Percentages are an important concept in mathematics and are also commonly used in everyday life to represent a value relative to a whole. Therefore, knowing how to calculate percentages is essential and useful. In this article, FPT Shop will help you learn how to calculate percentages with detailed examples.
1. What is a percentage ratio?
A percentage ratio is commonly used to express the relative size of one quantity compared to another quantity, where we convert the numerator to 100. More specifically, the number 1 usually represents the corresponding part or the part with a change compared to number 2.
- Example 1: 50/100 = 50% or 2/100 = 2%.
- Example 2: You have 100,000 VND and an additional interest of 5,000 VND, then the total amount will increase by 5,000/10,000 = 0.05 compared to the initial amount. If we have to express it as a percentage, we can say that this 100,000 VND has an additional interest of 5%.
2. The meaning of the percentage ratio
In mathematics, the percentage ratio is a ratio represented as a fraction that always has a denominator of 100. In addition, the percentage ratio is also represented in other forms using the % sign that you often see like 1%, 5%, and 10%.
One special thing is that the percentage ratio does not have a unit of measurement. You will often see the percentage ratio used to compare one number to another.
3. Fastest way to calculate the percentage ratio
In addition to using a calculator, you can also quickly calculate the percentage ratio using the following formula.
General formula for calculating the percentage ratio of x in the sum (x+y): x (%)=x/(x+y)×100 (%)
Example: A fruit basket has 10 oranges and 5 apples. To calculate the percentage of oranges in this fruit basket, we first have to calculate the total of the fruit basket and then calculate the percentage. Currently, there are 10 oranges in the fruit basket, we have the calculation as follows: (10/(10+5)) x 100(%). Similarly, the calculation is also used to calculate the percentage of apples in this fruit basket: (5/(10+5)) x 100 (%).
4. How to calculate the percentage of two numbers
The way to calculate the percentage of two numbers a and b is to divide the number a by the number b and then multiply by 100. The result obtained is the percentage (%).
General formula for calculating the percentage of two numbers: a (%) = a/b×100 (%)
Example: A soccer match has 22 players. Among them, there are 5 yellow players and 17 white players. What is the percentage of yellow players compared to the total number of players?
Solution: The ratio of yellow players to the total number of players on the field is: (5 : 22) x 100 = 22.72%. Answer: 22.72% of the players are yellow compared to the total number of players on the field.
5. Calculating the growth rate comparison
A very familiar concept in economics that you may have heard of is the growth rate. So what is the growth rate? The growth rate shows the rate of development of a company, business, or economy in terms of growth/decrease/stagnation compared to previous quarters, seasons, or years.
Formula for calculating the growth rate: Growth rate = ((Current year revenue – Previous year revenue)/ Previous year revenue) x100
Example: The revenue of a company in 2022 is 50 billion VND, and in 2021, it is 35 billion VND. Therefore, the growth rate of this company is: ((50-35)/ 35)*100 = 42.86%.
Note: The growth rate can have a negative value because the current period’s profit may be lower than the previous period, this phenomenon is called a decreasing or lower growth rate.
6. How to calculate the completion rate
Sometimes we also need to know how to calculate the completion percentage to estimate the percentage of work completed. Currently, this formula has also been updated to calculate the estimated completion rate of a project, making it easier to plan for the future.
Formula for calculating the percentage of work completed: (Number of completed tasks/ Total number of initial tasks) x 100(%)
Example: A tailor is required to make 50 shirts in one month, and she has made 20 shirts. Therefore, the completion rate of her is: (20/50) x 100 = 40%.
7. Calculating the percentage in Excel
Nowadays, you can calculate percentages using software or websites such as Excel, Google Sheet, which saves you a lot of time and effort, especially when dealing with large amounts of data. Let’s take a look at a trick to calculate percentages using Excel.
Example: The monthly KPI of every salesperson in terms of the number of phones is 100. After one month, calculate the achieved KPI percentage of each salesperson.
Step 1: First, you create a summary table of the total number of phones sold by salespeople.
Step 2: Next, you enter the percentage calculation formula into the % Completion cell.
Step 3: If you want the result to be in percentage form, you highlight the cells you want and right-click and select Format Cells.
Step 4: At this point, the Format Cells dialog box will appear and you select Percentage under the Number section.
Step 5: Adjust the number of decimal places you want by selecting Decimal places.
Step 6: Finally, click OK.
