# What is 25% of 90?

Apr 6, 2016

25% of 90 is 22.5.

#### Explanation:

A percent is any number over 100, so 25% is 25 over 100, this means that 25% can be written as:

$\frac{25}{100}$

Now, any number in fractional form (a number over a number) is the same as division so 25% can also be written as a decimal, we just move the decimal point 2 places to the right of 25, like this:

$\frac{25}{100} = 0.25$

Now we have two ways that we can solve this problem! I'll start with the fractional method of solving.

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The Fractional Method

So we have a fraction: $\frac{25}{100}$, lets think, how many 25's do we need to get to 100? Well:

$25 + 25 = 50$

and

$50 + 50 = 100$

so that means,

$25 + 25 + 25 + 25 = 100$

or

$25 \cdot 4 = 100$

This means that we need four 25's to get 100.

or,

$\frac{25}{100} = \frac{1}{4}$

(we could also divide both numerator and denominator by 5 to get the same result:

$\frac{25}{100} \div \left(\frac{5}{5}\right) = \frac{5}{20} \div \left(\frac{5}{5}\right) = \frac{1}{4}$

Now that we know 25% is equal to $\frac{1}{4}$ we can either multiply 90 by $\frac{1}{4}$ or we can divide 90 by 4, its easiest (for me anyway) to just divide 90 by 4.

$90 \div 4 = 22.5$

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The Decimal Method

As we found out above 25% equals 0.25 so we can solve this problem using decimals too! All we need to do is multiply 90 by 0.25, which gives us the same answer as above.

$0.25 \cdot \left(90\right) = 22.5$

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Despite the fact that that mathematics seemed to be a lot more involved in the fractional method, the calculations were a lot easier and personally I found it to be faster than the decimal method. The decimal method is great when you're working with fractions that aren't equal to 100 (For example: $\frac{3}{7}$ of 21 is what number?) or when you have a calculator.

Sorry this is so long, I hope it helped though!