# What is percentage

Introduction to percentage

Every day we face percentages. We constantly have to calculate promotions, discounts, taxes, length of service, insurance, the interest rate on deposits, installments, and more. Therefore, it is useful to know how to calculate percentages - calculating a percentage of a number, how to express one number as a percentage of another, how to find a number by a percentage of it.

How to calculate percentage

Calculate the percentage of an integer
The percentage is 1/100 of an integer. It is marked with the% sign. To calculate the percentage, the integer is considered to be equal to 100%

Example:
We have 10 apples. 10 apples are 100%. We eat 2 apples. It follows that we have eaten 2/10 x 100% = 20% of the apples and we are left with 80% of the original number of apples.

From this example, we can derive the formula for calculating the percentage of a number

percentage of whole = part x 100 / whole

or in our example:

20% = 2 apples x 100/10 apples

Another example:
We have a promotion of 8% of goods for BGN 200. We use the following formula:

200 x 8/100 = 16 lev. Therefore, the price of the goods is BGN 184.

Find a number by a percentage
If we bought a product reduced by 20% and paid a price of BGN 160, what was the price of the product without the discount. The discount was 20%, so we paid 80% of the price of the goods. The goods cost X leva. We calculate by the formula:

80/100 * X = 160 When calculating the equation, it turns out that the price before the reduction was BGN 200.
When a number increases relative to another, the increase is expressed as follows:

Increase = new number - old number

However, when a number decreases relative to another, the decrease is expressed as follows:

Reduction = old number - new number

The percentage increase or decrease of a number is always expressed relative to the base of the old number.
Or:

% Increase = 100 ⋅ (new number - old number) ÷ old number

% Reduction = 100 ⋅ (old number - new number) ÷ old number

For example, you had 90 postage stamps and continued to collect until the total number of postage stamps reached 150. By what percentage did your stamps increase?

150 - 90/90 ×100 = 66.6%

Application of percentage

There are two ways in which percentages help us solve everyday problems:

1. We can compare between individual quantities, as all quantities refer to the same basic quantity, which is 100.
To illustrate this, let us consider the following example:

Example: Tom starts a new grocery store business. In the first month, he bought groceries for\ display style 650650 BGN and sold them for \ display style 800800 The second month he bought for \ display style 800800 BGN and sold them for \ display style 12001200 We need to know if Tom earns more or not.

We cannot judge directly from these numbers whether Tom's profit increases or decreases, as costs and profits are different each month.

Let's express the profit in terms of his expenses for the first month in percentages:

(800 - 650) ÷ 650 ⋅ 100 = 23.08%

This means that if Tom invests BGN 100, he would have a profit of BGN 23.08. in the first month.

Let's do the same for the second month:

(1200 - 800) ÷ 800 ⋅ 100 = 50%

Therefore, in the second month, if Tom invests BGN 100. he would have a profit of BGN 50 (since\ display style 100 \ cdot 50 \% = 100 \ cdot 50 \ div 100 = 50100⋅50%=100⋅50÷100=50). It is now clear that Tom's profit has increased (more than 2 times because\ display style 50> 23.08 \ times 250>23,08×2).