What are Percentages?

In order to recognise and calculate percentages, we need to understand two basic concepts:

  • How to determine a part of a whole without percentages
  • How to determine a part of a whole with percentages

When we are discussing percentages, one should always ask the question "percentage of what?", meaning, there must be some whole from which the percentage is calculated. The whole serves as a reference point for the percentages.

Let's demonstrate this using two examples.

Example 1.

What is 141\over4 of 2020?

Solution:

When we are asked to find a part (141\over4) of a whole (2020), we need to multiply the part by the whole.

Therefore we obtain the following: 1420=204=5\frac{1}{4} \cdot 20 = \frac{20}{4} = 5

Example 2.

A shirt originally cost 4040 dollars and it's currently on sale with a 2020% discount.

We are asked to calculate the price of the shirt after the price reduction.

Solution:

After the price reduction, the shirt's price is 8080% (before the reduction the price was 100100%).

8080% is actually 80100=810=0.8\frac{80}{100}= \frac{8}{10}= 0.8.

In order to calculate 8080% of 4040, we perform a simple multiplication - 400.8=3240\cdot0.8 = 32.

In other words, the price of the shirt after the price reduction is 3232 dollars.

Join Over 30,000 Students Excelling in Math!
Endless Practice, Expert Guidance - Elevate Your Math Skills Today