The calculation of percentages is extremely useful and highly applicable. We see it every day in real life, a mathematical calculation that we cannot ignore. When we talk about the cost of living increasing by 5%, or that for cash payment of an item you want to buy you get a 10% discount, or if you pay in installments you have 3% monthly interest, etc. As there are thousands and thousands of these everyday examples, this is the reason why we cannot ignore how to calculate percentages.
The expression ” percent ” derives from Latin. It was originally “per centum”, which means “per hundred”. Thus, it is often stated that “percent” means hundredths: A hundredth is one hundredth of something and can be written:
One hundredth == 0.01 = 1% = one percent
Percent concerns a group of decimal fractions whose denominators are 100. 25% represents the same value as “twenty-five hundredths”:
25% = = 0.25 = twenty five percent
For example, if we say that 60% of a group of people are women, we are saying that out of every 100 people, 60 are women. It does not mean that there are exactly 100 people and within them 60 women, there may be many more or less than a hundred, 60% represents a relationship between the total number of people and the total number of women.
It is expressed as follows: = 0.60 = 0.6= 60%
Instructions for calculating percentages
- Let’s look at an example: Sales commissions are paid to employees or companies that sell merchandise in businesses or by calling customers. The purpose of the commission is to motivate sales agents to sell more. A commission can be paid in addition to salary or instead of salary. A commission is a percentage of the sale price of a product. It is also well known that those who are in charge of buying and selling properties charge a very interesting percentage for the sale made.
- For example, if a vendor receives a 10% commission on their sales and sells €15,000 worth of merchandise, they would earn a commission of €1,500.
- It is calculated: €15,000 x 10 : 100= €1,500 or directly € 15,000 x 10 = €1,500 because as we saw before, 10% is the same as 0.10
- One way to apply percentages is in discount problems, that is, businesses sell products at a discount on the original price.
- For example, a product that originally cost €200 could be 25% off.
- To find out the amount of the discount, calculate 25% of €200, that is, €200 x 0.25 = €50
- Finally, to calculate the sale price, we subtract the discount that we calculated from the original price: €200 – €50 = €150
- Another case in which we apply percentages is when we buy something in installments and they charge us interest, that is, we will return more money than is due, or we will pay for the refrigerator that we bought more expensive than if we did it in cash.
- Suppose we want to buy a refrigerator whose price is €600, that price is what we would pay if we had the €600 in hand, but since this is not the case, we decide to buy it in installments. The seller tells us that he can sell us this item in 12 installments with interest of 2% per month. If we pay it in 12 installments, we will have to know what 24%of the price of the refrigerator is. We calculate it like this: €600 x 0.24 = €144 (this is the interest we will pay on the original price).
- Now we add this increase to the original price: €600 + €144 = €744
- Finally, if we want to know how much we will pay each month, we must divide that total amount (€744) by the 12 installments that we agreed on:
- €744 : 12 = €62 we will pay 12 installments of €62You can also calculate percentages using the calculator, since they all have the % key. For example, you need to know how much 35% of 750 is. For this you must write the number 750, then touch the % key and write the number 35, finally touch the key = and you will get the result. The sequence with the calculator will be: 750% 35 = 262.5
- Another different example: suppose we want to know what percentage one number represents with respect to another, so that you can see it very clearly: what percentage does 8 out of 16 represent? Without doing calculations we realize that it is half, 8 is half of 16, that is, 8 is 50% of 16. Very easy
- And if I ask you: what percentage is 30 of 120? The result is…25% It’s also easy, it’s just a quarter, but to generalize it and so you can calculate any percentage you should proceed like this:
- 30 :120 = 0.25, then multiply it by 100 and it will give you the percentage:
- 25 x 100 = 25%
- Let’s see if it is true for the previous case: We said that 8 is 50% of 16, because it was the fair half. Then
- 8 : 16 = 0.5 so 0.5 x 100 = 50%
- Another problem with percentages: if there are 130 chocolates in a box, 52 are plain chocolate, 56 are filled with dulce de leche and the rest are filled with coconut, what percentage is there of each flavor?
- First let’s calculate how many chocolates there are filled with coconut: 130 – 52 – 56 = 22.
- In other words, we have: plain chocolate: 52, filled with dulce de leche: 56 and filled with coconut: 22, a total of 130 chocolates.
- Let’s apply the rule to calculate what percentage there is of each flavor:
- Chocolate: (52 : 130) x100 = 40%
- Dulce de leche filling: (56:130) x 100 = 08%
- Coconut fillings: (22 : 130) x 100 = 92%
- If we want to check that we calculated correctly, we add the 3 percentages and we should have 100% as a result.
- 40% + 43.08% + 16.92% = 100%
What do you need to calculate percentages?
- Calculator, paper and pencil
- Problems and exercises to practice
Tips for Calculating Percentages
- When the divisions give you decimals, when they are not integer results, approximate correctly and leave the number with two decimal places, for percentages it is enough.
- There are programs on the Web that directly calculate the percentages just by entering the numbers, search and use them, although it is always better to know how to calculate by hand in case you do not have a computer.