How to calculate percentage with examples | Pdf

How to calculate percentage with Examples | Pdf

One of the most demanded topic in Mathematics and mostly asked in national and international level entrance exams is calculation of percentages is a topic that still generates a lot of doubt, not only for students and pre-university students, but for everyone. This is because the action of calculating the percentage of a value is quite common in people's routine, whether it is buying products with discounts, to analyze fees in general, financing and even to calculate profit in various situations in the labor market etc. 

Learning how to calculate percentage is fundamental to solving many Mathematics problems for competitions , of the most varied subjects, such as Rule of Three , Proportionality, First Degree Equation, Probability , Financial Mathematics and even Geometry . Thinking about it, and knowing that although it is very useful, it is not always easy to calculate percentage, Today we developed an article to clarify everything about the How to calculate percentage. Are you interested in how to calculate the percentage? Then keep Reading on!

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What is percentage?

A percentage is a mathematical calculation to find the proportion between the whole and one of its parts. It is a mathematical measure that is used to compare quantities and to determine discounts, increase values, quantities, etc. The percentage is also often used to determine commissions, that is, an amount of money that is received or paid for a product or service. It is a word often used in the context of business, because it is the basis for calculating profits, losses and discounts.

To better understand, imagine the Following example : In an a event there has 160 guests on the list (here, the “whole” is represented by the total number and corresponds to 100% of the people invited) and 25% of these guests will not attend. How is it possible to know the total number of people missing? The percentage represents a value divided by 100. Thus, speaking 25% of a value is the same as saying 25 out of 100, that is, 25 divided by 100. And, to find out the exact number of absentees in the event, just multiply the whole by percentage. 

Thus: 160 x 25% = 160 (25/100) = 160 x 0.25 = 40.

Thus, we will have 40 people absent from the event. Ready! ?


Percentage symbol origin

The current symbol used to represent the percentage (%) is relatively recent. Some old documents show different ways of indicating the percentage during the Middle Ages, for example. Initially the expression "per cent" was used, which quickly evolved to "per 100". Over the centuries, other ways of representing the percentage have emerged, such as: pc-o , o / o and, finally, % .


What is the percentage point?

The percentage point (pp) consists of the unit that represents the difference between percentages. For example, when a discount goes from 30% to 45% it means that there has been a 50% increase in the discount amount. Some people may think that the increase is 15%, since this is the percentage that was added to the initial 30%. However, it is necessary to take into account the fact that 15% represents half of the initial percentage (30%), that is, it means 50% of this number. Thus, it can be said that the result between the increase from 30% to 45% is whether 15 percentage points or 50% increase.


What are the types of representation of a percentage?

Percentage Representation : Although the most common way to represent a percentage is with the % symbol, this is not the only one. We can also say "percent or" percent "in a fractional or decimal way. Check out how it is done in each situation using, as an example, 50 percent:

  1. Percentage form : As we have already seen, the symbol is used: 50%.
  2. Fractional form : When we have the denominator of the fraction with the number 100: 50/100.
  3. Decimal form : Decimal numbers are calculated by places and using commas. That way, 50 percent is 0.25.


Percentage Formula

To Calculate the percentage, we have to divide the value by the total value and then multiply the resultant by 100.

Percentage formula = (Value/Total value)×100

Percentages have no dimension. Hence it is called a dimensionless number. If we say, 50% of a number, then it means 50 per cent of its whole.


How to calculate percentage

In mathematics, calculating a percentage can be done using the simple 3 rule , as in the examples below.

  1. Determine the total or whole amount.
  2. Divide the number to be expressed as a percent by the total.In most cases, you'll divide the smaller number by the larger number.
  3. Multiple the resulting value by 100


Example 1 To determine the value of 30% of 200 , it is necessary to keep in mind that 100% is always equal to the total of the units, that is, 200.

The value of units referring to 30% is unknown, this number "x" being the answer obtained with the rule of three.

100% = 200 | 30% = X

So X over 30 is equal to 200 over 100:

X / 30 = 200/100

Thus, we have:

100X = 200.30

We multiply 200 by 30 and we get the result of:

100X = 6000

With the result of the multiplication, and following the rule of three, we divide the value by 100 to find the value of X.

X = 6000/100

X = 60 .

So, 30% of 200 is 60 .


Example 2Imagine that a teacher has 450 students and, in the final exams, only 8% of the total of her students got the maximum grade. To find out how many students scored, the percentage calculation should be done as follows:

To find the value of 8% of 450, one must keep in mind that 100% is always equal to the total of the units, that is, 450.

