How to Calculate Percentage

🏆Practice percentage

Formula to calculate percentage

What is a percentage?

A percentage is a way to define a part, or fraction of a total.

When we talk about percentages, we should always ask ourselves the following: "the percentage of what?". Saying 50% without specifying 50% of what, makes no sense. However, if we say "the 50% 50\% of 80 80 " is 40 40 . In summary, the percentage represents what part of 100 100 is the number in question.

The percentage symbol is % \% :
when we want to express that a%a\%
We will write it as: a100a \over 100

To solve percentage problems, we will use the following formula

Percentage valueInitial amount=The percentage100 \frac{Percentage~value}{Initial~amount}=\frac{The~percentage}{100}

Percentage value: is the actual value that this percentage represents.

Initial amount: is the initial figure before being changed.
Percentage: is the percentage of change.

B - To solve percentage problems, we will use the following formula

You can use this formula for any percentage exercise, as long as you note the data correctly, and verify what has been asked.


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Test yourself on percentage!

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What percentage is 30 out of 1000?

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How to calculate the percentage?

If we want to know what percentage (Y) (Y) of a certain number (X) (X) is, the formula to use is:

X100×Y \frac{X}{100}×Y

If we want to know what percentage A A is of B B , the formula to use is:

AB×100 \frac{A}{B}×100

How to calculate the percentage?

To better assimilate the topic of percentages, you must first understand the concept behind it. Imagine you have a board of squares, as in the following drawing:

New square board

This board has 10 10 columns and 10 10 rows, so there are a total of 100 100 squares. One percent of the board is just one square. The 5% 5\% will be five squares. And the 100% 100\% will be the entire board.

In other words, one percent is a hundredth, or one hundredth part. When we are given percentages, we can always represent them as fractions, where the numerator is the percentage, and the denominator is 100 100 . This is represented with the percentage sign % \% . The line between the two small circles represents the fraction line, and the two circles indicate the two zeros in the number 100 100 .


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How to calculate percentages?

For example

30% 30\% , are 30 30 out of 100 100 . 3010030 \over 100

B2 - Example of new percentage calculation

6% 6\% are 61006 \over 100

75%=75100 75\%=\frac{75}{100}

So, 100% 100\% , are 100 within 100 100 100100100 \over 100That is, the whole total.


How do you calculate the percentage of something?

Another topic we must understand clearly is the concept of "total". When we talk about percentages, we always have to ask ourselves, "the percentage of what?". Saying 50% 50\% without specifying 50% 50\% of what, makes no sense.

Let's look at a very simple example: 50% 50\% of 100 100 is 50 50 ; 50% 50\% of a million is 500,000;50% 500,000; 50\% of 8 8 is 4 4 , and so on.

In other words, to solve percentage problems, first, you have to understand what the total is, and what 100% 100\% is before proceeding to calculate the percentage itself.


Do you know what the answer is?

How to calculate percentages?

First, you must understand the function of each piece of data: the total and the percentage. For example: a shirt that costs 200 200 dollars, will be the total, while the percentage will be, let's say as an example, a 25% 25\% discount. Without understanding the function of each of these pieces of data, it will be very difficult for you to solve this type of exercises.

Let's suppose we are asked how much we should pay for a shirt that costs 200, when we receive a discount of 25% 25\% . In this case, we must do the following calculation: 25 25 times 200=5000 200 = 5000 . This is the initial step to know what discount you will receive. In summary, you must perform a multiplication operation between the percentage (discount) and the total (price).

Now you must divide 5000 5000 by 100 100 . The result obtained is 50 50 . So in this case, a discount of 25% 25\% , actually means that the discount received is 50 50 dollars. How much will the shirt cost you after the discount? 150 150 pesos. This is a classic example of an exercise where you must demonstrate your knowledge on how percentages are calculated.


How to Calculate the Discount Percentage, Exercise with Solution

Imagine you have won 120 120 dollars in a bet, and that you have promised to give your little brother 30% 30\% of what you have won.
How much do you owe your brother?
The number we want to find will be represented by the letter X X .

