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GED Math : Complex Operations

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Example Questions

Example Question #51 : Proportions And Percentages

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

Possible Answers:

$\frac{8}{7}$

$\frac{15}{7}$

$\frac{15}{4}$

Correct answer:

Explanation:

Cross-multiply both sides.

8(7) = 4x

Divide by four on both side.

$\frac{8(7) }{4}=\frac{ 4x}{4}$

2(7) =x

Simplify the left side.

x=14

The answer is:

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Example Question #57 : Proportions And Percentages

What is 20% of 45?

Possible Answers:

Correct answer:

Explanation:

To find a percentage of a number, we will multiply the two together. So, we get

$20\% \cdot 45$

$\frac{20}{100} \cdot 45$

We can simplify to make things easier. The zero in 20 and the zero in 100 can cancel. So, we get

$\frac{2}{10} \cdot 45$

$\frac{2}{10} \cdot \frac{45}{1}$

$\frac{2 \cdot 45}{10 \cdot 1}$

$\frac{90}{10}$

Therefore, 20% of 45 is 9.

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Example Question #421 : Numbers And Operations

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

Possible Answers:

$\frac{1}{14}$

$\textup{The answer is not given.}$

$\frac{17}{26}$

$\frac{17}{14}$

$\frac{6}{7}$

Correct answer:

$\frac{1}{14}$

Explanation:

Cross multiply both sides.

3(2x+3) = 4(5x+2)

Distribute both sides.

6x+9 = 20x+8

Subtract on both sides.

6x+9 -6x= 20x+8-6x

9 = 14x+8

Subtract 8 on both sides.

9 -8= 14x+8-8

1=14x

Divide by 14 on both sides.

$\frac{1}{14}=\frac{14x}{14}$

The answer is: $\frac{1}{14}$

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Example Question #422 : Numbers And Operations

What is 15% of 40?

Possible Answers:

Correct answer:

Explanation:

To find a percentage of a whole number, we will multiply the two together. So, we get

$15\% \cdot 40$

$\frac{15}{100} \cdot 40$

$\frac{15}{100} \cdot \frac{40}{1}$

Now, the zero in 100 can cancel the zero in 40. We get

$\frac{15}{10} \cdot \frac{4}{1}$

$\frac{15 \cdot 4}{10 \cdot 1}$

$\frac{60}{10}$

Therefore, 15% of 40 is 6.

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Example Question #61 : Proportions And Percentages

Solve the proportion: $\frac{x}{10} = \frac{5}{2x}$

Possible Answers:

$\pm \frac{1}{4}$

$\pm 2\sqrt5$

$\pm 5$

$\pm \frac{1}{5}$

$\pm 4$

Correct answer:

$\pm 5$

Explanation:

Cross multiply the fractions.

x(2x) = 5(10)

2x^2 =50

Divide by two on both sides.

$\frac{2x^2 }{2}=\frac{50}{2}$

x^2 = 25

Square root both sides.

$\sqrt{x^2 }= \sqrt{25}$

$x=\pm 5$

Verify that both the positive and negative roots will satisfy the solution.

The answer is: $\pm 5$

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Example Question #91 : Complex Operations

What is 25% of 240?

Possible Answers:

215

Correct answer:

Explanation:

To find a percentage of a whole number, we will multiply the two together. So, we get

$25\% \cdot 240$

$\frac{25}{100} \cdot 240$

$\frac{25}{100} \cdot \frac{240}{1}$

Now, the zero in 100 and the zero in 240 can cancel. We get

$\frac{25}{10} \cdot \frac{24}{1}$

$\frac{25 \cdot 24}{10 \cdot 1}$

$\frac{600}{10}$

$\frac{60}{1}$

Therefore, 25% of 240 is 60.

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Example Question #63 : Proportions And Percentages

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

Possible Answers:

$\frac{1}{9}$

$\frac{5}{8}$

$\frac{3}{7}$

$-\frac{3}{7}$

$\frac{3}{2}$

Correct answer:

$-\frac{3}{7}$

Explanation:

Cross multiply the two fractions.

3(3x+1) = 2x

Distribute the terms on the left.

9x+3 = 2x

Subtract from both sides.

9x+3-9x= 2x-9x

3=-7x

Divide by negative seven on both sides.

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

The answer is: $-\frac{3}{7}$

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Example Question #92 : Complex Operations

Solve the proportion: $\frac{5x}{2} = \frac{4x-1}{3}$

Possible Answers:

$\frac{2}{23}$

$-\frac{2}{23}$

$\frac{2}{7}$

$-\frac{2}{7}$

$-\frac{2}{21}$

Correct answer:

$-\frac{2}{7}$

Explanation:

Cross multiply the two fractions.

5x(3) = 2(4x-1)

Expand both sides.

15x = 8x-2

Subtract on both sides.

15x-8x= 8x-2-8x

7x = -2

Divide by seven on both sides.

$\frac{7x }{7}=\frac{ -2}{7}$

The answer is: $-\frac{2}{7}$

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Example Question #91 : Complex Operations

Solve the proportion: $\frac{x+3}{2} = \frac{2x-9}{3}$

Possible Answers:

Correct answer:

Explanation:

Cross multiply the fractions.

3(x+3) = 2(2x-9)

3x+9 = 4x-18

Subtract from both sides.

3x+9 -3x= 4x-18-3x

9= x-18

Add 18 on both sides.

9+18= x-18+18

27 =x

The answer is:

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Example Question #66 : Proportions And Percentages

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

Possible Answers:

$-\frac{4}{3}$

$-\frac{3}{4}$

$\frac{14}{3}$

$-\frac{14}{3}$

$\frac{3}{4}$

Correct answer:

$\frac{14}{3}$

Explanation:

Cross multiply the two fractions.

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

Expand both sides.

6x-18 = 10

Add 18 on both sides.

6x-18 +18= 10+18

6x = 28

Divide by 6 on both sides.

$\frac{6x }{6}= \frac{28}{6}$

Reduce both fractions.

The answer is: $\frac{14}{3}$

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GED Math : Complex Operations

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #51 : Proportions And Percentages

Example Question #57 : Proportions And Percentages

Example Question #421 : Numbers And Operations

Example Question #422 : Numbers And Operations

Example Question #61 : Proportions And Percentages

Example Question #91 : Complex Operations

Example Question #63 : Proportions And Percentages

Example Question #92 : Complex Operations

Example Question #91 : Complex Operations

Example Question #66 : Proportions And Percentages

All GED Math Resources

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