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Praxis Math : Number and Quantity

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Example Questions

Example Question #1 : Number And Quantity

is $18\%$ of which of the following numbers?

Possible Answers:

120.2

$130.\bar{3}$

1800

2400

$133.\bar{3}$

Correct answer:

$133.\bar{3}$

Explanation:

In order to solve this problem, we need to understand the relationship between percentages and ratios. Percents can be written as a value over a whole. In this case , our whole is one-hundred percent; therefore, we can write the following:

$18\%=\frac{18}{100}$

Now, we need to create a relationship between our known value and the number we need to calculate. In the problem, we know that is $18\%$ of another number we will name, . Using this information we need to construct a proportion. We can write the following proportion:

$\frac{24}{x}=\frac{18}{100}$

We can cross multiply and solve for the unknown variable.

$\frac{24}{x}\times\frac{18}{100}$

Rewrite.

$24\times100=18\times x$

Simplify.

2400=18x

Divide both sides of the equation by .

$\frac{2400}{18}=\frac{18x}{18}$

Solve.

$x=133.\bar{3}$

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Example Question #2 : Number And Quantity

is $60\%$ of which of the following numbers?

Possible Answers:

Correct answer:

Explanation:

$60\%=\frac{60}{100}$

Now, we need to create a relationship between our known value and the number we need to calculate. In the problem, we know that is $60\%$ of another number we will name, . Using this information we need to construct a proportion. We can write the following proportion:

$\frac{30}{x}=\frac{60}{100}$

We can cross multiply and solve for the unknown variable.

$\frac{30}{x}\times\frac{60}{100}$

Rewrite.

$30\times100=60\times x$

Simplify.

3000=60x

Divide both sides of the equation by .

$\frac{3000}{60}=\frac{60x}{60}$

Solve.

x=50

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Example Question #3 : Number And Quantity

Calculate $22\%$ of 188 .

Possible Answers:

41.36

13.64

31.36

31.46

41.31

Correct answer:

41.36

Explanation:

$22\%=\frac{22}{100}$

Now, we need to create a relationship between our known value and the number we need to calculate. In the problem, we know that ore whole number is 188 and we need to calculate $22\%$ of this number. We will name this variable, . Using this information we need to construct a proportion. We can write the following proportion:

$\frac{x}{188}=\frac{22}{100}$

We can cross multiply and solve for the unknown variable.

$\frac{x}{188}\times\frac{22}{100}$

Rewrite.

$100\times x=22\times 188$

Simplify.

100x=4136

Divide both sides of the equation by 100 .

$\frac{4136}{100}=\frac{100x}{100}$

Solve.

x=41.36

Report an Error

Example Question #4 : Number And Quantity

Calculate $20\%$ of 300 .

Possible Answers:

600

Correct answer:

Explanation:

$20\%=\frac{20}{100}$

Now, we need to create a relationship between our known value and the number we need to calculate. In the problem, we know that ore whole number is 300 and we need to calculate $20\%$ of this number. We will name this variable, . Using this information we need to construct a proportion. We can write the following proportion:

$\frac{x}{300}=\frac{20}{100}$

We can cross multiply and solve for the unknown variable.

$\frac{x}{300}\times\frac{20}{100}$

Rewrite.

$100\times x=20\times 300$

Simplify.

100x=6000

Divide both sides of the equation by 100 .

$\frac{6000}{100}=\frac{100x}{100}$

Solve.

x=60

Report an Error

Example Question #5 : Number And Quantity

Solve:

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

Possible Answers:

$2\tfrac{2}{3}$

$3\tfrac{1}{3}$

$3\tfrac{2}{3}$

$2\tfrac{1}{3}$

Cannot be determined

Correct answer:

$2\tfrac{2}{3}$

Explanation:

In order to divide a fraction by a second fraction, we can change the problem to a division problem by multiplying the first fraction by the reciprocal of the second fraction. It can be written algebraically in the following way:

$\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a}{b}\times\frac{d}{c}$

Let's use this rule to solve our problem.

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

Rewrite.

$\frac{\frac{1}{3}}{\frac{1}{8}}=\frac{1}{3}\times\frac{8}{1}$

Solve.

$\frac{1}{3}\times\frac{8}{1}=\frac{8}{3}$

Convert to a mixed number.

$\frac{8}{3}=2\tfrac{2}{3}$

Report an Error

Example Question #6 : Number And Quantity

Solve:

$\frac{\frac{2}{21}}{\frac{5}{7}}$

Possible Answers:

$\frac{2}{15}$

$\frac{4}{15}$

$\frac{2}{11}$

$\frac{3}{13}$

Correct answer:

$\frac{2}{15}$

Explanation:

$\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a}{b}\times\frac{d}{c}$

Let's use this rule to solve our problem.

$\frac{\frac{2}{21}}{\frac{5}{7}}$

Rewrite.

$\frac{\frac{2}{21}}{\frac{5}{7}}=\frac{2}{21}\times\frac{7}{5}$

Cross out like terms.

$\frac{2}{21}\times\frac{7}{5}=\frac{2}{3}\times\frac{1}{5}$

Solve.

$\frac{2}{3}\times\frac{1}{5}=\frac{2}{15}$

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Example Question #7 : Number And Quantity

Solve:

$\frac{\frac{5}{16}}{\frac{3}{4}}$

Possible Answers:

$\frac{6}{11}$

$\frac{5}{11}$

$\frac{5}{12}$

$\frac{6}{13}$

$\frac{5}{13}$

Correct answer:

$\frac{5}{12}$

Explanation:

$\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a}{b}\times\frac{d}{c}$

Let's use this rule to solve our problem.

$\frac{\frac{5}{16}}{\frac{3}{4}}$

Rewrite.

$\frac{\frac{5}{16}}{\frac{3}{4}}=\frac{5}{16}\times\frac{4}{3}$

Cross out like terms.

$\frac{5}{16}\times\frac{4}{3}=\frac{5}{4}\times\frac{1}{3}$

Solve.

$\frac{5}{4}\times\frac{1}{3}=\frac{5}{12}$

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Praxis Math : Number and Quantity

Study concepts, example questions & explanations for Praxis Math

All Praxis Math Resources

Example Questions

Example Question #1 : Number And Quantity

Example Question #2 : Number And Quantity

Example Question #3 : Number And Quantity

Example Question #4 : Number And Quantity

Example Question #5 : Number And Quantity

Example Question #6 : Number And Quantity

Example Question #7 : Number And Quantity

All Praxis Math Resources

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