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ACT Math : Algebraic Fractions

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Example Questions

Example Question #41 : How To Solve For A Variable As Part Of A Fraction

Solve for $\displaystyle x.$

$\frac{5x+1}{2} = \frac{-3x}{6}$ $\displaystyle \frac{5x+1}{2} = \frac{-3x}{6}$

Possible Answers:

$-\frac{12}{18}$ $\displaystyle -\frac{12}{18}$

$\frac{12}{18}$ $\displaystyle \frac{12}{18}$

$\displaystyle 6$

$\displaystyle 0$

$-\frac{1}{6}$ $\displaystyle -\frac{1}{6}$

Correct answer:

$-\frac{1}{6}$ $\displaystyle -\frac{1}{6}$

Explanation:

To solve these types of problems, you need to cross multiply the fractions

$\frac{5x+1}{2}=\frac{-3x}{6} \rightarrow (5x+1)6 = 2*-3x$ $\displaystyle \frac{5x+1}{2}=\frac{-3x}{6} \rightarrow (5x+1)6 = 2*-3x$.

Then, all we need to do is distribute the $\displaystyle 6$, combine like terms, and solve the algebraic equation.

$30x + 6 = -6x \rightarrow 36x = -6 \rightarrow x = -\frac{1}{6}$ $\displaystyle 30x + 6 = -6x \rightarrow 36x = -6 \rightarrow x = -\frac{1}{6}$.

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Example Question #41 : How To Solve For A Variable As Part Of A Fraction

Solve for $\displaystyle x$:

$\frac{x+7}{4}=\frac{3}{2}$ $\displaystyle \frac{x+7}{4}=\frac{3}{2}$

Possible Answers:

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

$\displaystyle 2$

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

$\displaystyle -1$

Correct answer:

$\displaystyle -1$

Explanation:

Cross-multiply:$\displaystyle 2(x+7)=12$

Distribute: $\displaystyle 2x+14=12$

Solve for x: 2x=-2 $\displaystyle 2x=-2$

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

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Example Question #3111 : Act Math

Solve for $\displaystyle y:$

$\frac{4}{y+2}=\frac{6}{10}$ $\displaystyle \frac{4}{y+2}=\frac{6}{10}$

Possible Answers:

$\displaystyle 5$

$\frac{16}{3}$ $\displaystyle \frac{16}{3}$

$\displaystyle 3$

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

Correct answer:

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

Explanation:

Solve this question by cross-multiplying:

$\displaystyle 40=6y+12$

6y=28 $\displaystyle 6y=28$

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

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Example Question #8 : How To Solve For A Variable As Part Of A Fraction

If x=-5 $\displaystyle x=-5$, what is the value of $\frac{x^{2}+20}{x-4}$ $\displaystyle \frac{x^{2}+20}{x-4}$?

Possible Answers:

$\displaystyle -5$

$\displaystyle 25$

$\displaystyle 9$

$\displaystyle 45$

Correct answer:

$\displaystyle -5$

Explanation:

To solve this question, substitute -5 in for x in the numerator and denominator. Remember that the square of a negative number is positive.

45 / -9 = -5

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ACT Math : Algebraic Fractions

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #41 : How To Solve For A Variable As Part Of A Fraction

Example Question #41 : How To Solve For A Variable As Part Of A Fraction

Example Question #3111 : Act Math

Example Question #8 : How To Solve For A Variable As Part Of A Fraction

All ACT Math Resources

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