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Praxis Math : Praxis Core Skills: Math

Study concepts, example questions & explanations for Praxis Math

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9 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Number And Quantity

$\displaystyle 24$ is $18\%$ $\displaystyle 18\%$ of which of the following numbers?

Possible Answers:

2400 $\displaystyle 2400$

120.2 $\displaystyle 120.2$

$133.\bar{3}$ $\displaystyle 133.\bar{3}$

1800 $\displaystyle 1800$

$130.\bar{3}$ $\displaystyle 130.\bar{3}$

Correct answer:

$133.\bar{3}$ $\displaystyle 133.\bar{3}$

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:

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

Now, we need to create a relationship between our known value and the number we need to calculate. In the problem, we know that $\displaystyle 24$ is $18\%$ $\displaystyle 18\%$ of another number we will name, $\displaystyle x$. Using this information we need to construct a proportion. We can write the following proportion:

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

We can cross multiply and solve for the unknown variable.

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

Rewrite.

$24\times100=18\times x$ $\displaystyle 24\times100=18\times x$

Simplify.

$\displaystyle 2400=18x$

Divide both sides of the equation by $\displaystyle 18$.

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

Solve.

$x=133.\bar{3}$ $\displaystyle x=133.\bar{3}$

Report an Error

Example Question #2 : Number And Quantity

$\displaystyle 30$ is $60\%$ $\displaystyle 60\%$ of which of the following numbers?

Possible Answers:

$\displaystyle 6$

$\displaystyle 50$

$\displaystyle 60$

$\displaystyle 5$

$\displaystyle 30$

Correct answer:

$\displaystyle 50$

Explanation:

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

Now, we need to create a relationship between our known value and the number we need to calculate. In the problem, we know that $\displaystyle 30$ is $60\%$ $\displaystyle 60\%$ of another number we will name, $\displaystyle x$. Using this information we need to construct a proportion. We can write the following proportion:

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

We can cross multiply and solve for the unknown variable.

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

Rewrite.

$30\times100=60\times x$ $\displaystyle 30\times100=60\times x$

Simplify.

$\displaystyle 3000=60x$

Divide both sides of the equation by $\displaystyle 60$.

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

Solve.

x=50 $\displaystyle x=50$

Report an Error

Example Question #1 : Praxis Core Skills: Math

Calculate $22\%$ $\displaystyle 22\%$ of 188 $\displaystyle 188$.

Possible Answers:

41.36 $\displaystyle 41.36$

13.64 $\displaystyle 13.64$

41.31 $\displaystyle 41.31$

31.36 $\displaystyle 31.36$

31.46 $\displaystyle 31.46$

Correct answer:

41.36 $\displaystyle 41.36$

Explanation:

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

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 $\displaystyle 188$ and we need to calculate $22\%$ $\displaystyle 22\%$ of this number. We will name this variable, $\displaystyle x$. Using this information we need to construct a proportion. We can write the following proportion:

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

We can cross multiply and solve for the unknown variable.

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

Rewrite.

$100\times x=22\times 188$ $\displaystyle 100\times x=22\times 188$

Simplify.

$\displaystyle 100x=4136$

Divide both sides of the equation by 100 $\displaystyle 100$.

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

Solve.

x=41.36 $\displaystyle x=41.36$

Report an Error

Example Question #2 : Praxis Core Skills: Math

Calculate $20\%$ $\displaystyle 20\%$ of 300 $\displaystyle 300$.

Possible Answers:

600 $\displaystyle 600$

$\displaystyle 6$

$\displaystyle 3$

$\displaystyle 30$

$\displaystyle 60$

Correct answer:

$\displaystyle 60$

Explanation:

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

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 $\displaystyle 300$ and we need to calculate $20\%$ $\displaystyle 20\%$ of this number. We will name this variable, $\displaystyle x$. Using this information we need to construct a proportion. We can write the following proportion:

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

We can cross multiply and solve for the unknown variable.

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

Rewrite.

$100\times x=20\times 300$ $\displaystyle 100\times x=20\times 300$

Simplify.

$\displaystyle 100x=6000$

Divide both sides of the equation by 100 $\displaystyle 100$.

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

Solve.

x=60 $\displaystyle x=60$

Report an Error

Example Question #1 : Number And Quantity

Solve:

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

Possible Answers:

$3\tfrac{1}{3}$ $\displaystyle 3\tfrac{1}{3}$

$3\tfrac{2}{3}$ $\displaystyle 3\tfrac{2}{3}$

$2\tfrac{2}{3}$ $\displaystyle 2\tfrac{2}{3}$

Cannot be determined

$2\tfrac{1}{3}$ $\displaystyle 2\tfrac{1}{3}$

Correct answer:

$2\tfrac{2}{3}$ $\displaystyle 2\tfrac{2}{3}$

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:

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

Let's use this rule to solve our problem.

