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Algebra 1 : Proportions

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Example Questions

Example Question #71 : Proportions

Solve the proportion: $\frac{2x}{9} = \frac{4}{3}$ $\displaystyle \frac{2x}{9} = \frac{4}{3}$

Possible Answers:

$\frac{13}{6}$ $\displaystyle \frac{13}{6}$

$\displaystyle 6$

$\frac{81}{2}$ $\displaystyle \frac{81}{2}$

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

$\frac{13}{5}$ $\displaystyle \frac{13}{5}$

Correct answer:

$\displaystyle 6$

Explanation:

To solve the proportion, cross multiply the fractions.

$\displaystyle (2x)(3)=(9)(4)$

Simplify both sides.

6x=36 $\displaystyle 6x=36$

Divide by six on both sides.

$\frac{6x}{6}=\frac{36}{6}$ $\displaystyle \frac{6x}{6}=\frac{36}{6}$

Simplify both sides.

The answer is: x=6 $\displaystyle x=6$

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Example Question #71 : Proportions

Solve the proportion: $\frac{6}{x} = \frac{1}{7}$ $\displaystyle \frac{6}{x} = \frac{1}{7}$

Possible Answers:

$\displaystyle 13$

$\displaystyle 1$

$\displaystyle 42$

$\frac{7}{6}$ $\displaystyle \frac{7}{6}$

$\frac{6}{7}$ $\displaystyle \frac{6}{7}$

Correct answer:

$\displaystyle 42$

Explanation:

Cross multiply the fractions.

$\displaystyle (6)(7)=(x)(1)$

Simplify both sides.

x=42 $\displaystyle x=42$

The answer is: $\displaystyle 42$

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Example Question #73 : Proportions

Solve the proportion: $\frac{2x+3}{6} = \frac{4x-3}{5}$ $\displaystyle \frac{2x+3}{6} = \frac{4x-3}{5}$

Possible Answers:

$-\frac{14}{33}$ $\displaystyle -\frac{14}{33}$

$\frac{14}{33}$ $\displaystyle \frac{14}{33}$

$\frac{33}{14}$ $\displaystyle \frac{33}{14}$

$-\frac{33}{14}$ $\displaystyle -\frac{33}{14}$

$\frac{33}{8}$ $\displaystyle \frac{33}{8}$

Correct answer:

$\frac{33}{14}$ $\displaystyle \frac{33}{14}$

Explanation:

Cross multiply the fractions.

$\displaystyle (2x+3)(5)=(4x-3)(6)$

Use the distributive property to simplify the equation.

$\displaystyle 10x+15= 24x-18$

In order to group the terms, subtract 10x $\displaystyle 10x$ on both sides, and add 18 on both sides.

$\displaystyle 10x+15 -(10x)+[18]= 24x-18-(10x)+[18]$

Simplify the equation.

$\displaystyle 33 = 14x$

Divide by 14 on both sides and simplify.

$\frac{33}{14} = \frac{14x}{14}$ $\displaystyle \frac{33}{14} = \frac{14x}{14}$

$x=\frac{33}{14}$ $\displaystyle x=\frac{33}{14}$

The answer is: $\frac{33}{14}$ $\displaystyle \frac{33}{14}$

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Example Question #74 : Proportions

Solve the proportion: $\frac{3}{8x}= \frac{8}{3}$ $\displaystyle \frac{3}{8x}= \frac{8}{3}$

Possible Answers:

$\frac{8}{3}$ $\displaystyle \frac{8}{3}$

$\frac{9}{64}$ $\displaystyle \frac{9}{64}$

$\frac{64}{9}$ $\displaystyle \frac{64}{9}$

$\frac{3}{8}$ $\displaystyle \frac{3}{8}$

$\displaystyle 1$

Correct answer:

$\frac{9}{64}$ $\displaystyle \frac{9}{64}$

Explanation:

In order to solve for the unknown variable, cross multiply both fractions.

$\displaystyle (3)(3)= (8)(8x)$

Simplify both sides.

9=64x $\displaystyle 9=64x$

Divide by 64 on both sides.

$x= \frac{9}{64}$ $\displaystyle x= \frac{9}{64}$

The answer is: $\frac{9}{64}$ $\displaystyle \frac{9}{64}$

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Example Question #75 : Proportions

Solve the proportion: $\frac{2}{x} = \frac{3}{x+2}$ $\displaystyle \frac{2}{x} = \frac{3}{x+2}$

Possible Answers:

$\displaystyle 4$

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

$\displaystyle 1$

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

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

Correct answer:

$\displaystyle 4$

Explanation:

Cross multiply the two fractions.

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

Distribute the left side.

2x+4=3x $\displaystyle 2x+4=3x$

Subtract $\displaystyle 2x$ from both sides.

$\displaystyle 2x+4-2x=3x-2x$

Simplify both sides.

4=x $\displaystyle 4=x$

The answer is: $\displaystyle 4$

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Example Question #76 : Proportions

Solve the proportion: $\frac{8}{7x} =\frac{3}{4}$ $\displaystyle \frac{8}{7x} =\frac{3}{4}$

Possible Answers:

$\frac{7}{3}$ $\displaystyle \frac{7}{3}$

$\frac{6}{5}$ $\displaystyle \frac{6}{5}$

$\frac{28}{11}$ $\displaystyle \frac{28}{11}$

$\frac{3}{7}$ $\displaystyle \frac{3}{7}$

$\frac{32}{21}$ $\displaystyle \frac{32}{21}$

Correct answer:

$\frac{32}{21}$ $\displaystyle \frac{32}{21}$

Explanation:

Cross multiply the two fractions.

