The word “percentage” comes from the expression “per cent”, and is used to relate quantities to each other, using the hundred as the reference measure. Percent means “per 100” or “over 100”, and is a quick way to represent a fraction whose denominator is the number 100.
Let´s see a simple example : when we say “This player scored a goal in 50 games out of the 100 he played” we are actually saying “This player scored a goal in 50% of the games he played”.
Index:
1. How to get the percentage
2. % with the rule of three
3. % with the calculator
4. Remove percentage of head
5. Common errors when drawing the percentage
6. Divide instead of multiply
7. Confusing expressions
8. Examples and case studies
Techniques for calculating a percentage
In this little tutorial we are going to explain several methods to get the percentage. From the simple rule of three to get the percentages out of the head, the techniques that follow are designed to solve the doubts of both the most beginners and some advanced users of mathematics.
How to get the percentage with the rule of three
The rule of three is a simple method for calculating a percentage, especially when we don´t feel like thinking too much. Just repeat the same operation (cross-multiply and then divide) to get the number you want. Now, the most important thing to get the percentage with the rule of three will be to represent our problem correctly.
Example of a rule of three resolution
Example of a rule of three: We have a company in which a total of 120 people work. In the accounting department there are 6 people working, and we want to know how much percentage of the total those 6 people represent.
The problem will be as follows:
If 100 workers is 100%
Then 6 workers will be X
120 — 100
6 — X
Step 1: Cross-multiply. We will multiply 35×100, since this is the only cross operation we can do.
6 x 100 = 600
Step 2: We divide the result by the remaining number.
600 / 120 = 5
Solution: 5% of the company works in the accounting department
Take out the percentage with the calculator
The calculator is undoubtedly the easiest method to get percentages when we can´t do it upside down. Nowadays, all smartphones come with this function, and with a few simple clarifications we will all be able to get a percentage using the calculator. Here are some tips.
All calculators, no matter how simple they are, come with a button with a percentage (%) symbol that will make the process of calculating the percentages much easier. To perform the operation, we only have to multiply the number we want by the percentage we are going to apply, and then press the percentage button mentioned above.
An example: We want to know how much 20% of 150 is.
1- We open the calculator
2- Enter the main number (150)
3- Multiply by the desired percentage (20) Press the multiply button and then type in the number 20.
4- Push the percentage (%) button
Option 2: apply the percentage to integers
Another interesting option to apply the percentage to any number is to do it by multiplying. Thus, we will have to know how to transform the percentage into a whole number (go from 20% to 0.2) and thus multiply the number we are interested in.
For example, to recalculate 20% of 150, we can simply do it as follows:
We convert our 20% to a numerical expression (0.2). This is correct since 0.2×100 is 20.
Multiply 150×0.2, and you get the same result as above (30)
How to get the percentage of head
If we have a certain amount of ease with mathematical operations, we can calculate simple percentages without the need for a calculator or the rule of three. In fact, we will be using these operations, but we will be able to do them from memory, without the need to put them on paper. Especially for simple operations, if we get a little practice we can learn how to get the percentage out of our heads.
To get head percentages, we have to have clear the relationship between what is a percentage and what is a fraction . As you know, each percentage can also be expressed as a fraction , so, for example, 25% is the same as saying 25/100, and if we know how to simplify, 25/100 is the same as 1/4, that is, a quarter.
An example: How much is 25% of 200?
- Since we know that 25% is the same as saying a quarter (or a quarter), we can get this percentage out of our heads if we are a little meticulous.
- We can also rely on the mathematical logic rules , because for example: 25% is the same as a quarter. 200 is the same as twice 100
- We know that a quarter of 100 is 25
- If one quarter of 100 is 25, then u a quarter of 200 (double) will be 50 .
Common errors when getting the percentage
1. Divide instead of multiply
It may be that, when using the technique explained above – applying percentages to whole numbers – we are tempted to divide instead of multiply. This happens because, in our head, we always relate the multiplication with getting a number bigger than the previous one (for example 3×2=6). Nothing could be further from the truth, because when we multiply by a number less than 1 (such as 0.2) we will always get a lower result than the original one.
2. Confusing expressions
Another very frequent mistake when it comes to getting the percentage is to confuse expressions, which leads us to make mistakes. We must be clear that when working with percentages we are working with two types of expressions:
- The expressions decimal (0,2)
- Fractional expressions (1/4, or 25%)
Decimal expressions can be compared to other decimal expressions, just as fractional expressions can be compared to other expressions of the same type. Thus, we cannot do operations by mixing a decimal expression (0.2) with a fractional expression (such as 20%). Before doing the operation, we must choose a type of expression and pass all the data to that type.
A practical example: to get 20% of 150, we can´t just multiply 150×20. First we must transform 20% into its decimal expression (0.2). It is then when we can perform the operation quietly:
150 x 0.2 = 30
Examples and case studies
Example#1
A candy bar that´s worth $1.5 today is going to be worth 20% more next week. How much will the candy bar cost next week?
1. Convert data into similar expressions
We will convert 20% (or 20/100) into its decimal expression, 0.2.
2. C we calculate how much the price increase will be
Before we know the final price, we have to find out how much the price increase will be, i.e. how much is 20% of $1.5. To do this, we will multiply 1.5×0.2. The result is $0.3, which means that the candy bars will become more expensive by that amount
3. We calculate the total price
The total price will be the sum of the current price plus the price increase.
So, if the current price is $1.5, and the price increase will be $0.3, a simple sum will give us the result.
The chocolates will be worth: 1.5 + 0.3 = $1.8.
Final price = Start price + price increase
Example#2
A 500-employee company announces that it is going to lay off 30% of its staff. How many employees will be out of work?
Option 1: Multiply 500*0.3 (30% decimal expression) The result: 500*0.3 = 150 employees will be out of work.
Option 2: Rule of Three
If 500 workers is 100%, then 30% is x
500 — 100
x — 30
Solution: (500×30)/100 = 150.
Example#3
Now, an example for you: if the day has 24 hours and I sleep 8 what percentage of the day do I spend sleeping? We encourage you, if you know the answer, to write to us and show it by leaving a comment in this article.
Without further ado, we hope that this article has been useful in helping you with the operations of how to get the percentage. If you have any questions, don´t be afraid to ask. Remember that in our website you can find information on how to download videos from Facebook, how to access the deep web, how to hack Twitter or tutorials of all kinds. Greetings!