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Example Questions

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Example Question #4 : How To Solve For A Variable As Part Of A Fraction

Solve the following equation for the given variable:

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

Possible Answers:

$x = \frac{1}{5}$

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

$x = \frac{1}{6}$

$x = \frac{8}{3}$

$x = \frac{3}{2}$

Correct answer:

$x = \frac{1}{6}$

Explanation:

To solve this equation we have to multiply both sides by the denominator to get rid of the fraction.

Doing this yields

2 = 12x

Then to solve the last step is to isolate the variable by dividing both sides by 12.
Thus,

$x = \frac{2}{12}=\frac{1}{6}$ .

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Example Question #5 : How To Solve For A Variable As Part Of A Fraction

For what value of is the equation $\frac{4}{12}=\frac{5}{x}$ true?

Possible Answers:

Correct answer:

Explanation:

When the equation is cross multiplied, it becomes

$\\ 4\cdot x=5\cdot 12 \\4x = 60$ .

Hence,

$x =\frac{60}{4}$ , or x=15 .

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Example Question #6 : How To Solve For A Variable As Part Of A Fraction

Solve the following equation for :

$\frac{36}{5x} = 4$ .

Reduce any fractions in your final answer.

Possible Answers:

$x = \frac{36}{20}$

$x = \frac{9}{5}$

x = 3

$x = \frac{5}{9}$

x = 5

Correct answer:

$x = \frac{9}{5}$

Explanation:

To solve an equation with a variable in a fraciton, treat the denominator as a constant value and multiply both sides of the equation by the denominator in order to eliminate it.
$\\5x * \left(\frac{36}{5x}\right) = 4 * 5x\\ \newline 36 = 20x \newline \newline \frac{36}{20} = x \\ \newline \frac{9}{5}= x$

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Example Question #1 : How To Solve For A Variable As Part Of A Fraction

Solve for : $\frac{x}{12}=3$

Possible Answers:

$\frac{1}{3}$

$\frac{1}{36}$

Correct answer:

Explanation:

To find the answer, multiply the right side by . The result is 36=x .

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Example Question #11 : How To Solve For A Variable As Part Of A Fraction

Solve for :

$\frac{3}{4}=\frac{5x+10}{20}$

Possible Answers:

Correct answer:

Explanation:

To solve this problem you must cross mutiply, then set the two equations equal to each other. Your first equation is $3\left ( 20\right )$ , your second is $4\left ( 5x+10\right )=20+40$ . This gives you 60=20x+40 . Subtract from both sides, so you have 20=20x , divide by on both sides and you have x=1 .

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Example Question #12 : How To Solve For A Variable As Part Of A Fraction

Solve for :

$\frac{14}{x+3}=\frac{2}{3}$

Possible Answers:

19.5

Correct answer:

Explanation:

Cross multiply: 42=2(x+3)

Distribute: 42=2x+6

Solve for : 36=2x

18=x

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Example Question #13 : How To Solve For A Variable As Part Of A Fraction

Solve for :

$\frac{x}{3}=\frac{3}{12}$

Possible Answers:

$\frac{3}{4}$

$\frac{4}{3}$

Correct answer:

$\frac{3}{4}$

Explanation:

Cross-multiply: 12x=9

Solve for : $x=\frac{9}{12}$

Simplify: $x=\frac{3}{4}$

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Example Question #14 : How To Solve For A Variable As Part Of A Fraction

Solve for :

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

Possible Answers:

$-\frac{1}{12}$

$\frac{-7}{60}$

$-\frac{1}{10}$

Correct answer:

$\frac{-7}{60}$

Explanation:

Cross-multiply: 5(12x+3)=8

Distribute: 60x+15=8

Solve for : 60x=-7

$x=\frac{-7}{60}$

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Example Question #15 : How To Solve For A Variable As Part Of A Fraction

Solve for :

$\frac{x+4}{3}=\frac{4}{5}$

Possible Answers:

$-\frac{8}{5}$

$\frac{2}{3}$

$-\frac{5}{8}$

$\frac{1}{3}$

Correct answer:

$-\frac{8}{5}$

Explanation:

Begin by cross-multiplying:

5x+20=12

Now, solve for .

5x=-8

$x=-\frac{8}{5}$

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Example Question #16 : How To Solve For A Variable As Part Of A Fraction

Solve for :

$\frac{2}{x-2}=\frac{3}{4}$

Possible Answers:

$\frac{14}{3}$

$\frac{11}{3}$

$\frac{4}{3}$

$\frac{13}{3}$

Correct answer:

$\frac{14}{3}$

Explanation:

Begin by cross multiplying.

8=3x-6

Next, solve for .

14=3x

$x=\frac{14}{3}$

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ACT Math : ACT Math

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #4 : How To Solve For A Variable As Part Of A Fraction

Example Question #5 : How To Solve For A Variable As Part Of A Fraction

Example Question #6 : How To Solve For A Variable As Part Of A Fraction

Example Question #1 : How To Solve For A Variable As Part Of A Fraction

Example Question #11 : How To Solve For A Variable As Part Of A Fraction

Example Question #12 : How To Solve For A Variable As Part Of A Fraction

Example Question #13 : How To Solve For A Variable As Part Of A Fraction

Example Question #14 : How To Solve For A Variable As Part Of A Fraction

Example Question #15 : How To Solve For A Variable As Part Of A Fraction

Example Question #16 : How To Solve For A Variable As Part Of A Fraction

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