The value of units for 8% is unknown. Then, we will call it “X” to get the answer using the rule of three:

100% = 450 | 8% = X

X over 8 is equal to 450 over 100:

X / 8 = 450/100

Applying the rule of three, we have:

100X = 450.8

So, we multiply 450 by 8 and we get the result of:

100X = 3600

With the result of the multiplication, and following the rule of three, we divide the value by 100 to find the value of X.

X = 3600/100

X = 36 .

Thus, we know that 36 students got the maximum grade in the final exams, because 8% of 450 = 36 .


How to calculate percentage quickly?

If you've made it this far, you've already realized that some percentage calculations do take some time to solve and require a little concentration. The good news is that not all are so complex - the vast majority are quite simple.

For this reason the questions do not take so much time when taking a test or exam, we have brought two methods to calculate percentage quickly. Calculate with us:


Method 1: calculate percentage using 1%

One of the quickest ways to find out what percentage is to use the one corresponding to 1% of the value. To better explain this method, let's use the example of 30% of 300, okay?

The first step, then, is to divide the value by 100, finding the result that represents 1%. Thus:

$\frac{300}{100}=3$

So, just multiply this value, which represents 1%, by the percentage we want to find out. So:

3.30 = 90

Ready, result found! We found that 30% of 300 is equal to 90.


Method 2: calculate percentage using equivalent fractions

Another very quick way to arrive at a percentage result is through equivalent fractions. They, in turn, represent the same part of the whole and are found when we divide the numerator and denominator of the fraction by the same natural number. Check out the example:

$\frac{50}{100}$

How to find fraction that equals 

$\frac{50 \div 50}{100 ; 5=}=\frac{1}{2}$

We found, then, that the fraction 50/100 equals ½. Now, to find 50% of the value, just divide it by 2. Thus:

$50 \%$ of $100=100 / 2$

$\frac{50}{100}$ equnae $\frac{1}{2}$

$50 \%$ of $100=50$

$50 \%$ of $100=\frac{100}{2}$

$50 \%$ of $100=50$


How to calculate percentage on the calculator?

To calculate the percentage in a common calculator is quite simple, since the vast majority have their own key for this type of account, the “%”. See step by step to calculate 5% of 200:

Enter the whole number you want to calculate a part of: 200

Now, press the times key: X

Enter the percentage number: 5

To finish, press the percentage key: %

The result that will appear on the calculator is 10 .


How to calculate percentage in Excel?

To calculate a percentage using Excel is also very simple, just a few formulas are enough. Let's assume, then, that you are going to buy a product and discover that 23% of it is related to taxes. To calculate the value in cash, the process is very simple: enter the total value of the product in the first column of the table and, in the second, put the percentage that needs to be calculated. Then, just divide by one another!

In the example below, we enter the total value of the product in cell B4 and the percent we want to calculate in C4. In the third column, then, we put the formula to find the result = B4 / C4. Check out.


How to calculate a percentage increase?

The percentage increase can be obtained in two different ways. The first is to calculate it from an untransformed value, in other words a value on which the percentage has not yet been taken into account. In this case, multiply the original amount by the percentage rate to get the increase. It suffices then to carry out an addition to have the amount which includes this same increase. Another possibility: you do not have the percentage itself, but only the values ​​before and after its application. In this case, make a cross product: amount of the sum with increase x 100 / initial value. For example for 50 with application of the percentage on an initial basis of 40 (translated by 100 in percentage), we obtain 125 (125% of the base amount) in equivalence for the 50. The increase is then 25%.


How to calculate a percentage reduction?

Although we have to take the problem backwards, the calculation method for a percentage reduction remains similar to what was mentioned previously. On a basis of comparison between the initial value and the sum obtained after applying the percentage, you must also produce the same cross product as for a percentage increase. Another example: for an amount of 60 after applying a discount based on a starting price of 80 (percentage value: 100), the value of 60 is 75 (75% of the base amount ). The reduction is therefore 25%.


How to calculate a percentage without a calculator?

While the calculator is still handy, calculating a percentage using the cross product on paper is just as quick and easy. Place your values ​​vertically on the left (as for an Excel column) and, to their right, the percentages. Since we are looking for the latter, the only one you have is 100 for the initial value. Perform the following operation to discover the increase or reduction equivalent to your new value: value obtained after applying the percentage x 100 / initial value.


