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ACT Math : Algebraic Fractions

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Example Questions

Example Question #1244 : Algebra

Solve for $\displaystyle x$.

$\frac{x-3}{3}=\frac{12}{7}$ $\displaystyle \frac{x-3}{3}=\frac{12}{7}$

Possible Answers:

$\frac{49}{4}$ $\displaystyle \frac{49}{4}$

$\frac{57}{7}$ $\displaystyle \frac{57}{7}$

$\frac{40}{3}$ $\displaystyle \frac{40}{3}$

$\frac{58}{7}$ $\displaystyle \frac{58}{7}$

Correct answer:

$\frac{57}{7}$ $\displaystyle \frac{57}{7}$

Explanation:

First, cross-multiply.

$\displaystyle 7(x-3)=12(3)$

Now, simplify and solve for $\displaystyle x$.

$\displaystyle 7x-21=36$

7x=57 $\displaystyle 7x=57$

$x=\frac{57}{7}$ $\displaystyle x=\frac{57}{7}$

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Example Question #1245 : Algebra

Solve for $\displaystyle x$.

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

Possible Answers:

$\frac{11}{6}$ $\displaystyle \frac{11}{6}$

$\displaystyle 2$

$\frac{17}{5}$ $\displaystyle \frac{17}{5}$

$\frac{4}{5}$ $\displaystyle \frac{4}{5}$

Correct answer:

$\frac{11}{6}$ $\displaystyle \frac{11}{6}$

Explanation:

First, cross-multiply.

6x+9=20 $\displaystyle 6x+9=20$

Now, solve for $\displaystyle x$.

6x=11 $\displaystyle 6x=11$

$x=\frac{11}{6}$ $\displaystyle x=\frac{11}{6}$

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Example Question #31 : How To Solve For A Variable As Part Of A Fraction

Solve for $\displaystyle x$.

$\frac{5}{3x-8}=\frac{7}{3}$ $\displaystyle \frac{5}{3x-8}=\frac{7}{3}$

Possible Answers:

$\frac{21}{71}$ $\displaystyle \frac{21}{71}$

$-\frac{21}{71}$ $\displaystyle -\frac{21}{71}$

$-\frac{71}{21}$ $\displaystyle -\frac{71}{21}$

$\frac{71}{21}$ $\displaystyle \frac{71}{21}$

Correct answer:

$\frac{71}{21}$ $\displaystyle \frac{71}{21}$

Explanation:

First, cross-multiply.

$\displaystyle 3(5)=7(3x-8)$

Now, simplify and solve for $\displaystyle x$.

$\displaystyle 15=21x-56$

71=21x $\displaystyle 71=21x$

$x=\frac{71}{21}$ $\displaystyle x=\frac{71}{21}$

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Example Question #1251 : Algebra

Solve for $\displaystyle x$.

$\frac{7x}{2}=\frac{5}{4}$ $\displaystyle \frac{7x}{2}=\frac{5}{4}$

Possible Answers:

$\frac{7}{12}$ $\displaystyle \frac{7}{12}$

$\frac{1}{4}$ $\displaystyle \frac{1}{4}$

$\frac{2}{13}$ $\displaystyle \frac{2}{13}$

$\frac{5}{14}$ $\displaystyle \frac{5}{14}$

Correct answer:

$\frac{5}{14}$ $\displaystyle \frac{5}{14}$

Explanation:

First, cross-multiply.

$\displaystyle 7x(4)=5(2)$

Now, simplify and solve for $\displaystyle x$.

28x=10 $\displaystyle 28x=10$

$x=\frac{10}{28}=\frac{5}{14}$ $\displaystyle x=\frac{10}{28}=\frac{5}{14}$

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Example Question #31 : How To Solve For A Variable As Part Of A Fraction

Solve for $\displaystyle x$.

$\frac{4x}{3}=\frac{9}{5}$ $\displaystyle \frac{4x}{3}=\frac{9}{5}$

Possible Answers:

$\frac{20}{27}$ $\displaystyle \frac{20}{27}$

$\frac{4}{7}$ $\displaystyle \frac{4}{7}$

$\frac{27}{20}$ $\displaystyle \frac{27}{20}$

$\frac{2}{5}$ $\displaystyle \frac{2}{5}$

Correct answer:

$\frac{27}{20}$ $\displaystyle \frac{27}{20}$

Explanation:

First, cross-multiply.

