Percentage

How do I find what percentage any number is of another number?

Ever stuck on questions like what percentage 14 is of 15? Or how do you find what percentage is 1.2 of 3?

The trick here is pretty simple to first imagine the numbers in the form of a fraction. For ex., 14/15 will be the fraction if you want to calculate what percentage of 15 is 14.

The next step is always to get the denominator up to 100. For fractions that have denominators such as 5, 10, 20, etc, you can easily multiply the numerators and the denominators by integers and transform the denominator to 100. For denominators like 15, however, you can get them up to 100 using 2 small steps:

  1. Multiply the numerator and denominator with an integer in such a manner to give you a denominator which is a multiple of 100. You can also multiply them with 100 if you can't think of any other integer to multiply it with.

  2. Divide the numerator and denominator with an integer in such a manner that it gives you 100 as the final denominator. In the final fraction, the numerator denotes what percentage the initial fraction denoted.

Let's try this with the fraction 14/15:

  1. Multiplying the numerator and denominator with 20, so that the new denominator is 300, i.e., a multiple of 100. The new fraction is 280/300.

  2. Divide the numerator and denominator with 3, so that the final denominator is 100. Using the methods on the division page, we can easily divide 280 with 3 to give 93.3333/100 as the final fraction. The numerator is 93.3333, therefore, 14 is 93.3333% of 15.

Let's try the above method with the fraction 1.2/3:

  1. Multiplying the numerator and denominator with 100, so that the new denominator is 300, i.e., a multiple of 100. The new fraction is 120/300.

  2. Divide the numerator and denominator with 3, so that the final denominator is 100. Divide 120 with 3 to give 40/100 as the final fraction. The numerator is 40, therefore, 1.2 is 40% of 3.

If you find the above method easy, you can increase your pace by simply multiplying the numerator by 100 and then dividing it by the denominator. Let's try this for 1.2/3:

Multiplying 1.2 (numerator) by 100 gives us 120. Dividing it by 3 gives us the final answer as 40%.

The reason you might not want to use the latter without practicing enough with the first is because of the complex divisions that it might offer. dividing 280 by 3 is a bit easier and faster to do than dividing 1400 by 15.