We know that X X is a part of the money we have won in the bet.
Therefore, we can write it as follows:
X100X \over 100

Check your understanding

How to Calculate Percentage

What part does X X represent?
the 30% 30\%
So that means:
X120=30% \frac{X}{120}=30\%
As we have already learned, 30% 30\% is: 3010030 \over 100
Therefore, we can say that:

B3 - Example of percentage calculation

X120=30100\frac{X}{120}=\frac{30}{100}
We can easily solve this equation. We multiply crosswise and this is the result:
100×X=30×120 100\times X=30\times 120

100X=3600100X=3600
X=36X=36

So, the 30% 30\% of 120 120 , is 36 36 .
Keep in mind that the value of the percentage represents the real value that the percentage represents.
In this case, the value of the percentage represents the money we will give to our brother, for having promised him the 30% 30\% .
In summary, the percentage is 30% 30\% , and the value of the percentage is 36 36


Let's look at another example

How to calculate the percentage of a quantity

Alejandra and Natalia bought 30 30 hair ribbons. Alejandra took 10% 10\% of the ribbons, and the rest were given to Natalia as a gift. How many did Alejandra keep? We will perform the calculation in exactly the same way:

Since the total is 30 30 , and the percentage is 10 10 . First, we multiply 10 10 by 30 30 , which gives us 300 300 . Then we divide this figure by 100 100 , resulting in 3 3 . Therefore, Alejandra kept 3 3 hair ribbons, and the rest (27 27 ), were given to Natalia as a gift.

In fact, if we formulate it as a formula, we can find the missing data.
The formula will be:

X30=10100 \frac{X}{30}=\frac{10}{100}

This formula will be used in any percentage exercise.
You must understand the data well, and introduce it very carefully into the formula.
To show you various cases where you will use this formula (each time in a slightly different way), we will show you the following examples:


Do you think you will be able to solve it?

Another example of how to calculate percentages

How to Calculate the Percentage of a Number

Suppose that in a clothing store, you find a shirt you want to buy.
The shirt costs 200 200 dollars, but there is a 20% 20\% discount.

How much will the shirt cost after the discount?

Solution:
Let's look at the formula we wrote earlier, and place in it the data we already have.
It must be taken into account that if the shirt is sold with a 20% 20\% discount, it currently costs 80% 80\% , so our percentage will be 80 80 .
The percentage =80 =80 .
The initial amount, that is, the original price is 200 200
The percentage value is what we are missing, since we do not know how much we will have to pay after the discount. Therefore, the percentage value will be X X .
Which we will formulate in the following way:
80100=X200\frac{80}{100}=\frac{X}{200}
We multiply crosswise and this is the result:
100X=16000100X=16000
X=160X=160

After the discount, the price of the shirt is 160 160 dollars.


Another way to reach the same result is to calculate what the discount is

So, the first thing would be to reveal what the amount of the discount is.
Then, we will have to subtract this discount from the original price, and only then will we arrive at the price of the shirt after the discount:

Percentage =20 =20
Initial amount =200 =200
What we do not know is what the discount amount (20% 20\% ) will be. We will call this the Percentage Value. We call this missing data X X .
Which can be represented as follows:
20100=X200\frac{20}{100}=\frac{X}{200}
We multiply crosswise and this is the result:
100X=4000100X=4000
X=40X=40

Whose result is:
 X=40X=40
40 40 is not the amount we will have to pay after the discount.
40 40 represents the true value of 20% 20\% of200 200 .
So 40 40 dollars is the discount when buying the shirt.

Look again at what we have been asked in this exercise: the price of the shirt after the discount.
Now that we know that the discount is 40 40 dollars. We can calculate:

200-40=160 - Example of percentage calculation


Tricky question that might confuse you

The shorts are sold with a 40% 40\% discount.
After the discount, they cost 300 300 dollars (they seem to be luxury pants).
How much did the pants originally cost, before the discount?
Keep in mind,
that we have the price after the discount and the discount percentage.
If the pants were sold with a 40% 40\% discount, now it costs 60% 60\% of the price.
We can deduce that:
the percentage is equal to 60 60 .
We know that the value of 60% 60\% of the pants is equal to 300 300 dollars, because 300 300 dollars is the price of the pants after the discount.
Therefore,
the value of the percentage is equal to 300 300 .

