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GED Math : Complex Operations

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Example Questions

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Example Question #47 : Proportions And Percentages

What is 90% of 750?

Possible Answers:

650

595

575

675

660

Correct answer:

675

Explanation:

To find a percentage of a whole number, we will multiply the percentage by the whole number.

So, we get

$90\% \cdot 750$

$\frac{90}{100} \cdot 750$

$\frac{90}{100} \cdot \frac{750}{1}$

To simplify, we can cancel. The zeros will cancel each other out. We get

$\frac{9}{10} \cdot \frac{750}{1}$

$\frac{9}{1} \cdot \frac{75}{1}$

$\frac{9 \cdot 75}{1 \cdot 1}$

$\frac{675}{1}$

675

Therefore, 90% of 750 is 675.

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Example Question #48 : Proportions And Percentages

Solve the proportion: $\frac{2x}{5} = \frac{7}{3}$

Possible Answers:

$\frac{6}{35}$

$\frac{7}{3}$

$\frac{ 35}{6}$

Correct answer:

$\frac{ 35}{6}$

Explanation:

Cross multiply the terms.

(2x)(3) = 7(5)

6x = 35

Divide by six on both sides.

$\frac{6x }{6}=\frac{ 35}{6}$

The answer is: $\frac{ 35}{6}$

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Example Question #411 : Ged Math

Solve the proportion: $\frac{3x}{4} = \frac{7x+1}{9}$

Possible Answers:

$-\frac{4}{55}$

$\frac{4}{55}$

$-\frac{1}{4}$

Correct answer:

Explanation:

Cross multiply the terms.

(3x)(9)= (7x+1)(4)

Distribute the terms.

27x = 28x+4

Subtract 28x on both sides.

27x -28x= 28x+4-28x

-x = 4

Divide or multiply by negative one to isolate the x-variable.

-x (-1)= 4(-1)

The answer is: x=-4

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Example Question #50 : Proportions And Percentages

Solve the proportion: $\frac{4}{3} =\frac{8x}{5}$

Possible Answers:

$\frac{5}{6}$

$\frac{6}{5}$

$\frac{11}{20}$

$\frac{20}{11}$

$\frac{3}{8}$

Correct answer:

$\frac{5}{6}$

Explanation:

Cross multiply the terms.

4(5) = 3(8x)

20 = 24x

Divide by 24 on both sides.

$\frac{20}{24} =\frac{ 24x}{24}$

Reduce the fractions.

The answer is: $\frac{5}{6}$

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Example Question #51 : Proportions And Percentages

Solve the proportion: $\frac{2}{x} = \frac{19}{3}$

Possible Answers:

$\frac{19}{3}$

$\frac{6}{19}$

$\frac{19}{6}$

$\frac{5}{19}$

$\frac{38}{3}$

Correct answer:

$\frac{6}{19}$

Explanation:

To solve for the unknown variable, we will need to cross multiply both sides.

2(3) =19x

6 = 19x

Divide by 19 on both sides.

$\frac{6}{19} =\frac{ 19x}{19}$

The answer is: $\frac{6}{19}$

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Example Question #81 : Complex Operations

What percent of 60 is 5?

Possible Answers:

$4\frac{1}{2}\%$

$\frac{1}{12}\%$

$6\frac{3}{4}\%$

$7\frac{2}{3}\%$

$8\frac{1}{3}\%$

Correct answer:

$8\frac{1}{3}\%$

Explanation:

Set up an equation such that some number out of 100 times 60 is equal to 5.

$x\% \cdot 60 = 5$

$\frac{x}{100}\cdot 60 = 5$

$\frac{3}{5}x = 5$

Multiply both sides by $\frac{5}{3}$ .

$\frac{3}{5}x \cdot \frac{5}{3}= 5 \cdot \frac{5}{3}$

$x=\frac{25}{3} = 8\frac{1}{3}$

The answer is: $8\frac{1}{3}\%$

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Example Question #53 : Proportions And Percentages

What is $44\%$ of ?

Possible Answers:

3212

60.27

32.12

163.63

31.22

Correct answer:

32.12

Explanation:

For percentage problems, the following is the easiest way to get to the correct answer. Always convert the following:

"is":

"of":

For your problem, it is very easy, for you are merely looking for $44\%$ of . Remember that $44\%$ is 0.44 . Therefore, your answer is merely:

0.44*73=32.12

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Example Question #54 : Proportions And Percentages

What is $58\%$ of $63\%$ of $124\%$ of 891 ? Round to the nearest hundredth.

Possible Answers:

375.22

322.87

403.71

421.22

544.85

Correct answer:

403.71

Explanation:

For percentage problems, the following is the easiest way to get to the correct answer. Always convert the following:

"is":

"of":

For your problem, it is relatively easy. First convert your percentages into the following decimal values:

$58\%:0.58$

$63\%:0.63$

$124\%:1.24$

Therefore, your answer is merely:

0.58*0.63*1.24*891=403.708536

Round this to 403.71

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Example Question #55 : Proportions And Percentages

What is 10% of 140 ?

Possible Answers:

130

Correct answer:

Explanation:

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

$10\% \cdot 140$

$\frac{10}{100} \cdot 140$

$\frac{10}{100} \cdot \frac{140}{1}$

Now, the zero in the 10 and the 100 can cancel. We get

$\frac{1}{10} \cdot \frac{140}{1}$

The zero in 10 and in 140 can cancel. We get

$\frac{1}{1} \cdot \frac{14}{1}$

Now, we can multiply.

$\frac{1 \cdot 14}{1 \cdot 1}$

$\frac{14}{1}$

Therefore, 10% of 140 is 14.

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Example Question #56 : Proportions And Percentages

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

Possible Answers:

$\frac{4}{5}$

$-\frac{2}{13}$

$-\frac{6}{7}$

$-\frac{18}{7}$

$\frac{3}{2}$

Correct answer:

$-\frac{18}{7}$

Explanation:

Cross multiply to solve.

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

10x = 3x-18

Subtract from both sides.

10x -3x= 3x-18-3x

7x = -18

Divide by 7 on both sides.

$\frac{7x }{7}=\frac{ -18}{7}$

The answer is: $-\frac{18}{7}$

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GED Math : Complex Operations

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #47 : Proportions And Percentages

Example Question #48 : Proportions And Percentages

Example Question #411 : Ged Math

Example Question #50 : Proportions And Percentages

Example Question #51 : Proportions And Percentages

Example Question #81 : Complex Operations

Example Question #53 : Proportions And Percentages

Example Question #54 : Proportions And Percentages

Example Question #55 : Proportions And Percentages

Example Question #56 : Proportions And Percentages

All GED Math Resources

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