In this lesson, students will learn about the absolute basics of Percentages. The purpose of this lesson is to help the student to get an answer one simple question related to percentage. We make a lot of use of percentage calculation in our day-to-day life. A percentage is a portion of a whole expressed as a number between the zero and 100 rather than as a fraction. Thus all of something is 100 percent. Sometimes to know the discounts on the price value the percentage formula proves much important. In this topic, we will discuss the percentage formula with examples. Let us learn it!

## Percentage Formula

### What is the Percentage?

Percent implies “for every hundred” and its sign is “%”.It is read as the percentage and therefore x% is read as x percent. Therefore, a fraction with denominator 100 is called a percent. For example, 30 % means \(\frac{30}{100}\) (i.e. 30 parts from 100). This can also be written as 0.30.

### Formula for Percentage

To calculate p % of q, use the following formula:

\(\frac{p}{100} \times q \)

Also remember here : p % of q = q % of p

For Examples:

- \(100% of 60 is 60 \times \frac{100}{100} = 60\)
- \(50% of 60 is \frac{50}{100} \times 60 = 30\)
- \(5% of 60 is \frac {5} {100} \times 60 = 3\)

**Steps to find out percentage value:**

- Visualize what a percentage represents. A percentage is an expression of some part of the whole.
- Determine the value of the whole first.
- Then find the value that we want to turn into a percentage.
- Then put the two values into a fraction.
- Convert the fraction into its decimal equivalent.
- Finally, convert the decimal into a percent.

### Some important tips are given as follows:

Basic Tip-1: If the new value of something is p times the previously given value, then the percentage increase will be \( (p-1) \times 100 %. \)

Basic Tip-2: When a quantity n is increased by k %, then the:

New quantity = \(n \times (1+ \frac { k }{ 100 }) \)

Basic Tip 3: When a quantity p is decreased by k %, then the:

New quantity = \(p (1 – \frac {k} {100} ) \)

**Understanding the concept:**

To determine the percentage value we divide the portion of the whole by the whole itself and then multiply it by 100. Therefore, if we just ate two pieces of an eight-piece pie, then we may calculate the percentage of the pie which we have consumed.

First, we will divide 2 by 8 which will be o.25. Then multiply 0.25 by 100 to get 25 percent. A percentage may also mean a portion of something but only when it has to do with numbers. When we buy furniture, then the salesman gets a percentage of what we spend.

## Solved Examples

Q.1: 60 % of some number is 360. What will be 99 % of the same number?

Solution: Let the number be x.

Given here, \(\frac{60}{100} \times x = 360\)

i.e. x = 600

Now, 99 % of 600

= \(\frac {99}{100}\times 600\)

= 594

Q.2. 50 % of some number is 360. What will be 99 % of the same number?

Solution: Let the number be y.

Given \(\frac {50}{100} \times q\)

= 360

i.e q = 720

99% of 720

\(\frac {99}{100} \times 720\)

= 712.80

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