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Algebra 1 : Proportions

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Example Question #91 : Proportions

Solve the proportion: $\frac{2\sqrt5}{x} = \frac{\sqrt{10}}{2}$

Possible Answers:

$2\sqrt2$

$2\sqrt5$

$4\sqrt5$

$\sqrt5$

$5\sqrt2$

Correct answer:

$2\sqrt2$

Explanation:

Cross multiply both fractions.

$2(2)\sqrt 5 = x\sqrt {10}$

Simplify the left side and divide by square root ten on both sides.

$\frac{4\sqrt 5 }{\sqrt {10}}= \frac{x\sqrt {10}}{\sqrt {10}}$

Cancel out the right side. The equation becomes:

$x=\frac{4\sqrt 5 }{\sqrt {10}}$

Rationalize the denominator by multiplying this fraction by $\frac{\sqrt {10}}{\sqrt {10}}$ .

$x=\frac{4\sqrt{5}}{\sqrt {10}} \cdot \frac{\sqrt {10}}{\sqrt {10}} = \frac{4\sqrt{50}}{10}= \frac{4\cdot 5\sqrt{2}}{10} = \frac{20\sqrt2}{10}$

Divide the coefficients.

The answer is: $2\sqrt2$

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Example Question #92 : Proportions

Solve the proportion: $\frac{x}{8} = \frac{3}{5}$

Possible Answers:

$\frac{24}{5}$

$\frac{40}{3}$

$\frac{3}{40}$

$\frac{19}{40}$

$\frac{5}{24}$

Correct answer:

$\frac{24}{5}$

Explanation:

To solve for , cross multiply both sides.

5x=24

Divide both sides by five.

$\frac{5x}{5}=\frac{24}{5}$

Simplify the left side.

The answer is: $x=\frac{24}{5}$

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Example Question #91 : Proportions

Solve the proportion: $\frac{5x}{6}= \frac{7}{4}$

Possible Answers:

$\frac{13}{20}$

$\frac{21}{5}$

$\frac{21}{10}$

$\frac{14}{9}$

$\frac{9}{5}$

Correct answer:

$\frac{21}{10}$

Explanation:

Cross multiply both fractions.

(5x)(4)=(7)(6)

Simplify both sides.

20x=42

Divide by twenty on both sides.

$\frac{20x}{20}=\frac{42}{20}$

Simplify the left side, and rewrite the right side using common factors. Both the numerator and denominator are divisible by two.

$x=\frac{42}{20} = \frac{2\times 21}{2 \times 10}$

Cancel the twos.

The answer is: $\frac{21}{10}$

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Example Question #94 : Proportions

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

Possible Answers:

$\frac{1}{5}$

$-\frac{25}{3}$

$-\frac{7}{6}$

$-\frac{3}{10}$

Correct answer:

Explanation:

Cross multiply both sides.

5(3x+3) = 6x(2)

Simplify both sides.

15x+15 = 12x

Subtract 15x on both sides.

15x+15 -15x= 12x-15x

Simplify both sides.

15 = -3x

Divide by negative three on both sides.

$\frac{15}{-3} =\frac{ -3x}{-3}$

Simplify both fractions.

The answer is:

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Example Question #95 : Proportions

Solve the proportion: $\frac{x}{2} = \frac{-3(x+2)}{5}$

Possible Answers:

$-\frac{12}{11}$

$-\frac{2}{11}$

$-\frac{1}{5}$

$-\frac{11}{12}$

$\frac{2}{11}$

Correct answer:

$-\frac{12}{11}$

Explanation:

Cross multiply the two fractions.

5x = -3(2)(x+2)

Simplify the right side by distribution.

5x = -6(x+2)

Distribute the negative six through both terms in the parentheses.

5x=-6x-12

Add on both sides to group the x-variable.

5x+6x=-6x-12+6x

Simplify both sides.

11x= -12

Divide by 11 on both sides.

$\frac{11x}{11}= \frac{-12}{11}$

The answer is: $x=-\frac{12}{11}$

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Example Question #96 : Proportions

Solve the proportion: $\frac{7}{2x} = \frac{3}{x+2}$

Possible Answers:

$\frac{7}{13}$

$-\frac{7}{15}$

Correct answer:

Explanation:

Solve by cross multiplying both fractions.

