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ACT Math : Operations and Fractions

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Example Questions

Example Question #1 : Operations And Fractions

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

Possible Answers:

$9.25$

$7.5$

$9.5$

$9$

$8.75$

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 #2 : Operations And Fractions

Simplfiy the following expression;

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

Possible Answers:

$\frac{1}{6}$

$\frac{5}{6}$

$\frac{1}{2}$

$\frac{3}{4}$

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 #3 : 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 #1 : How To Multiply Fractions

Simplify the following into one fraction

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

Possible Answers:

$\frac{20}{7}$

$\frac{2}{5}$

$\frac{15}{35}$

$\frac{50}{42}$

$\frac{5}{6}$

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 : Operations And Fractions

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

Possible Answers:

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

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

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

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

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

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:

$\frac{1}{5}$

$\frac{4}{5}$

$\frac{5}{9}$

$\frac{7}{9}$

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 #3 : Operations And Fractions

Evaluate the following:

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

Possible Answers:

$1\frac{1}{10}$

$6\frac{1}{10}$

$1\frac{6}{10}$

$\frac{65}{60}$

$1\frac{1}{3}$

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:

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

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

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

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

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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Example Question #4 : Operations And Fractions

Solve for x where

$4\frac{1}{3}=x+1\frac{1}{2}$

Possible Answers:

$5\frac{2}{3}$

$3\frac{5}{6}$

$5\frac{2}{5}$

$3\frac{1}{5}$

$2\frac{5}{6}$

Correct answer:

$2\frac{5}{6}$

Explanation:

To solve this, subtract 1 1/2 from both sides. Convert to common denominators.

4 1/3 – 1 1/2 = 4 2/6 – 1 3/6.

In order to subtract, you'll want to "borrow" from the 4 2/6. Rewrite 4 2/6 as 3 8/6 and then subtract 1 3/6 from this. Your solution is 2 5/6. Most calculators will also do these calculations for you.

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Example Question #483 : Arithmetic

Solve for :

$\frac{7}{12}x+\frac{5}{4}=\frac{1}{2}+\frac{4}{3}x$

Possible Answers:

$-\frac{3}{16}$

$\frac{5}{16}$

$\frac{1}{4}$

Correct answer:

Explanation:

$\frac{7}{12}x+\frac{5}{4}=\frac{1}{2}+\frac{4}{3}x$

Begin by isolating your variable:

$\frac{7}{12}x-\frac{4}{3}x=\frac{1}{2}-\frac{5}{4}$

Next, you need to find the common denominator. For the left side of your equation, it is . For the right, it is . This means that you need to rewrite as follows:

$\frac{7}{12}x-\frac{4}{3}*\frac{4}{4}x=\frac{2}{4}-\frac{5}{4}$

Now, simplify and combine terms:

$\frac{7}{12}x-\frac{16}{12}x=-\frac{3}{4}$

$-\frac{9}{12}x=-\frac{3}{4}$

You can further simplify the left side:

$-\frac{3}{4}x=-\frac{3}{4}$

Next, multiply both sides by $-\frac{4}{3}$ . This gives you:

$x=-\frac{3}{4}*-\frac{4}{3}=1$

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ACT Math : Operations and Fractions

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : Operations And Fractions

Example Question #2 : Operations And Fractions

Example Question #3 : How To Multiply Fractions

Example Question #1 : How To Multiply Fractions

Example Question #1 : Operations And Fractions

Example Question #2 : Operations And Fractions

Example Question #3 : Operations And Fractions

Example Question #481 : Arithmetic

Example Question #4 : Operations And Fractions

Example Question #483 : Arithmetic

All ACT Math Resources

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