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ACT Math : Algebraic Fractions

Study concepts, example questions & explanations for ACT Math

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Example Questions

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Example Question #21 : How To Solve For A Variable As Part Of A Fraction

Solve for :

$\frac{x-2}{1}=\frac{2}{4}$

Possible Answers:

$\frac{7}{2}$

$\frac{5}{2}$

Correct answer:

$\frac{5}{2}$

Explanation:

First, cross multiply:

4(x-2)=2

$x-2=\frac{1}{2}$

$x=\frac{5}2{}$

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Example Question #22 : How To Solve For A Variable As Part Of A Fraction

Solve for :

$\frac{3}{x}=\frac{12}{36}$

Possible Answers:

$\frac{14}{3}$

Correct answer:

Explanation:

First, cross-multiply: 12x=108

$x=\frac{108}{12}=9$

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Example Question #23 : How To Solve For A Variable As Part Of A Fraction

Solve for :

$\frac{2x}{5}=\frac{1}{3}$

Possible Answers:

$\frac{5}{6}$

$\frac{7}{6}$

Correct answer:

$\frac{5}{6}$

Explanation:

First, cross-multiply:

6x=5

$x=\frac{5}{6}$

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Example Question #24 : How To Solve For A Variable As Part Of A Fraction

Solve for :

$\frac{x^{2}}{4}=\frac{18}{8}$

Possible Answers:

4, -4

3, -3

Correct answer:

3, -3

Explanation:

Begin by cross-multiplying.

$8x^{2}=72$

$x^{2}=9$

x=3, -3

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Example Question #25 : How To Solve For A Variable As Part Of A Fraction

Solve for :

$\frac{3}{x^2}=\frac{1}{3}$

Possible Answers:

2, -2

3, -3

Correct answer:

3, -3

Explanation:

Begin by cross-multiplying.

x^2(1)=3(3)

x^2=9

x=3, -3

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Example Question #26 : How To Solve For A Variable As Part Of A Fraction

Solve for :

$\frac{x^2+2}{3}=\frac{6}{1}$

Possible Answers:

4, -4

6, -6

Correct answer:

4, -4

Explanation:

Begin by cross-multiplying.

x^2+2(1)=18

Now, solve for .

x^2=16

x=4, -4

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Example Question #27 : How To Solve For A Variable As Part Of A Fraction

Solve for :

$\frac{2}{x-6}=\frac{4}{3}$

Possible Answers:

$\frac{11}{2}$

$\frac{17}{2}$

$\frac{15}{2}$

$\frac{13}{2}$

Correct answer:

$\frac{15}{2}$

Explanation:

Begin by cross-multiplying.

6=4x-24

Now, solve for

4x=30

$x=\frac{15}{2}$

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Example Question #21 : How To Solve For A Variable As Part Of A Fraction

Solve for :

$\frac{3}{x-5}=\frac{5}{3}$

Possible Answers:

$\frac{32}{3}$

$\frac{27}{4}$

$\frac{34}{5}$

$\frac{37}{4}$

Correct answer:

$\frac{34}{5}$

Explanation:

First, cross-multiply.

9=5x-25

Now, solve for

34=5x

$\frac{34}{5}=x$

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Example Question #29 : How To Solve For A Variable As Part Of A Fraction

Solve for .

$\frac{3}{2x}=\frac{7}{9}$

Possible Answers:

$\frac{27}{14}$

$\frac{3}{2}$

$\frac{29}{14}$

Correct answer:

$\frac{27}{14}$

Explanation:

First, cross multiply.

3(9)=7(2x)

Now, simplify and solve for .

27=14x

$x=\frac{27}{14}$

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Example Question #26 : How To Solve For A Variable As Part Of A Fraction

Solve for .

$\frac{3x}{5}=\frac{13}{10}$

Possible Answers:

$\frac{13}{6}$

$\frac{7}{3}$

Correct answer:

$\frac{13}{6}$

Explanation:

First, cross multiply.

3x(10)=13(5)

30x=65

$x=\frac{65}{30}=\frac{13}{6}$

Report an Error

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ACT Math : Algebraic Fractions

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #21 : How To Solve For A Variable As Part Of A Fraction

Example Question #22 : How To Solve For A Variable As Part Of A Fraction

Example Question #23 : How To Solve For A Variable As Part Of A Fraction

Example Question #24 : How To Solve For A Variable As Part Of A Fraction

Example Question #25 : How To Solve For A Variable As Part Of A Fraction

Example Question #26 : How To Solve For A Variable As Part Of A Fraction

Example Question #27 : How To Solve For A Variable As Part Of A Fraction

Example Question #21 : How To Solve For A Variable As Part Of A Fraction

Example Question #29 : How To Solve For A Variable As Part Of A Fraction

Example Question #26 : How To Solve For A Variable As Part Of A Fraction

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