7(x+2)= (2x)(3)

Distribute the seven across both terms of the binomial on the left side. Simplify the right side.

7x+14=6x

Subtract on both sides.

7x+14-6x=6x-6x

x+14=0

Subtract 14 on both sides and simplify.

x+14-14=0-14

The answer is: x=-14

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Example Question #97 : Proportions

Solve the proportion: $\frac{x} {2\sqrt5}= \frac{3\sqrt2}{\sqrt3}$

Possible Answers:

$2\sqrt{30}$

$3\sqrt5$

$2\sqrt{15}$

$\sqrt{15}$

$5\sqrt3$

Correct answer:

$2\sqrt{30}$

Explanation:

Cross multiply both sides.

$x\sqrt3 = 3\sqrt 2 \cdot 2\sqrt5$

Simplify the right side. Multiply the integers together, and multiply the terms inside the square root together.

$x\sqrt3 = 6\sqrt{10}$

Divide both sides by square root three.

$\frac{x\sqrt3 }{\sqrt3}= \frac{6\sqrt{10}}{\sqrt3}$

$x= \frac{6\sqrt{10}}{\sqrt3}$

Rationalize the right side of the equation.

$x= \frac{6\sqrt{10}}{\sqrt3} \cdot \frac{\sqrt3}{\sqrt3}$

Multiply the numerator with the numerator and denominator with denominator.

$x= \frac{6\sqrt{10}}{\sqrt3} \cdot \frac{\sqrt3}{\sqrt3} = \frac{6\sqrt{30}}{3}= 2\sqrt{30}$

The answer is: $2\sqrt{30}$

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Example Question #98 : Proportions

Solve the proportion: $\frac{x+5}{3} = \frac{x}{7}$

Possible Answers:

$\frac{41}{4}$

$\frac{35}{4}$

$-\frac{35}{4}$

$\frac{5}{4}$

$-\frac{5}{4}$

Correct answer:

$-\frac{35}{4}$

Explanation:

Cross multiply the fractions.

7(x+5)=3x

Distribute the integer to both terms in the binomial.

7x+35 = 3x

Subtract from both sides.

7x+35 -35= 3x-35

Simplify both sides.

7x=3x-35

Subtract on both sides.

7x-3x=3x-35-3x

Simplify both sides.

4x=-35

Divide by four on both sides.

$\frac{4x}{4}=\frac{-35}{4}$

Simplify the left side.

The answer is: $x=-\frac{35}{4}$

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Example Question #99 : Proportions

Solve the proportion: $-\frac{6}{x} = \frac{10}{x+1}$

Possible Answers:

$\frac{3}{8}$

$\frac{3}{2}$

$-\frac{3}{8}$

$-\frac{3}{2}$

Correct answer:

$-\frac{3}{8}$

Explanation:

Solve by cross multiplying both fractions. We can choose to multiply on both sides of the equation so that we do not have to distribute a negative six across both terms the binomial.

6(x+1) = -10x

Simplify the left side.

6x+6=-10x

Subtract six from both sides.

6x+6-6=-10x-6

6x=-10x-6

Add 10x on both sides.

6x+10x=-10x-6+10x

16x=-6

Divide by 16 on both sides.

$\frac{16x}{16}=\frac{-6}{16}$

Simplify both sides.

The answer is: $x=-\frac{3}{8}$

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Example Question #100 : Proportions

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

Possible Answers:

$\frac{3}{2}$

$\frac{6}{5}$

$\frac{3}{4}$

Correct answer:

Explanation:

Solve by cross multiplying both fractions.

3(4-x)=9x

Simplify the left side. Distribute the three across the binomial.

12-3x= 9x

Add on both sides.

12=12x

Divide by twelve on both sides.

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

The answer is: x=1

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Algebra 1 : Proportions

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #91 : Proportions

Example Question #92 : Proportions

Example Question #91 : Proportions

Example Question #94 : Proportions

Example Question #95 : Proportions

Example Question #96 : Proportions

Example Question #97 : Proportions

Example Question #98 : Proportions

Example Question #99 : Proportions

Example Question #100 : Proportions

All Algebra 1 Resources

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