What remains for us to find is the initial amount. We will call it X X .
We will formulate it as follows:
60100=300X\frac{60}{100}=\frac{300}{X}
We multiply crosswise and this is the result:
60X=3000060X=30000
X=500X=500

Therefore, 500 500 is the original price of the pants before the discount. (We have already told you that these are luxury pants).


Test your knowledge

Example of How to Find the Percentage

So far, we have known the value of the percentage. Now, we want to find the percentage itself.

Let's look at the following example

A bracelet originally costs 50 50 dollars.
Now, the selling price is 58 58 dollars.
What? Has the price gone up? Yes!
By what percentage did the price of the bracelet increase?
Solution:
Keep in mind that in this case, the initial amount is given and we can also find the percentage value, but the percentage itself is what is missing.
The initial amount is 50 50 .
Its current value after the price increase is 5858.
The percentage is what is missing (X X ).
Which we will formulate as follows:
X100=5850\frac{X}{100}=\frac{58}{50}
We multiply crosswise and this is the result:
50X=580050X=5800
X=116X=116

In fact, the percentage we received is higher than 100100.

What does this mean?
It means that the bracelet is sold at 116% 116\% of its original price.
The bracelet has become more expensive, and therefore now costs more than it did before.
How much more?
A 16% 16\%.
116100=16116-100=16

Sometimes, you will find complex exercises that have several stages to be solved. For example, a product that costs a certain price, and the value has gone up by 20% 20\%.
After that, it was reduced by 10% 10\% of the new price.
How much does the product cost now?
First, you must calculate the new price after the price increase.
Only then can you calculate the new price, that is, the reduction of 10% 10\% of the new price.


Do you know what the answer is?

Additional Information

If we take any number, increase it by a certain percentage, and then subtract that same percentage from the resulting number, we get a number that is lower than the initial number!
And also, keep the following in mind:
X% X\% of Y Y
is exactly equal to
Y% Y\% of X X.

The secret to success in this type of exercise is practice!
Practice the entire topic of percentages using the indicated formulas, and try to solve all kinds of exercises.
This way, you will know how to use the formulas effectively, and you will get the correct answers.


Examples of exercises

Exercise 1

How much is ¼ ¼ of 20 20?

Solution:

When we are asked to find a part (¼ ¼) of a whole number (20 20), we must multiply the part (in this case ¼ ¼), by the whole number.

Therefore: 14×20=204=5 \frac{1}{4}\times 20=\frac{20}{4}=5


Check your understanding

Exercise 2

The price of a shirt was 40 40 dollars, and now that there are discounts; its price has dropped by 20% 20\% .

We are asked to calculate the price of the shirt, after the 20% 20\% discount.

Solution: 

After the price discount, the shirt costs 80% 80\% (of the original price). 

The 80% 80\% are actually 80100=810=0.8 \frac{80}{100}=\frac{8}{10}=0.8

To calculate 80% 80\% of 40 40 we will perform a simple multiplication: 40×0.8=32 40\times 0.8=32

Therefore, the price of the shirt after the price discount, is 32 32 dollars. 


Exercise 3

Luis bought Juana a gift for the end-of-year holidays. When Juana asked him how much the gift cost, Luis replied that its real value is 400 400 dollars, but that he got a 30% 30\% discount. How much did Luis pay for the gift?

Here is the calculation:

30×400=12000 30\times 400=12000

12000100=120 \frac{12000}{100}=120

The discount Luis received on the purchase of the gift was 20% 20\% dollars. Here is the complete calculation: 400120=280 400-120=280 , so he paid 280 280 dollars for the gift.


Do you think you will be able to solve it?

Exercise 4

Ana and María bought 50 50 cookies. Ana ate 20% 20\% of the cookies and María ate the rest. How many cookies did María eat?

This is the calculation:

The total number of cookies is 50 50 , and Ana ate 20% 20\% of them. Therefore, we will perform the following multiplication: 20×50=1000 20\times 50=1000

The number we obtained was 1000 1000 , divided by 100=10 100=10 . So, Ana ate 10 10 cookies.