$\displaystyle 8(4)= (7x)(3)$

Simplify both sides.

$\displaystyle 32 = 21x$

Divide by 21 on both sides to isolate the x-variable.

$\frac{32}{21} =\frac{ 21x}{21}$ $\displaystyle \frac{32}{21} =\frac{ 21x}{21}$

Reduce the right side of the equation. The left side of the equation is irreducible.

The answer is: $x=\frac{32}{21}$ $\displaystyle x=\frac{32}{21}$

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Example Question #77 : Proportions

Solve the proportion: $\frac{3}{4} = \frac{2(x+2)}{3}$ $\displaystyle \frac{3}{4} = \frac{2(x+2)}{3}$

Possible Answers:

$\displaystyle 1$

$\frac{1}{8}$ $\displaystyle \frac{1}{8}$

$\displaystyle 0$

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

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

Correct answer:

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

Explanation:

Cross multiply the two fractions.

$\displaystyle (3)(3)= 2(4)(x+2)$

Simplify both sides of the equation.

9=8x+16 $\displaystyle 9=8x+16$

Subtract 16 from both sides and simplify the equation.

$\displaystyle 9-16=8x+16-16$

-7=8x $\displaystyle -7=8x$

Divide by eight on both sides.

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

The answer is: $x=-\frac{7}{8}$ $\displaystyle x=-\frac{7}{8}$

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Example Question #78 : Proportions

Solve the proportion: $\frac{2}{x+1} = \frac{3}{x+2}$ $\displaystyle \frac{2}{x+1} = \frac{3}{x+2}$

Possible Answers:

$\displaystyle 1$

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

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

$\frac{3}{4}$ $\displaystyle \frac{3}{4}$

$\displaystyle -1$

Correct answer:

$\displaystyle 1$

Explanation:

To solve the proportion, cross multiply both sides of the equation.

$\displaystyle 2(x+2)=3(x+1)$

Distribute the terms to simplify.

$\displaystyle 2x+4=3x+3$

Subtract $\displaystyle 2x$ from both sides.

4=x+3 $\displaystyle 4=x+3$

Subtract three from both sides.

x=1 $\displaystyle x=1$

The answer is: $\displaystyle 1$

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Example Question #79 : Proportions

Solve the proportion: $\frac{3x}{2x+1} = \frac{8}{3}$ $\displaystyle \frac{3x}{2x+1} = \frac{8}{3}$

Possible Answers:

$-\frac{10}{13}$ $\displaystyle -\frac{10}{13}$

$-\frac{5}{3}$ $\displaystyle -\frac{5}{3}$

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

$\textup{No solution.}$ $\displaystyle \textup{No solution.}$

$-\frac{1}{7}$ $\displaystyle -\frac{1}{7}$

Correct answer:

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

Explanation:

Before we cross multiply, we have to make sure to note that there is an $\displaystyle x$ existent in the denominator. Recall that a denominator cannot be zero.

Set the denominator equal to zero and solve for $\displaystyle x$.

2x+1=0 $\displaystyle 2x+1=0$

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

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

The final answer cannot be $x=-\frac{1}{2}$ $\displaystyle x=-\frac{1}{2}$ after solving the proportion.

Cross multiply the fractions given.

$\displaystyle 3(3x)=8(2x+1)$

Simplify by distribution.

$\displaystyle 9x=16x+8$

Subtract $\displaystyle 9x$ on both sides and simplify.

$\displaystyle 9x-9x=16x+8-9x$

0=7x+8 $\displaystyle 0=7x+8$

Subtract $\displaystyle 8$ on both sides.

-8=7x $\displaystyle -8=7x$

Divide by $\displaystyle 7$on both sides.

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

The answer is: $x=-\frac{8}{7}$ $\displaystyle x=-\frac{8}{7}$

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Example Question #80 : Proportions

Solve the proportion: $\frac{3x}{7} = \frac{1}{14}$ $\displaystyle \frac{3x}{7} = \frac{1}{14}$

Possible Answers:

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

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

$\displaystyle 6$

$-\frac{97}{3}$ $\displaystyle -\frac{97}{3}$

$\frac{97}{3}$ $\displaystyle \frac{97}{3}$

Correct answer:

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

Explanation:

Cross multiply both fractions.

$\displaystyle (3x)(14) = 7(1)$

Simplify both sides.

42x=7 $\displaystyle 42x=7$

In order to isolate x, we will need to divide both sides by 42.

$\frac{42x}{42}=\frac{7}{42}$ $\displaystyle \frac{42x}{42}=\frac{7}{42}$

Reduce both fractions on the left and right side.

The answer is: $x= \frac{1}{6}$ $\displaystyle x= \frac{1}{6}$

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Algebra 1 : Proportions

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #71 : Proportions

Example Question #71 : Proportions

Example Question #73 : Proportions

Example Question #74 : Proportions

Example Question #75 : Proportions

Example Question #76 : Proportions

Example Question #77 : Proportions

Example Question #78 : Proportions

Example Question #79 : Proportions

Example Question #80 : Proportions

All Algebra 1 Resources

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