**Percentage**

In mathematics, percentage or percent is a number or ratio (ratio) to express the fraction of one hundred. Percentage is indicated by the symbol % to calculate percentages. In this article, you will find, how to calculate percentage increase, decrease, the formula for calculating the loss if you know the percent loss and the purchase price, to calculate the percentage of profit…

Percentages are also used although they are not the hundreds element. The number is then scaled so that it can be compared to a hundred.

For example, 4 lecturers are supervising exams on campus, 3 of them are not wearing glasses, and 1 person is wearing glasses. The percentage of glasses without glasses is 3 of 4 = 3/4 = 75/100 = 75%, while lecturers with glasses are 1 in 4 = 1/4 = 25/100

**Formulas to Calculate Percentage**

**The formula to calculate percent**

Percentage (%) = (share / whole) x 100

**The formula to calculate the percent value**

Percent value = [Percent Value] x [100] x [Fraction Value]

Percent value = [Percent Value] x [Fraction Value]: [100]

**Looking for the percent value (%)**

Percent = [Value]: [Fraction Value] x [100]

Discount Price = Initial Price x Discount Percentage.

**The formula to calculate the percentage of profit**

% Profit = profit / purchase price x 100%

**The formula to calculate the profit if you know the percent profit and the purchase price**

Profit =% profit / 100 x purchase price

**The formula to calculate the percentage of loss**

% Loss = loss / purchase price x 100

**The formula for calculating the loss if you know the percent loss and the purchase price**

Loss =% loss / 100 x Purchase price

**The formula for calculating the selling price with a certain percentage of profit**

Selling price = [100 +% profit] / 100 x Purchase price

**The formula for calculating the purchase price which is known as the percentage of profit and the selling price**

Purchase price = 100 / [100 +% profit] x Selling price

**The formula for calculating the selling price with a certain percentage loss**

Selling price = [100 – loss] / 100 x selling price

**The formula for calculating the purchase price which is known as the percentage loss and the selling price**

Purchase price = 100 / [100 -% loss] x Selling price

**How to calculate percentage increase**

In order to calculate the value of an increase, the following calculation should be used: increase value = initial value * percentage increase / 100. To know the price after an increase, the following calculation must be carried out: End value = Initial value x (1 + Percentage increase / 100). Take the case of a rent payment here: today if you pay $ 500 and you are going to be increased by 2% for the following year, this is how it will work:

The rent increase = 500 * 2/100 = $ 10

The rent will therefore be 500 + 500 * 2/100 = $ 510

**How to calculate percentage decrease**

To calculate percentage decrease:

First: work out the difference (decrease) between the two numbers you are comparing. Then: divide the decrease by the original number and multiply the answer by 100. If your answer is a negative number, then this is a percentage increase.

**Reverse percent calculation**

Knowing how to evaluate the reverse percentage is a mathematical operation that finds its place in many everyday cases: if you want, for example, to know the gain obtained when purchasing a product at a discount at a certain percentage or to establish the rate of the VAT of an item. The calculation of the reverse percentage is essential to know two numerical values and to define the percentage of reduction granted. For example, during sales a merchant tells you your profit as a percentage:

Pants that have a base value of $ 80 but are 40% off. The amount of the discount will therefore be evaluated as follows: (starting price * rate) / 100. Which makes: (80 * 40) / 100 or $ 32.

To get the final price, the following calculation will be made: base price – amount of the discount; either: 80 – 32 or $ 48.

**How to calculate percentage of a sum?**

Use the following formula: partial value / total value = percentage, or 30.85 / 64.4 = 0.479, which corresponds to 47.9%.

