Praxis Math - Understand ratio concepts and use ratio reasoning to solve problems

1

is of which of the following numbers?

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:

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

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.

2

Calculate of .

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:

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

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.

3

is of which of the following numbers?

$133.\bar{3}$

$130.\bar{3}$

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 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.

$x=133.\bar{3}$

4

Calculate of .

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:

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

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: