At percentages are numbers that indicate how much a part represents in a whole.
There are a few ways to express a percentage. The most common is with the percent symbol, for example 30%, 40%, 90%.
But in addition to these forms, we can write a percentage as a fraction of denominator 100 or as a decimal number.
Several situations involve percentage calculations. Next, see how to count percentage.
Index
- How to calculate percentage
- How to Calculate Percentage of Increases and Discounts
- How to calculate percentage change
How to calculate percentage
Given any value, which can refer to money, distance, height, time or any other quantity, we only consider the number to calculate a percentage.
Examples: Calculating any percentage of:
R$ 150.00 → we consider the number 150
30 km → we consider the number 30
12:00 → we consider the number 12
That said, let's show how to calculate percentage of one value, in two different ways.
1) Multiplying the number by a fraction.
5% of BRL 150.00:
→
→
→ 5% of R$150.00 is equal to R$7.5.
10% of 30 km:
→
→
→ 10% of 30 km equals 3 km.
75% of 12h:
→
→
→ 75% of 12h is equal to 9h.
2) Multiplying the number by a decimal number.
5% of BRL 150.00:
→ 5% of R$150.00 is equal to R$7.5.
10% of 30 km:
→ 10% of 30 km equals 3 km.
75% of 12h:
→ 75% of 12h is equal to 9h.
How to Calculate Percentage of Increases and Discounts
To calculate percentage increases and discounts, the procedure is simple:
- The percentage of the product's starting price is calculated.
- If increase, final price = start price + percentage value.
- If discount, final price = start price – percentage value.
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Remember: in increases, money increases, in discounts, money decreases. It sounds obvious, but confusion is common.
Example: A bag costs R$120.00. How much would the scholarship cost if it had:
a) an increase of 15%
→ percentage calculation: 120 × 0.15 = 18
→ final price = 120 + 18 = 138
Therefore, the scholarship would cost R$ 138.00 with a 15% increase.
b) a 15% discount
→ percentage calculation: 120 × 0.15 = 18
→ final price = 120 – 18 = 102
Therefore, the scholarship would cost R$ 102.00 with a 15% discount.
How to calculate percentage change
Given two values, we might want to calculate the percentage variation between the two, also known as percentage change.
It is a very used calculation when we have the starting price of a product and the final price, which can be a lower price if there is a discount, or a higher price if there is an increase.
Percentage variation formula:
On what:
FV: final value (price after increase or discount)
VI: initial value (price before increase or discount)
In the example of the $120.00 scholarship, suppose that with a raise it costs $145.00. What is the percentage rate of increase?
In other words, by how many percent did the price increase?
As we have VF = 145 and VI = 120, just substitute in the formula:
Therefore, the stock price increased by 20.83%.
Now, imagine the opposite, the bag cost R$145.00, had a discount and started to cost R$120.00. What is the discount percentage rate?
In this case, we have VF = 120 and VI = 145, so:
Therefore, the price of the bag was discounted by 17.24%.
Note: the minus sign in the result indicates discount.
You may also be interested:
- How to calculate percentage using calculator?
- Percentage Exercises
- Decimal numbers and percentage
- List of Rule of Three Exercises
- Probability
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