Praxis Core Skills: Math

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Questions 1 - 10

1

Solve:

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

$\frac{2}{15}$

$\frac{3}{13}$

$\frac{2}{11}$

$\frac{4}{15}$

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.

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

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.

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

2

Solve for .

Cannot be determined

Explanation

In order to solve for the variable, , 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.

Add to both sides of the equation.

Simplify.

Divide both sides of the equation by .

$\frac{9x}{9}=\frac{126}{9}$

Solve.

3

Solve for .

Cannot be determined

Explanation

In order to solve for the variable, , 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.

Add to both sides of the equation.

Simplify.

Divide both sides of the equation by .

$\frac{9x}{9}=\frac{126}{9}$

Solve.

4

Solve:

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

$\frac{2}{15}$

$\frac{3}{13}$

$\frac{2}{11}$

$\frac{4}{15}$

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.

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

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.

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

5

Solve:

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

$\frac{2}{15}$

$\frac{3}{13}$

$\frac{2}{11}$

$\frac{4}{15}$

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.

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

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.

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

6

Solve:

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

$\frac{2}{15}$

$\frac{3}{13}$

$\frac{2}{11}$

$\frac{4}{15}$

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.

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

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.

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

7

Solve for .

Cannot be determined

Explanation

In order to solve for the variable, , 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.

Add to both sides of the equation.

Simplify.

Divide both sides of the equation by .

$\frac{9x}{9}=\frac{126}{9}$

Solve.

8

Solve for .

Cannot be determined

Explanation

In order to solve for the variable, , 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.

Add to both sides of the equation.

Simplify.

Divide both sides of the equation by .

$\frac{9x}{9}=\frac{126}{9}$

Solve.

9

Solve for .

Cannot be determined

Explanation

In order to solve for the variable, , 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.

Add to both sides of the equation.

Simplify.

Divide both sides of the equation by .

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

Solve.

10

Solve for .

Cannot be determined

Explanation

In order to solve for the variable, , 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.

Subtract from both sides of the equation.

Simplify.

Divide both sides of the equation by .

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

Solve.

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