The complete calculation is:5010=40 50-10=40 . Therefore, María ate 40 40 cookies. 


Exercise 5

How much is 40% 40\% of 500 500 ?

This is a question that is formulated differently compared to the previous questions. Therefore, we will have to use a different calculation formula. In this case, you should divide the whole number by 100 100 and then multiply by the percentage.

For example: 

500100=5 \frac{500}{100}=5

5×40=200 5\times 40=200

The answer is: 40% 40\% of 500 500 is 200 200 .


Test your knowledge

Exercise 6

Given the fraction 35 \frac{3}{5} , convert the fraction to a percentage.

Solution:

The formula to calculate percentage

from a fraction is simple: we multiply the fraction by 100 100 .

35×100=3005=60% \frac{3}{5}\times100=\frac{300}{5}=60\operatorname{\%}

Answer:

The correct answer is 60% 60\%


Exercise 7

They filled a fish pond over two days. The first day they filled 180 180 cubic meters of water, and this amount constitutes 40% 40\% of the amount filled over two days.

Task:

How much water was filled over two days?

Solution:

Given that 180 180 cubic meters were filled in a pond and it is 40% 40\% of the amount filled over two days and it is 100% 100\% .

The question asks us to calculate how many cubic meters were filled in two days.

We calculate:

40% = 180 40\%\text{ = 180}

100=?

180×10040=18004=450 \frac{180\times 100}{40}=\frac{1800}{4}=450

The amount after two days is: 450 450


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The Multiplication Tables

In the blog of Tutorela you will find a variety of articles about mathematics.


Do you know what the answer is?

examples with solutions for percentage

Exercise #1

How much is the 42 % of 15?

Video Solution

Step-by-Step Solution

To solve the exercise, first we will convert the percentage to its fractional form:

42%=42100 42\%=\frac{42}{100}

Now, we multiply the fractional form by 15

15×42100= 15\times\frac{42}{100}=

Let's break down the 15 for the multiplication exercise and also the 100 in the denominator for the multiplication exercise:

3×5×425×20 3\times5\times\frac{42}{5\times20}

Keep in mind that the five in the two exercises can be reduced to maintain the exercise:

3×4220=3×(2×21)2×10 3\times\frac{42}{20}=\frac{3\times(2\times21)}{2\times10}

Here we can also reduce the 2 in the numerator and the denominator:

3×2110=6310=6.3 \frac{3\times21}{10}=\frac{63}{10}=6.3

Answer

6.3

Exercise #2

A 20% discount is applied to a toy ordinarily priced at $40.

What is the new price after the discount?

Video Solution

Step-by-Step Solution

408=32 40-8=32 To find percentages, we must use two pieces of information we have: the total amount (40)andthediscount(2040) and the discount (20%).</p><p>This information can be placed in the following formula:</p><p><span class="katex">\( \frac{Price\times\text{Percentage}}{100} Which allows us to find the percentage of something.

We replace:

40×20100= 40\times\frac{20}{100}=
800100= \frac{800}{100}=

8 8

We discover that the value of the discount is 8.

But we are not finished yet!

We need to subtract the discount from the original amount to find the sale price:
\( 40-8=32

Answer

32

Exercise #3

The price of to movie ticket htos risen from 40 to 45 pesos By whtot percenttoge did the price incretose?

Step-by-Step Solution

To answer the question, first we have to understand how much the ticket costs:

45-40=5

That is, the price of the ticket went up by 5$.

Now we would like to know what is the percentage value of 5 and, for that, we will divide the increase by the original price and multiply it by 100 to convert it into a percentage.

5/40 * 100

First we can start by converting the 100 into fraction form.

5/40 * 100/1

When there is multiplication of fractions, we can multiply numerator by numerator and denominator by denominator.

5*100 / 40*1

500 / 40

We simplify:

50/4

And now we will move to the complete form.

50/4 = 12.5

Answer

12.5%

Exercise #4

What percentage is 30 out of 1000?

Video Solution

Answer

3%

Exercise #5

What percentage is 8 out of 50?

Video Solution

Answer

16%

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