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# 120 percent of 40?

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### Solution for 'What is 120% of 40?'

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 120 percent of 40. What are the steps?

Step 1: first determine the value of the whole amount. We assume that the whole amount is 40.

Step 2: determine the percentage, which is 120.

Step 3: Convert the percentage 120% to its decimal form by dividing 120 into 100 to get the decimal number 1.2:

120100 = 1.2

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

120.0 → 12.00 → 1.20

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

1.2 x 40 = 48 (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 = 40 × 120100 = 40 × 1.2 = 48 (answer)

Therefore, the answer is 48 is 120 percent of 40.

### Solution for '120 is what percent of 40?'

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 40.

(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 × 12040

X% = 1200040

So, the answer is 120 is 300.00 percent of 40

### Solution for '40 is 120 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 40.

Step 2: identify the percent, which is 120.

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 × 40120

W = 100 × 0.33333333333333