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ACT Math : Arithmetic

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Example Questions

Example Question #471 : Arithmetic

Which of the following is equivalent to $\frac{82}{4}$ ?

Possible Answers:

$20\frac{1}{4}$

$15\frac{1}{2}$

$15\frac{3}{4}$

$20\frac{3}{8}$

$20\frac{1}{2}$

Correct answer:

$20\frac{1}{2}$

Explanation:

Although there are many ways to convert improper fractions into mixed fractions, the easiest way is to use your calculator to your advantage. Begin by dividing by . This gives you 20.5 . Therefore, you can eliminate all the options that have do not have for their first portion. Next, multiply 0.5 by the denominator (), and get . This means that you have and $\frac{2}{4}$ , or $\frac{1}{2}$ . Thus, your answer is $20\frac{1}{2}$ .

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Example Question #1 : 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:

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

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

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

$3\tfrac{1}{7}$

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

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 : Operations And Fractions

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

Possible Answers:

$7.5$

$9$

$8.75$

$9.5$

$9.25$

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 : Operations And Fractions

Simplfiy the following expression;

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

Possible Answers:

$\frac{3}{4}$

$\frac{1}{2}$

$\frac{5}{6}$

$\frac{1}{6}$

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 #2 : How To Multiply Fractions

Evaluate –3^–2* 2^–3.

Possible Answers:

$\frac{1}{72}$

$-\frac{3}{2}$

$-\frac{1}{72}$

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 #2 : Operations And Fractions

Simplify the following into one fraction

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

Possible Answers:

$\frac{5}{6}$

$\frac{2}{5}$

$\frac{20}{7}$

$\frac{15}{35}$

$\frac{50}{42}$

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 #3 : Operations And Fractions

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

Possible Answers:

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

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

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

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

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

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 #1 : How To Divide Fractions

Simplify the following expression:

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

Possible Answers:

$\frac{1}{5}$

$\frac{4}{5}$

$\frac{7}{9}$

$\frac{5}{9}$

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 #4 : Operations And Fractions

Evaluate the following:

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

Possible Answers:

$1\frac{1}{3}$

$\frac{65}{60}$

$6\frac{1}{10}$

$1\frac{1}{10}$

$1\frac{6}{10}$

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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ACT Math : Arithmetic

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #471 : Arithmetic

Example Question #1 : 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 : Operations And Fractions

Example Question #1 : Operations And Fractions

Example Question #2 : How To Multiply Fractions

Example Question #2 : Operations And Fractions

Example Question #3 : Operations And Fractions

Example Question #1 : How To Divide Fractions

Example Question #4 : Operations And Fractions

All ACT Math Resources

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