fraction From An Improper Fraction

What does $\small \small \small \small \frac{32}{14}+\frac{6}{7}$ equal, expressed as a mixed number?

Possible Answers:

$\small 1\tfrac{5}{14}$

$\small 2\tfrac{2}{7}$

$\small 1\tfrac{4}{7}$

$\small 1\tfrac{17}{21}$

$3\tfrac{1}{7}$

Correct answer:

$3\tfrac{1}{7}$

Explanation:

Simplify the two fractions, then find a common denominator, then solve. $\small \small \frac{32}{14}+\frac{6}{7}=\frac{16}{7}+\frac{6}{7}=\frac{22}{7}=3\tfrac{1}{7}$

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Example Question #2 : How To Find Out A Mixed Fraction From An Improper Fraction

Convert the improper fraction $\frac{27}{6}$ to a mixed number. Reduce all fractions if possible.

Possible Answers:

$5\frac{1}{6}$

$\frac{6}{27}$

$4\frac{1}{2}$

$1\frac{6}{21}$

$4\frac{3}{6}$

Correct answer:

$4\frac{1}{2}$

Explanation:

To convert a mixed number into a fraction, first divide the denominator into the numerator and record the remainder:

$27/6 = 4 \:\textup{remainder} \: 3$ .

the result is the mixed number, with the remainder being put as the numerator over the old denominator:
$\frac{27}{6} = 4 \frac{3}{6} = 4 \frac{1}{2}$ when we reduce.

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Example Question #1 : How To Multiply Fractions

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

Possible Answers:

$8.75$

$9.5$

$9.25$

$7.5$

$9$

Correct answer:

$8.75$

Explanation:

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

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Example Question #1 : How To Multiply Fractions

Simplfiy the following expression;

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

Possible Answers:

$\frac{5}{6}$

$\frac{3}{4}$

$\frac{1}{2}$

$\frac{1}{6}$

Correct answer:

$\frac{1}{6}$

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.

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Example Question #1 : How To Multiply Fractions

Evaluate –3^–2* 2^–3.

Possible Answers:

$-\frac{1}{72}$

$\frac{1}{72}$

$-\frac{3}{2}$

Correct answer:

$\frac{1}{72}$

Explanation:

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

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Example Question #154 : Fractions

Simplify the following into one fraction

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

Possible Answers:

$\frac{15}{35}$

$\frac{5}{6}$

$\frac{2}{5}$

$\frac{20}{7}$

$\frac{50}{42}$

Correct answer:

$\frac{20}{7}$

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

$\frac{20}{7}$

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Example Question #1 : How To Divide Fractions

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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

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Example Question #2 : Operations And Fractions

Simplify the following expression:

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

Possible Answers:

$\frac{4}{5}$

$\frac{5}{9}$

$\frac{7}{9}$

$\frac{1}{5}$

Correct answer:

$\frac{4}{5}$

Explanation:

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

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Example Question #3 : Operations And Fractions

Evaluate the following:

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

Possible Answers:

$1\frac{1}{3}$

$1\frac{1}{10}$

$1\frac{6}{10}$

$6\frac{1}{10}$

$\frac{65}{60}$

Correct answer:

$1\frac{1}{10}$

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.

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

Possible Answers:

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

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

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

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

Correct answer:

Explanation:

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

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ACT Math : ACT Math

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #3 : How To Find Out A Mixed Fraction From An Improper Fraction

Example Question #2 : How To Find Out A Mixed Fraction From An Improper Fraction

Example Question #1 : How To Multiply Fractions

Example Question #1 : How To Multiply Fractions

Example Question #1 : How To Multiply Fractions

Example Question #154 : Fractions

Example Question #1 : How To Divide Fractions

Example Question #2 : Operations And Fractions

Example Question #3 : Operations And Fractions

Example Question #481 : Arithmetic

All ACT Math Resources

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