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

Rewrite.

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

Solve.

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

Convert to a mixed number.

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

Report an Error

Example Question #3 : Praxis Core Skills: Math

Solve:

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

Possible Answers:

$\frac{2}{15}$ $\displaystyle \frac{2}{15}$

$\frac{4}{15}$ $\displaystyle \frac{4}{15}$

$\displaystyle 2$

$\frac{2}{11}$ $\displaystyle \frac{2}{11}$

$\frac{3}{13}$ $\displaystyle \frac{3}{13}$

Correct answer:

$\frac{2}{15}$ $\displaystyle \frac{2}{15}$

Explanation:

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

Let's use this rule to solve our problem.

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

Rewrite.

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

Cross out like terms.

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

Solve.

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

Report an Error

Example Question #1 : Number And Quantity

Solve:

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

Possible Answers:

$\frac{5}{12}$ $\displaystyle \frac{5}{12}$

$\frac{5}{13}$ $\displaystyle \frac{5}{13}$

$\frac{6}{13}$ $\displaystyle \frac{6}{13}$

$\frac{6}{11}$ $\displaystyle \frac{6}{11}$

$\frac{5}{11}$ $\displaystyle \frac{5}{11}$

Correct answer:

$\frac{5}{12}$ $\displaystyle \frac{5}{12}$

Explanation:

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

Let's use this rule to solve our problem.

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

Rewrite.

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

Cross out like terms.

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

Solve.

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

Report an Error

Example Question #4 : Praxis Core Skills: Math

Solve for $\displaystyle x$.

$\displaystyle 18+4x=98$

Possible Answers:

$\displaystyle 4$

Cannot be determined

$\displaystyle 10$

$\displaystyle 40$

$\displaystyle 20$

Correct answer:

$\displaystyle 20$

Explanation:

In order to solve for the variable, $\displaystyle x$, we need to isolate it on the left side of the equation. We will do this by reversing the operations done to the variable by performing the opposite of each operation on both sides of the equation.

Let's begin by rewriting the given equation.

$\displaystyle 18+4x=98$

Subtract $\displaystyle 18$ from both sides of the equation.

$\displaystyle 18-18+4x=98-18$

Simplify.

4x=80 $\displaystyle 4x=80$

Divide both sides of the equation by $\displaystyle 4$.

$\frac{4x}{4}=\frac{80}{4}$ $\displaystyle \frac{4x}{4}=\frac{80}{4}$

Solve.

x=20 $\displaystyle x=20$

Report an Error

Example Question #5 : Praxis Core Skills: Math

Solve for $\displaystyle x$.

$\displaystyle 21+5x=71$

Possible Answers:

$\displaystyle 15$

$\displaystyle 5$

Cannot be determined

$\displaystyle 10$

$\displaystyle 25$

Correct answer:

$\displaystyle 10$

Explanation:

Let's begin by rewriting the given equation.

$\displaystyle 21+5x=71$

Subtract $\displaystyle 21$ from both sides of the equation.

$\displaystyle 21-21+5x=71-21$

Simplify.

5x=50 $\displaystyle 5x=50$

Divide both sides of the equation by $\displaystyle 5$.

$\frac{5x}{5}=\frac{50}{5}$ $\displaystyle \frac{5x}{5}=\frac{50}{5}$

Solve.

x=10 $\displaystyle x=10$

Report an Error

Example Question #6 : Praxis Core Skills: Math

Solve for $\displaystyle x$.

$\displaystyle 6x-22=44$

Possible Answers:

Cannot be determined

$\displaystyle 21$

$\displaystyle 11$

$\displaystyle 9$

$\displaystyle 13$

Correct answer:

$\displaystyle 11$

Explanation:

Let's begin by rewriting the given equation.

$\displaystyle 6x-22=44$

Add $\displaystyle 22$ to both sides of the equation.

$\displaystyle 6x-22+22=44+22$

Simplify.

6x=66 $\displaystyle 6x=66$

Divide both sides of the equation by $\displaystyle 6$.

$\frac{6x}{6}=\frac{66}{6}$ $\displaystyle \frac{6x}{6}=\frac{66}{6}$

Solve.

x=11 $\displaystyle x=11$

Report an Error

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Praxis Math : Praxis Core Skills: Math

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 #1 : Praxis Core Skills: Math

Example Question #2 : Praxis Core Skills: Math

Example Question #1 : Number And Quantity

Example Question #3 : Praxis Core Skills: Math

Example Question #1 : Number And Quantity

Example Question #4 : Praxis Core Skills: Math

Example Question #5 : Praxis Core Skills: Math

Example Question #6 : Praxis Core Skills: Math

All Praxis Math Resources

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