Number and Quantity - Praxis Math

Card 0 of 28

Question

is of which of the following numbers?

Answer

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 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.

Divide both sides of the equation by .

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

Solve.

$x=133.\bar{3}$

Compare your answer with the correct one above

Question

is of which of the following numbers?

Answer

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:

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

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 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.

Divide both sides of the equation by .

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

Solve.

Compare your answer with the correct one above

Question

Calculate of .

Answer

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:

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

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 and we need to calculate 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.

Divide both sides of the equation by .

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

Solve.

Compare your answer with the correct one above

Question

Calculate of .

Answer

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:

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

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 and we need to calculate 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.

Divide both sides of the equation by .

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

Solve.

Compare your answer with the correct one above

Question

Solve:

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

Answer

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.

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

Compare your answer with the correct one above

Question

Solve:

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

Answer

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.

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

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.

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

Compare your answer with the correct one above

Question

Solve:

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

Answer

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.

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

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.

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

Compare your answer with the correct one above

Question

is of which of the following numbers?

Answer

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 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.

Divide both sides of the equation by .

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

Solve.

$x=133.\bar{3}$

Compare your answer with the correct one above

Question

is of which of the following numbers?

Answer

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:

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

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 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.

Divide both sides of the equation by .

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

Solve.

Compare your answer with the correct one above

Question

Calculate of .

Answer

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:

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

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 and we need to calculate 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.

Divide both sides of the equation by .

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

Solve.

Compare your answer with the correct one above

Question

Calculate of .

Answer

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:

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

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 and we need to calculate 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.

Divide both sides of the equation by .

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

Solve.

Compare your answer with the correct one above

Question

Solve:

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

Answer

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.

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

Compare your answer with the correct one above

Question

Solve:

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

Answer

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.

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

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.

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

Compare your answer with the correct one above

Question

Solve:

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

Answer

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.

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

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.

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

Compare your answer with the correct one above

Question

is of which of the following numbers?

Answer

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 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.

Divide both sides of the equation by .

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

Solve.

$x=133.\bar{3}$

Compare your answer with the correct one above

Question

is of which of the following numbers?

Answer

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:

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

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 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.

Divide both sides of the equation by .

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

Solve.

Compare your answer with the correct one above

Question

Calculate of .

Answer

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:

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

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 and we need to calculate 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.

Divide both sides of the equation by .

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

Solve.

Compare your answer with the correct one above

Question

Calculate of .

Answer

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:

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

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 and we need to calculate 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.

Divide both sides of the equation by .

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

Solve.

Compare your answer with the correct one above

Question

Solve:

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

Answer

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.

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

Compare your answer with the correct one above

Question

Solve:

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

Answer

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.

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

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.

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

Compare your answer with the correct one above

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