**How to calculate percentage to the deduction of a discount**

During the sales period, it is necessary to properly assess the amount of reduction. The formula to calculate it is: the discount value = starting value * discount percentage / 100. In order to know the final value, follow this formula: final value = initial value * (1- discount percentage / 100).

deduction of a discount

Take the example of the winter sales: there is a 40% discount on boots that are normally worth $ 100. Here is how the calculation will be done:

Discount amount = 100 * 40/100 = $ 40

Price after discount = 100-100 * 40/100 = $ 60

In order to calculate the value of an increase, the following calculation should be used: increase value = initial value * percentage increase / 100. To know the price after an increase, the following calculation must be carried out: End value = Initial value x (1 + Percentage increase / 100). Take the case of a rent payment here: today if you pay $ 500 and you are going to be increased by 2% for the following year, this is how it will work:

The rent increase = 500 * 2/100 = $ 10

The rent will therefore be 500 + 500 * 2/100 = $510

**Calculation of the rate of change in %**

Let us end our explanation by evaluating the rate of change. Note that a variation between two numbers will correspond either to a discount or to an increase depending on the initial value. The formula for calculating the rate of change is as follows: Rate of change (%) = 100 x (End value – Initial value) / Initial value. Now let’s talk about business and turnover. If your company has a turnover of $12,000 and it has increased to $15,000 in one year, then it has increased by: 100 * (15,000-12,000) / 12,000 = 25%.

**How to convert a percentage to a decimal**

Remove the percentage sign and divide by 100

15.6% = 15.6/100 = 0.156

**How to convert a decimal to a percentage**

Multiply by 100 and add a percentage sign

0.876 = 0.876 * 100 = 87.6%

**Example Percentage Problems**

There are nine variations on the three basic problems involving percentages. See if you can match your problem to one of the samples below. The problem formats match the input fields in the calculator above. Formulas and examples are included.

**What is P percent of X?**

- Written as an equation: Y = P% * X
- The ‘what’ is Y that we want to solve for
- Remember to first convert percentage to decimal, dividing by 100
- Solution: Solve for Y using the percentage formula

**Y = P% * X**

**Example: What is 10% of 25?**

- Written using the percentage formula:
**Y = 10% * 25** - First convert percentage to a decimal 10/100 = 0.1
- Y = 0.1 * 25 = 2.5
- So 10% of 25 is 2.5

- Written using the percentage formula:

**Y is what percent of X?**

- Written as an equation: Y = P% ? X
- The ‘what’ is P% that we want to solve for
- Divide both sides by X to get P% on one side of the equation
- Y ÷ X = (P% ? X) ÷ X becomes Y ÷ X = P%, which is the same as P% = Y ÷ X
- Solution: Solve for P% using the percentage formula

**P% = Y ÷ X**

**Example: 12 is what percent of 40?**

- Written using the formula:
**P% = 12 ÷ 40** - P% = 12 ÷ 40 = 0.3
- Convert the decimal to percent
- P% = 0.3 × 100 = 30%
- So 12 is 30% of 40

- Written using the formula:

**Y is P percent of what?**

- Written as an equation: Y = P% * X
- The ‘what’ is X that we want to solve for
- Divide both sides by P% to get X on one side of the equation
- Y ÷ P% = (P% × X) ÷ P% becomes Y ÷ P% = X, which is the same as X = Y ÷ P%
- Solution: Solve for X using the percentage formula
- X = Y ÷ P%

**Example: 9 is 60% of what?**

- Writen using the formula: X = 9 ÷ 60%
- Convert percent to decimal
- 60% ÷ 100 = 0.6
- X = 9 ÷ 0.6
- X = 15
- So 9 is 60% of 15

Read also: Geometry Formulas with Questions and Answers

**What percent of X is Y?**

- Written as an equation: P% * X = Y
- The ‘what’ is P% that we want to solve for
- Divide both sides by X to get P% on one side of the equation
- (P% * X) ÷ X = Y ÷ X becomes P% = Y ÷ X
- Solution: Solve for P% using the percentage formula

**P% = Y ÷ X**

**Example: What percent of 27 is 6?**

- Written using the formula: P% = 6 ÷ 27
- 6 ÷ 27 = 0.2222
- Convert decimal to percent
- P% = 0.2222 × 100
- P% = 22.22%
- So 22.22% of 27 is 6