How to calculate percentage in questions involving variation

Above, you have already seen what are the main ways we have to calculate percentage. However, it is also quite common to come across situations in which it is necessary to calculate the percentage rate of change, especially students who take a math test

In this case, the percentage rate is given by:

$i=\frac{\text { variation }}{\text { inicial variation }} \cdot 100 \%$

To better explain, this means that the variation is due to the difference between the final value and the initial value. So, we can write the formula in another way to calculate the percentage:

$i=\frac{V_{\text {final }}-V_{\text {inicial }}}{V_{\text {inicial }}} \cdot 100 \%$


Simple and compound interest

When talking about percentage, one of the themes that comes to mind most is related to interest. That's because this is a subject that is present in our daily lives and that falls a lot in the entrance exams and in Enem. However, there are two types: simple interest and compound interest. Below, we’ll explain the difference between them so you don’t make mistakes in your account anymore:

Simple interest

They are additions added to the initial value at the end of an application and this growth occurs in a linear manner.

The formula for finding simple interest is : j = Cit (j = interest; C = capital; i = rate; t = time).


Compound interest

They are additions added to the value at the end of each stage of an application, resulting in a new value (this is also known as interest on interest). This growth occurs exponentially and, therefore, is much faster.

The formula for compound interest is: (S = amount; P = principal; i = interest rate; n = number of periods P has been applied to).


Reason and proportion

Now we can talk about mathematics without mentioning reason and proportion, a topic that is heavily demanded in entrance tests and that usually generates some doubts. Shall we clarify them, then?

The reason is given by the comparison between two large ones, that is the coefficient between two numerals. The proportion , in turn, determines the equality between two reasons, or better, when two reasons present equal results.


Some Solved examples to calculate percentage:

Question 1 : Rahul scored 736 marks out of 800 in her exams. What was the percentage she scored?

Solution:

Total marks of the examination = 800

Marks scored by rahul = 736

Suppose rahul scored A% marks x

$\begin{array}{ll}\frac{\mathrm{A}}{100}=\frac{736}{800} \\ \frac{\mathrm{A}}{100} \times 100=\frac{736}{800} \times 100 & \text { ....(Multiplying both sides by } 100 \\ \mathrm{~A}=\frac{736 \times 100}{800}\end{array}$

Rahul scored 92% Marks


Question 2. Rupali received 40 messages on his birthday. Of these, 90% were birthday greetings. How many other messages did he get besides the greetings?

Solution:

Total messages received by Rupali on his birthday = 40

Percentage of messages received for birthday greetings = 90%

Suppose Rupali got A number of birthday greetings.

$\frac{A}{40}=\frac{90}{100}$

$\frac{A}{40} \times 40=\frac{90}{100} \times 40 \quad \ldots$ (Multiplying both sides by 40

$A=\frac{90 \times 40}{100}$

∴ A = 36

∴ Number of messages received other than birthday greetings

= total messages received – total number of birthday greetings

= 40 – 36 = 4

∴ The number of messages received other than birthday greetings is 4.


Question 3. Of the 5675 people in a village 5448 are literate. What is the percentage of literacy in the village?

Solution:

Number of people in the village = 5675

Number of people who are literate = 5448

Suppose the percentage of literacy in the village is A%.

$\frac{\mathrm{A}}{100}=\frac{5448}{5675}$

$\frac{\mathrm{A}}{100} \times 100=\frac{5448}{5675} \times 100 \quad \ldots$ (Multiplying both sides by 100

$\mathrm{~A}=\frac{5448 \times 100}{5675}$


The percentage of literacy in the village is 96%.


Question 4. In the elections, 1080 of the 1200 women in Jambhulgaon cast their vote, while 1360 of the 1700 in Wadgaon cast theirs. In which village did a greater proportion of women cast their votes?

Solution:

Total number of women in Jambhulgaon = 1200

Number of women in Jambhulgaon who voted = 1080

Suppose A% women cast their vote in Jambhulgaon village.

$\frac{\mathrm{A}}{100}=\frac{1080}{1200}$

$\frac{\mathrm{A}}{100} \times 100=\frac{1080}{1200} \times 100$

.... (Multiplying both sides by 100

∴ A = 90%

In Jambhulgaon, the percentage of women who voted in the elections was 90%.

Total number of women in Wadgaon = 1700 Number of women in Wadgaon who voted = 1360

Suppose B% women cast their vote in Wadgaon.

$\frac{\mathrm{B}}{100}=\frac{1360}{1700}$

$\frac{\mathrm{B}}{100} \times 100=\frac{1360}{1700} \times 100$

$\ldots$. (Multiplying both sides by 100 $B=\frac{1360 \times 100}{1700}$

∴ B = 80%

∴ In Wadgaon, the percentage of women who voted in the elections was 80%.

∴ A greater proportion of women cast their votes in Jambhulgaon.