 # Percentage Formula  View Notes

## Calculate Percentage

There are various formulas to find a percentage that helps in solving percentage problems. Imagine the most basic percentage formula: P% × A = B. However, there are many mathematical variations of the percentage calculation formulas. Let's take a look at the three basic percentage problems that can be solved using percentage formulas. ‘A’ and ‘B’ are numbers and P is the percentage:

• Find P percent of A

• Find what percent of A is B

• Find A if P percent of it is B

For example, 25% of 1000 is 250

$\frac{is}{of}$ = %/100 or $\frac{part}{whole}$ = %/100

Percentage Formula

### How to Find what percent (%) of A is B.

Example: What percent of 75 is 15?

Follow the below step-by-step procedure and solve percentage problem in one go

1. First, you will require to convert the problem to an equation using the formula of percentage i.e. A/B = P%

2. Do the math, since A is 75, B is 15, so the equation becomes: 15/75 = P%

3. Solve the equation: 15/75 = 0.20

4. Note! The outcome tends to be always in decimal form, not a percentage. Therefore. We will require multiplying the outcome by 100 to obtain the percentage.

5. Convert the decimal 0.20 to a percent multiplying it by 100

6. We get 0.20 × 100 = 20%

So 20% of 75 is 15

### How to Find A if P percent of it is B

Example: 50 are 10% of what number?

Follow the below step-by-step procedure and solve percentage problem in one go

1. First, convert the problem to an equation using the formula of percentage i.e. B/P% = A

2. Given that value of ‘B’ is 50, P% is 10, so the equation is 50/10% = A

3. Convert the percentage to a decimal form, dividing by 100.

4. Converting 10% to a decimal brings us: 10/100 = 0.10

5. Substitute 0.10 for 10% in the equation: 50/0.10 = A

6. Do the math: 50/0.10 = A

A = 500

So 50 is 10% of 500

### Percentage Difference Formula

The percentage difference between the two values/numbers is reckoned by dividing the absolute value of the difference between the two values by the average of those two values. Multiplying the outcome by 100 is purposed to produce the solution in the form of percent, rather than in decimal. Take a look at the below equation for an easy explanation;-

Percentage Difference formula = |A1 – A2|/ (A1 + A2)/2× 100

For example: find out the percentage difference between two values of 20 and 4

Solution: given two values is 20 and 4

So,

|20 - 4| / (20 + 4)/2 × 100

= 4/3 × 100

= 1.33 × 100

= 133.33%

### Percentage Change Formula

Percentage decrease and increase are reckoned by determining by the difference between two values and comparing that difference to the primary value. With respect to mathematical concepts, this involves considering the absolute value of the difference between two values and dividing the outcome by the primary value, typically computing how much the primary value has changed.

The percentage change calculator computes an increase or decrease of a definite percentage of the input number. It typically takes into account converting a percent into its decimal equivalent, and either adding or subtracting the decimal equivalent from and to 1, respectively. Multiplying the primary number by this value will lead to either an increase or decrease of the number by the given percent. Refer to the example below for clarification.

Refer to the below equation for easy explanation:-

Example: 700 increased by 20% (0.2)

700 × (2 + 0.2) = 840

700 decreased by 10%

700 × (1 – 0.1) = 630

### Solved Examples

Example1

Find out ___% of 15 is 6

Solution1

Here whole = 15 and part = 6, but % is missing

We obtain:

6/15 = %/100

Replacing % by x and cross-multiplying provides:

6 × 100 = 15 × x

600 = 15 × x

Divide 600 by 15 to get x

600/15 = 40, so x = 40

Thus, __40_% of 15 is 6

Example2

The tax on a soap dispenser machine is Rs 25.00. The tax rate is 20%. What is the price without tax?

Solution2

P × 20/100 = 25

= 20/100 equal 5

Solve the equation multiplying both sides by 100 and then dividing both sides by 20.

The price without tax is Rs. = 125

### Fun Facts

1. The percentage (%) sign bears a significant ancient connection. Ancient Romans often performed calculations in fractions dividing by 100, which is presently equivalent to the computing percentages.

2. Calculations with a denominator of 100 became more typical since the introduction of the decimal system.

3. Percentage methods had frequently been used in medieval arithmetic texts to describe finances, such as interest rates.

Q1. How to know the percentage calculation is Accurate?

Ans. A common mistake we tend to do when finding percentages is division instead of multiplication of the decimal conversion. For the fact that percentages are often perceived as parts of a larger whole thing, there can be a likelihood of dividing instead of multiplying when met with a problem such as "find 30% of 160." Always remember, after converting the percent to a decimal form, next is to multiply, not divide.

A proper understanding of percent enables us to estimate whether the answer is logical. From the above example, knowing that 30% is between one-quarter and one-half, this would mean the answer should be somewhere between 30 and 50. And the answer is 48 (0.30×160). By dividing (0.30×160), you would get 533.33 which are completely wrong.

Q2. What is the Percentage?

Ans. Percent refers to a proportion "out of 100" or "for every 100”. It is denoted by the symbol (%) symbol. A percentage makes for a fast means to write down a fraction with a denominator of 100. For example, instead of saying “the tutor covered 17 history lessons out of every 100," we say "she covered 17% of the history syllabus."

Q3. How to convert a Percentage to a Decimal?

Ans. Eliminate the symbol of percentage and divide by 100

25.70% = 25.7/100 = 0.257

Q4. How to convert a Decimal to a Percentage?

Ans. Add the sign of percentage and multiply by 100

0.257 = 0.257 × 100 = 25.7%

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