**P percent of what is Y?**

- Written as an equation: P% × X = Y
- The ‘what’ is X that we want to solve for
- Divide both sides by P% to get X on one side of the equation
- (P% × X) ÷ P% = Y ÷ P% becomes X = Y ÷ P%
- Solution: Solve for X using the percentage formula

**X = Y ÷ P%**

**Example: 20% of what is 7?**

- Written using the formula: X = 7 ÷ 20%
- Convert the percent to a decimal
- 20% ÷ 100 = 0.2
- X = 7 ÷ 0.2
- X = 35
- So 20% of 35 is 7.

**P percent of X is what?**

- Written as an equation: P% * X = Y
- The ‘what’ is Y that we want to solve for
- Solution: Solve for Y using the percentage formula

**Y = P% * X**

**Example: 5% of 29 is what?**

- Written using the formula: 5% * 29 = Y
- Convert the percent to a decimal
- 5% ÷ 100 = 0.05
- Y = 0.05 * 29
- Y = 1.45
- So 5% of 29 is 1.45

**Y of what is P percent?**

- Written as an equation: Y / X = P%
- The ‘what’ is X that we want to solve for
- Multiply both sides by X to get X out of the denominator
- (Y / X) * X = P% * X becomes Y = P% * X
- Divide both sides by P% so that X is on one side of the equation
- Y ÷ P% = (P% * X) ÷ P% becomes Y ÷ P% = X
- Solution: Solve for X using the percentage formula

**X = Y ÷ P%**

**Example: 4 of what is 12%?**

- Written using the formula: X = 4 ÷ 12%
- Solve for X: X = Y ÷ P%
- Convert the percent to a decimal
- 12% ÷ 100 = 0.12
- X = 4 ÷ 0.12
- X = 33.3333
- 4 of 33.3333 is 12%

**What of X is P percent?**

- Written as an equation: Y / X = P%
- The ‘what’ is Y that we want to solve for
- Multiply both sides by X to get Y on one side of the equation
- (Y ÷ X) * X = P% * X becomes Y = P% * X
- Solution: Solve for Y using the percentage formula

**Y = P% * X**

**Example: What of 25 is 11%?**

- Written using the formula: Y = 11% * 25
- Convert the percent to a decimal
- 11% ÷ 100 = 0.11
- Y = 0.11 * 25
- Y = 2.75
- So 2.75 of 25 is 11%

**Y of X is what percent?**

- Written as an equation: Y / X = P%
- The ‘what’ is P% that we want to solve for
- Solution: Solve for P% using the percentage formula
- P% = Y / X

**Example: 9 of 13 is what percent?**

- Written using the formula: P% = Y / X
- 9 ÷ 13 = P%
- 9 ÷ 13 = 0.6923
- Convert decimal to percent by multiplying by 100
- 0.6923 * 100 = 69.23%
- 9 ÷ 13 = 69.23%
- So 9 of 13 is 69.23%

**Questions and Answers**

**1. The Holiday Sport company is organizing an exceptional sale of all its winter equipment, with a reduction of 65% on the normal price. You’ve found the snowboard jacket you’ve been wanting for a year. It was $ 220 before the sale. How much does it cost now?**

Nice find! Well, this jacket is 65% off the $ 220. First we need to find out what 65% of 220 is. Let’s translate this into an equation:

What is (x) (=) 65% (0.65) of (multiply) 220?

x = 0.65 × 220

Now solve the equation.

x = 0.65 × 220 = 143

**3. Question: 24% of ___ is 36**

This time, notice that is = 36, but of is missing

After you set up the formula, you get:

36/of = 24/100

Replace of by y and cross multiply to get:

36/y = 24/100

y × 24 = 36 × 100

y × 24 = 3600

Divide 3600 by 24 to get y

3600/24 = 150, y = 150

Therefore, 24 % of 150 is 36

**4. Linda was about to buy a new table, after choosing the table she wanted, Linda then went to the cashier to pay for the table. After being given a discount with an amount of 40% the price of the table becomes $ 650. Calculate what the initial price of the table is before the discount is given?**

Answer:

It is known: the final price = $ 650 Percentage discount = 50%. Asked: Initial price =…?