$\displaystyle 5(4x)=27$

Now, solve for $\displaystyle x$.

20x=27 $\displaystyle 20x=27$

$x=\frac{27}{20}$ $\displaystyle x=\frac{27}{20}$

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Example Question #81 : Algebraic Fractions

Solve for $\displaystyle x$.

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

Possible Answers:

$\frac{17}{4}$ $\displaystyle \frac{17}{4}$

$\frac{14}{3}$ $\displaystyle \frac{14}{3}$

$\frac{8}{7}$ $\displaystyle \frac{8}{7}$

$\frac{12}{3}$ $\displaystyle \frac{12}{3}$

Correct answer:

$\frac{14}{3}$ $\displaystyle \frac{14}{3}$

Explanation:

First, cross-multiply.

7(2)=3x $\displaystyle 7(2)=3x$

Now, solve for $\displaystyle x$.

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

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Example Question #3111 : Act Math

Solve for $\displaystyle x$.

$\frac{4x}{5}=\frac{2}{6}$ $\displaystyle \frac{4x}{5}=\frac{2}{6}$

Possible Answers:

$\frac{5}{7}$ $\displaystyle \frac{5}{7}$

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

$\frac{5}{12}$ $\displaystyle \frac{5}{12}$

$\frac{7}{12}$ $\displaystyle \frac{7}{12}$

Correct answer:

$\frac{5}{12}$ $\displaystyle \frac{5}{12}$

Explanation:

First, cross-multiply.

24x=10 $\displaystyle 24x=10$

Now, solve for $\displaystyle x$.

$x=\frac{10}{24}$ $\displaystyle x=\frac{10}{24}$

Simplify.

$\frac{5}{12}$ $\displaystyle \frac{5}{12}$

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Example Question #34 : How To Solve For A Variable As Part Of A Fraction

Solve for $\displaystyle x$.

$\frac{2x-4}{5}=\frac{2}{5}$ $\displaystyle \frac{2x-4}{5}=\frac{2}{5}$

Possible Answers:

$\displaystyle 2$

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

$\frac{2}{3}$ $\displaystyle \frac{2}{3}$

$\displaystyle 3$

Correct answer:

$\displaystyle 3$

Explanation:

First, cross-multiply.

$\displaystyle 10x-20=10$

Now, solve for $\displaystyle x$.

10x=30 $\displaystyle 10x=30$

$x=\frac{30}{10}=3$ $\displaystyle x=\frac{30}{10}=3$

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Example Question #32 : How To Solve For A Variable As Part Of A Fraction

Solve for $\displaystyle x$.

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

Possible Answers:

$\frac{3}{2}$ $\displaystyle \frac{3}{2}$

$\displaystyle 2$

$\frac{7}{2}$ $\displaystyle \frac{7}{2}$

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

Correct answer:

$\frac{3}{2}$ $\displaystyle \frac{3}{2}$

Explanation:

First, cross-multiply.

$\displaystyle 3(4x-2)=12$

Simplify.

$\displaystyle 12x-6=12$

Solve for $\displaystyle x$.

12x=18 $\displaystyle 12x=18$

$x=\frac{18}{12}=\frac{3}{2}$ $\displaystyle x=\frac{18}{12}=\frac{3}{2}$

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Example Question #3112 : Act Math

Solve for $\displaystyle x$.

$\frac{3}{5-x}=\frac{2}{3}$ $\displaystyle \frac{3}{5-x}=\frac{2}{3}$

Possible Answers:

$\frac{3}{2}$ $\displaystyle \frac{3}{2}$

$\displaystyle 2$

$\displaystyle 0$

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

Correct answer:

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

Explanation:

First, cross-multiply.

9=10-2x $\displaystyle 9=10-2x$

Now, solve for $\displaystyle x$.

-1=-2x $\displaystyle -1=-2x$

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

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ACT Math : Algebraic Fractions

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1244 : Algebra

Example Question #1245 : Algebra

Example Question #31 : How To Solve For A Variable As Part Of A Fraction

Example Question #1251 : Algebra

Example Question #31 : How To Solve For A Variable As Part Of A Fraction

Example Question #81 : Algebraic Fractions

Example Question #3111 : Act Math

Example Question #34 : How To Solve For A Variable As Part Of A Fraction

Example Question #32 : How To Solve For A Variable As Part Of A Fraction

Example Question #3112 : Act Math

All ACT Math Resources

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