# Praxis Math : Number and Quantity

## Example Questions

### Example Question #1 : Number And Quantity

is  of which of the following numbers?

Possible Answers:

Correct answer:

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:

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:

We can cross multiply and solve for the unknown variable.

Rewrite.

Simplify.

Divide both sides of the equation by .

Solve.

### Example Question #2 : Ratios And Proportional Relationships

is  of which of the following numbers?

Possible Answers:

Correct answer:

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:

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:

We can cross multiply and solve for the unknown variable.

Rewrite.

Simplify.

Divide both sides of the equation by .

Solve.

### Example Question #1 : Number And Quantity

Calculate  of .

Possible Answers:

Correct answer:

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:

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:

We can cross multiply and solve for the unknown variable.

Rewrite.

Simplify.

Divide both sides of the equation by .

Solve.

### Example Question #1 : Number And Quantity

Calculate  of .

Possible Answers:

Correct answer:

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:

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:

We can cross multiply and solve for the unknown variable.

Rewrite.

Simplify.

Divide both sides of the equation by .

Solve.

### Example Question #1 : Number And Quantity

Solve:

Possible Answers:

Cannot be determined

Correct answer:

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:

Let's use this rule to solve our problem.

Rewrite.

Solve.

Convert to a mixed number.

### Example Question #1 : Number And Quantity

Solve:

Possible Answers:

Correct answer:

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:

Let's use this rule to solve our problem.

Rewrite.

Cross out like terms.

Solve.

### Example Question #1 : Number And Quantity

Solve:

Possible Answers:

Correct answer:

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:

Let's use this rule to solve our problem.

Rewrite.

Cross out like terms.

Solve.