# 40 is 20 Percent of What Number

This calculator provides an easy method to solve percentage calculations such as 40 is 20 percent of what number. See explanation below.

You can solve this type of calculation with your own values by entering them into the calculator's fields, clicking 'calculate' and getting your answer!

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## What are Percentages?

Percentages are similar to fractions with an important difference. In fractions the whole is represented by the denominator (e.g. the number 5 in the fraction of 1/5) In percentages, the whole is represented by the number 100. In fact, "per cent" means "per 100" or "for each 100."

## How to Solve?

To solve the problem above, let’s convert it into equation form: 40 = 20% x __

In this example, the number that represents the whole is unknown, which we will call "Y". As a percentage, it would be equal to 100%. Written as a ratio, we would get: 100% : Y

If a student took a test with a number of questions equal to Y, and they got every answer correct, as a percentage they would get a 100% score on the test.

It is already given in this problem that 40 is equivalent to 20%. Written as a ratio, we would get: 20% : 40

To see a relationship between these two ratios, let’s combine them into an equation: 100% : Y = 20% : 40

It is critical that both of the % values should be on the same side of a ratio. For instance, if you decide to put the % value on the right side of a ratio, then the other % value should also be on the right side of its ratio.

"Y : 100% and 40 : 20%" is correct.
"Y : 100% and 20% : 40" is wrong.

Let’s solve the equation for Y by first rewriting it as: 100% / Y = 20% / 40

Drop the percentage marks to simplify your calculations: 100 / Y = 20 / 40

Multiply both sides by Y to move Y on the right side of the equation: 100 = ( 20 / 40 ) Y

Simplifying the right side, we get: 100 = 20 Y

Dividing both sides of the equation by 20, we will arrive at: 200 = Y

This leaves us with our final answer: 40 is 20% of 200