Calculating the Percentage, Percentage Increase, and Discount

How do you calculate the percentage?

Calculating the percentage of numbers is a basic knowledge that can be useful in different situations of life. For example, when deciding how much to pay for a car loan or a down payment on a house, you may need to know how to calculate percentages.

Percentage calculations are used in many different situations in the workplace, such as when calculating taxes or employee raises.

A percentage is also called a percent (%), which refers to the proportion of the total that is 100%. It means one-hundredth and represents a portion of the total amount.

The percentage is the ratio of the whole to 100.

The method of calculating the percentage is as shown in the following equation:

Percentage = Number of items ÷ Total number of items x 100

This tutorial explains how to calculate percentages, along with example problems and explanations.

Table of Contents:

What is a percentage?
Why do we use percentages?
How to find the percentages
Discount and percentage increase calculations
- How to calculate a percentage subtraction
- How to calculate a percentage increase

What is a percentage?

The percentage is the ratio of the whole to 100. It is expressed by using percent (symbol: %) as the unit of measure.

You can often find this notation used in supermarkets. For example, you may see a tag that says 50% off or a receipt that says 5% consumption tax.

Why do we use percentages?

The reason we use percentages is to make things easier to understand in our daily lives.

When doing calculations in arithmetic and mathematics, we use the ratio of the whole to one.

By multiplying the ratio of 1 as a whole by 100 and using the ratio of 100 as a whole, we will not have to use decimals. The percentage display makes it easier to imagine the percentage.

When using percentages, write a number followed by the symbol "%" as a mark. Note that when calculating as a percentage, you need to divide by 100 and convert the whole number to 1.

How to calculate the percentage

To calculate percentages, use the following formula:

Percentage = Number of items ÷ Total number of items x 100

As an example, let's consider the following example:

After shooting 20 times in basketball, you scored ten goals. Find the percentage of shoots.

Think about what the total number of items is and what the number of items is.

Once you know this, you can use the formula to get the percentages. Multiply by 100, and be careful not to forget to add the symbol "%" at the end.

Percentage = 10 ÷ 20 x 100% = 50%

Converting 50% to a ratio of 1 for the whole, you get 0.5 (= 50 ÷ 100).

Discount and percentage increase calculation

To solve the percentage calculation problem, you need to divide the percentage value by 100 and convert it to a percentage with the whole as 1.

For example, 100 % is 1, 20 % is 0.2, and 2 % is 0.02. After converting the values expressed as percentages in this way, you can calculate the percentages.

How to calculate the discount

In supermarkets, you will often see price tags that say "~% discount. Let's take a look at an example of such a calculation.

There are two different ways to calculate this problem.

1. Find a discounted price and subtract it from the original price

First, give the price you want to discount, then subtract it from the original price.

For example, let's calculate the discounted price of $1500 for 15%. If we convert 15% to a ratio of 1 as a whole, we get 15/100 = 0.15. Therefore, the discounted price is:

Discounted price =1500 × 0.15 = 225

Here, if you subtract the discounted price from the original price of $1,500, you will get the price after discount as follows:

Price after discount = 1500 − 225 = 1275.

2. Find the percentage after the discount and multiply it by the original price

The second method is to find the discounted percentage and multiply it by the original price.

A 15% discount means that the price after discounting is 85% of the original price. This is the result of subtracting the 15% discount from 100% (100% - 15% = 85%).

Converting 85% to a ratio of 1, you get 85%/100% = 0.85. Then multiply this by the original price, $1,500, and you have your answer.

Price after discount = 1500 × 0.85 = 1020.

How to calculate the percentage increase

There are many things, such as consumption tax, which can cause a percentage increase in the listed price. In the following example, let's find the price of a 15% increase in the original amount.

Find the price of 15% increase of $1,500.

There are two different ways of calculating this problem.

1. Find the price to be increased and then add it to the original price

First, let's solve the problem by thinking about the price that will be increased and adding it to the original price.

The price to be increased is 15% of $1,500, and if you convert 15% to a percentage of the whole, you get 15% ÷ 100 % = 0.15. Therefore, the price to be increased is:

= 1500 x 0.15 = 225.

Now you just need to add this extra price to the original price of $1,200.

= 1500 + 225 = 1725.

2. Find the percentage after the increase and then multiply it by the original price

The second method is to calculate the increased percentage and multiply it by the original price.

A 15% increase means that the price after the increase is 115% of the original price. This is the result of adding 15% of the increase to 100% of the total price (100% + 15% = 115%).

Converting 115% to a ratio of 1, we get 115% / 100% = 1.15. Then multiply this by the original price, $1,500, and you have your answer.

= 1500 x 1.15 = 1725.