# 45 percent of 72?

### Solution for 'What is 45% of 72?'

In all the following examples consider that:

- The percentage figure is represented by X%
- The whole amount is represented by W
- The portion amount or part is represented by P

#### Solution Steps

The following question is of the type "How much X percent of W", where W is the whole amount and X is the percentage figure or rate".

Let's say that you need to find 45 percent of 72. What are the steps?

Step 1: first determine the value of the whole amount. We assume that the whole amount is 72.

Step 2: determine the percentage, which is 45.

Step 3: Convert the percentage 45% to its decimal form by dividing 45 into 100 to get the decimal number 0.45:

45100 = 0.45

Notice that dividing into 100 is the same as moving the decimal point two places to the left.

45.0 → 4.50 → 0.45

Step 4: Finally, find the portion by multiplying the decimal form, found in the previous step, by the whole amount:

0.45 x 72 = 32.4 (answer).

The steps above are expressed by the formula:

P = W × X%100

This formula says that:

*"To find the portion or the part from the whole amount, multiply the whole by the percentage, then divide the result by 100"*.

The symbol % means the percentage expressed in a fraction or multiple of one hundred.

Replacing these values in the formula, we get:

P = 72 × 45100 = 72 × 0.45 = 32.4 (answer)

Therefore, the answer is 32.4 is 45 percent of 72.

### Solution for '45 is what percent of 72?'

The following question is of the type "P is what percent of W,” where W is the whole amount and P is the portion amount".

The following problem is of the type "calculating the percentage from a whole knowing the part".

#### Solution Steps

As in the previous example, here are the step-by-step solution:

Step 1: first determine the value of the whole amount. We assume that it is 72.

(notice that this corresponds to 100%).Step 2: Remember that we are looking for the percentage 'percentage'.

To solve this question, use the following formula:

X% = 100 × PW

This formula says that:

*"To find the percentage from the whole, knowing the part, divide the part by the whole then multiply the result by 100"*.

This formula is the same as the previous one shown in a different way in order to have percent (%) at left.

Step 3: replacing the values into the formula, we get:

X% = 100 × 4572

X% = 450072

X% = 62.50 (answer)

So, the answer is 45 is 62.50 percent of 72

### Solution for '72 is 45 percent of what?'

The following problem is of the type "calculating the whole knowing the part and the percentage".

### Solution Steps:

Step 1: first determine the value of the part. We assume that the part is 72.

Step 2: identify the percent, which is 45.

Step 3: use the formula below:

W = 100 × PX%

This formula says that:

*"To find the whole, divide the part by the percentage then multiply the result by 100"*.

This formula is the same as the above rearranged to show the whole at left.

Step 4: plug the values into the formula to get:

W = 100 × 7245

W = 100 × 1.6

W = 160 (answer)

The answer, in plain words, is: 72 is 45% of 160.