Fractions & DecimalsMathsPercentage

How to calculate percentage?

The percentage can be very confusing if you do not know exactly what it is. So, before we talk about how to calculate percentage we would like to start by making sure that we have a good understanding of percentage.

The percentage is a special type of fraction, where we represent a ratio out of 100. In other words, it is a fraction of 100. It is so special that even has its own symbol, i.e. %. The symbol represents a fraction of 100. So whenever you see the % symbol then you should immediately know that we are talking about a fraction of 100.

Why is the percentage important?

Percentage helps us understand many important concepts of everyday life financials. If you know how to calculate percentages then you can make money, save money, or in general find good deals cheap essays online

in shops or online. It can help you understand if you can afford to borrow money from a bank.

What are some of the real-life uses of the percentage?

There are many uses of the percentage that we encounter in our daily life. Some of those we really love like having a discount when we buy our favorite pizza.

Have you ever seen an ad like this? This is a good example of the use of percentages in everyday life. A shoe company giving a 15% discount on your birthday to try to attract you to buy the shoes.

Let’s look at some of the useful uses of the percentage.

  1. Discounts on shopping items – This is everyone’s favorite. When you visit your favorite shop and see 40% off sale on clothes, toys, or food, etc. then you are looking at a great use of a percentage. It is used to attract more customers to buy. We love having discounts on Pizzas for Friday nights.
    If you were a shop owner then you would need to know how to calculate the percentage to set discounts on products without making a loss.
    As a customer, you must know how to use percentages to find a better deal. For example, you must know if 30% off is better or 40% off is better. Even better if you know if £30 off is better or 30% off is better. If you know how to calculate percentages then you can find the best deals and save a lot of money.
  2. Bank interests on savings – When you put money in a bank and leave it in the bank for longer periods and banks give you interest on the money that you have in your bank. The interest is calculated using percentages. For example, the bank may say that they will pay you 10% interest on the money you have in the bank. This means that if you put £100 in your bank then the bank will pay you £10. If you know how to calculate percentages then you can help your parents find a good deal on bank interests.
  3. Borrowing money or taking a loan – When you borrow money from someone like a person or a bank they may ask you to pay some interest for the money you are borrowing. The interest you pay to the person who is lending you the money is often calculated in percentage. For example, the bank may say that if you borrow money from them then you may have to pay interest at 10%, which means that if you borrow £100 then you will have to pay an interest of £10 to the bank. This is the opposite of putting money in the bank. When you put money in the bank the bank pays you interest and when you borrow money from the bank then you pay them some interest.
  4. Statistics or data analysis – The percentage is often used to study the data and to interpret some useful information. For example, up to 60% of the human body is water. We do not need to know exactly how much water because every person will have a different amount of water but in general everyone has about 60% water in their body. Another example is that about 71% of the earth is covered by water.

Fractions refresher before we learn how to calculate the percentage

The key to percentage calculation is to remember that a percentage is a special fraction of 100.

If we say that 2 out of 10 boys in a class has brown hair then we can write that fraction as 2/10 but we cannot call this a percentage. We can also simplify this fraction from 2/10 to 1/5 and it will still be a valid fraction. So instead of saying that 2 out of 10 boys have brown hair, we can also say that 1 out of 5 boys has brown hair.

To calculate the percentage, we do the opposite of simplification. We change the fraction in a way so that we get 100 in the bottom part of the fraction.

To learn how to calculate percentages, let’s take an example of a group of 10 pupils.

two out of ten pupils are girls

If 2 out of 10 pupils in this group are girls then we can write the fraction of girls as 2/10. Now, let’s imagine that there is one more such group. In group one, 2 out of 10 pupils are girls and in group two, 2 out of 10 pupils are girls. This means that the ratio is the same in both groups.

two out of ten pupils are girls
two out of ten pupils are girls

When we combine the two groups to form one big group then we will have a total of 20 pupils and now 4 out of 20 pupils would be girls, represented as a ratio of 4/20.

four out of twenty pupils are girls

The fraction 4/20 is the same as 2/10, just like 2/10 is the same as 1/5. (When you simplify the fraction 4/10 we get 1/5). But note that the bottom number (or the denominator) has changed to 20. This means that we can increase the bottom number by simply adding more pupils as long as we keep the fraction as the same.

1/5 = 2/10 = 4/20 – Can you see the pattern?

The top number or the numerator is changing by a multiple of 2 and the bottom number or the denominator is also changing exactly by the multiple of 2. In other words, the pattern is that both numerator and denominator are changing by a multiple of 2 (multiplied by 2).

1/5 multiply the top and bottom by 2 = 2/10

2/10 multiply the top and bottom by 2 = 4/20

Golden Rule: If you multiply the top and the bottom by the same number then the fraction remains the same.

This rule is important to understand how to calculate percentage.

The final trick to master how to calculate the percentage

To learn how to calculate percentage from a fraction let’s take a look at the fraction again, 2 out of 10 pupils are girls i.e 2/10.

To calculate percentage the bottom part of the fraction must be 100. So, think about what must we do to change the bottom part of the above fraction to 100.

2/10 – multiply the bottom part with 10 to change 10 to 100 but we must remember the golden rule and multiple both top and bottom with the same number so that our fraction remains the same.

Bottom (Denominator) = 10 x 10 = 100
Top (Numerator) = 2 x 10 = 20

Now we got our special new fraction with denominator 100, which is 20/100.

This fraction when written with the percent symbol % is known as a percentage (20%). When using the % symbol we do not write the denominator because it is assumed that the bottom of a percentage is always 100.

So, 20/100 = 20%

A few quick example percentages converted to fractions

20% = 20/100
40% = 40/100
99% = 99/100
1% = 1/100
2.5% = 2.5/100

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