8. Calculating the percentage salary
In order to accurately calculate the percentage of salary increase, you can use the following formula:
% Monthly salary = (Basic salary + Possible bonuses, allowances/ Actual working days) x 100(%)
Note that you must convert the result into a decimal. For example, if the percentage is 15%, and your monthly salary is 20,000,000 VND, then it will increase by 15% compared to the old salary of 17,000,000 VND, or simply put, 15% is the additional percentage on your salary.
9. Calculating the percentage increase/decrease in price
Formula for calculating the discount percentage is as follows: Discounted amount = % Discount x Original price
Example: The starting price of a phone is 10,000,000 VND, and it is discounted by 20%. Now, the discounted amount is: 10,000,000 x 20% = 2,000,000 VND.
Formula for calculating the percentage increase is as follows: Increased quantity = % Increase x Original price
Example: One kilogram of sugar is priced at 15,000 VND. The price of sugar has increased by 12% due to the prolonged Covid epidemic. Therefore, the increased amount is: 15,000 x 12% = 1,800 VND.
10. Calculating the bank interest rate percentage
Using the percentage formula to calculate the interest rate will help you choose the most suitable and best bank interest rate for yourself.
Example: Person A deposits 200,000,000 VND into Bank B with an interest rate of 5%/year. The monthly savings interest rate is 5% over 12 months. Therefore, the monthly interest amount received by person A is: 200,000,000 x 5%/12 = 833,333.33 VND.
However, this is just a simple formula for calculating interest on bank deposits. The actual amount of interest you receive depends on the interest rates and interest calculation methods (simple interest, compound interest, payable interest at the end of the period or monthly, quarterly interest, etc.) of each bank. But no matter how it is calculated, it is based on the initial general formula. Just like borrowing money from a bank, calculating interest helps determine which bank is suitable for your needs.
Formula for calculating interest (when borrowing) is as follows: Interest amount = Initial amount x % Loan interest
Example: Person A borrows 50,000,000 VND from a bank at an interest rate of 9%/year (12 months). Therefore, the monthly interest amount that person A has to pay to the bank is: 50,000,000 x (9%/12) = 375,000 VND.
11. Types of percentage calculations
Mathematical exercises related to percentage calculations include addition, subtraction, multiplication, and division. We do the same as for natural numbers or decimals and add the% sign (%) to the right of the result.
Problem type |
Formula |
Example |
Addition problem |
A% + B% = (A + B)% |
70% + 30% = (70 + 30)% = 100% |
Subtraction problem |
A% – B% = (A – B)% |
10% + 50% = (10 + 50)% = 60% |
Multiplication problem |
A% x B = (A x B)% |
40% x 2 = (40 x 2)% = 80% |
Division problem |
A% : B = (A : B)% |
50% : 2 = (50 : 2)% = 25% |
12. Application exercise of calculating the percentage
In the above content, we have learned some simple and quick formulas for calculating percentages. Let’s practice the following percentage calculation exercises to better understand!
Exercise 1:
A farmer has 200 kg of fresh mangoes after drying them, which is 30 kg lighter. The moisture content of fresh mangoes is 20%. Calculate the percentage of moisture in the dried mangoes.
Solution:
The initial amount of water in 200 kg of fresh mangoes: 200/100 x 20 = 40 (kg). The remaining amount of water in 170 kg of dried mangoes: 40 – 30 = 10 (kg). Calculate the percentage of water in dried mangoes as follows: The remaining amount of water in dried mangoes/total number of dried mangoes x 100. We can calculate: 10/170 x 100 = 5.88%.
Exercise 2:
A fashion store calculates that if they decrease the price of winter clothes by 5%, the sales will increase by 30%. Will the store receive more or less money after implementing the discount program compared to not implementing it? Calculate the percentage of increased profit?
Solution:
Assume that the estimated quantity of clothes sold, prices, and the amount of money collected are 100% without the discount program.
- The ratio of the new price to the old price is: 100% – 5% = 95%.
- The ratio of the products sold after the discount to the products sold without the discount is: 100% + 30% = 130%.
- The revenue earned after the discount program compared to the revenue without the discount program is: 95% x 130% = 123.5%.
- Increased profit rate = 123.5% – 100% = 23.5%.
Conclusion
Mastering the calculation of percentages will help you understand and make many accurate decisions in daily life. Hopefully, through this article from FPT, you have learned how to apply percentage calculations to solve your own tasks or learning.