How much is 40 percent of one third

We think you reached us looking for answers to questions like: What is 40 percent of one third? Or maybe: How much is 40 percent of one third

See the detailed solutions to these problems below.

How to work out percentages explained step-by-step

Learn how to solve percentage problems through examples.

In all the following questions 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 for 'What is 40% of one third?'

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 40 percent of 0.33333333333333. What are the steps?

Step 1: first determine the value of the whole amount. We assume that the whole amount is 0.33333333333333.

Step 2: determine the percentage, which is 40.

Step 3: Convert the percentage 40% to its decimal form by dividing 40 into 100 to get the decimal number 0.4:

40100 = 0.4

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

40.0 → 4.00 → 0.40

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

0.4 x 0.33333333333333 = 0.13333333333333 (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 = 0.33333333333333 × 40100 = 0.33333333333333 × 0.4 = 0.13333333333333 (answer)

Therefore, the answer is 0.13333333333333 is 40 percent of 0.33333333333333.

Solution for '40 is what percent of one third?'

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 0.33333333333333.

(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 × 400.33333333333333

X% = 40000.33333333333333

X% = 12,000.00 (answer)

So, the answer is 40 is 12,000.00 percent of 0.33333333333333

Solution for '0.33333333333333 is 40 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 0.33333333333333.

Step 2: identify the percent, which is 40.

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 × 0.3333333333333340

W = 100 × 0.0083333333333333

W = 0.83333333333333 (answer)

The answer, in plain words, is: 0.33333333333333 is 40% of 0.83333333333333.

Sample percentage problems