Use comparative logic: X% + Y% = Z%

50% + 50% = 100% $ X + Rp. 650,000 = Rp. Z

($ 650 x 50%): 50% = $ 650

Then the initial price is $ 650 + $ 650 = $1,300

**5. Michael Jackson bought a nice house / villa. If Michael has $ 120 000 000 home installment loan, with monthly installments of 3 520 000, for 47 times, then what percentage of Michael’s monthly installments of his loan?**

**Based on the problem or percent question above, we know about the loan amount of $ 120 000 000.**

The monthly installments are $ 3 520 000

Because we are asked for the percent of installments each month, the value we have to look for is the amount of the increase in installment fees or loans that are charged to Michael each month.

First we look for the value of each month’s payment or monthly installments without loan interest, which is $120 000 000 / 47 installments = $ 2 553 191.

This is the whole value. So that the amount of the increase charged or the interest on Michael’s loan is Rp. 3,520,000 – $ 2,553,191 = $ 966,809. The $ value is then percentaged using the percent calculation formula above.

Percent = (share / whole) x 100% = ($ 966,809 / 2553,191) x 100% = 37, 87%. So that Michael’s monthly installment percent or Michael’s monthly loan interest is $ 966,809, high isn’t it!

**6. In January John worked a total of 35 hours, in February he worked 45.5 hours – by what percentage did John’s working hours increase in February?**

To answer this problem, first we calculate the difference in hours between the new and old numbers. 45.5 – 35 hours = 10.5 hours. We can see that John worked 10.5 hours more in February than he did in January – this is his **increase**. To work out the increase as a percentage it is now necessary to divide the increase by the original (January) number:

**10.5 ÷ 35 = 0.3 **(See our **division** page for instruction and examples of division.)

Finally, to get the percentage we multiply the answer by 100. This simply means moving the decimal place two columns to the right.

**0.3 × 100 = 30**

**John therefore worked 30% more hours in February than he did in January.**

In March John worked 35 hours again – the same as he did in January (or 100% of his January hours). What is the percentage difference between Dylan’s February hours (45.5) and his March hours (35)?

First calculate the decrease in hours, that is: **45.5 – 35 = 10.5**

Then divide the decrease by the original number (February hours) so:

**10.5 ÷ 45.5 = 0.23** (to two decimal places).

Finally multiply 0.23 by 100 to give 23%. **John’s hours were 23% lower in March than in February.**

You may have thought that because there was a 30% increase between John ’s January hours (35) and February (45.5) hours, that there would also be a 30% decrease between his February and March hours. As you can see, this assumption is incorrect.

The reason is because our original number is different in each case (35 in the first example and 45.5 in the second). This highlights how important it is to make sure you are calculating the percentage from the correct starting point.

Sometimes it is easier to show percentage decrease as a negative number – to do this follow the formula above to calculate percentage increase – your answer will be a negative number if there was a decrease. In John ’s case the *increase* in hours between February and March is -10.5 (negative because it is a decrease). Therefore -10.5 ÷ 45.5 = -0.23. -0.23 × 100 = -23%.

John ‘s hours could be displayed in a data table as:

Month | Hours Worked | Percentage Change |

January | 35 | |

February | 45.5 | 30% |

March | 35 | -23% |

**7. What is 10% of 150?**

Convert the problem to an equation using the percentage formula: P% * X = Y

P is 10%, X is 150, so the equation is 10% * 150 = Y

Convert 10% to a decimal by removing the percent sign and dividing by 100: 10/100 = 0.10

Substitute 0.10 for 10% in the equation: 10% * 150 = Y becomes 0.10 * 150 = Y

Do the math: 0.10 * 150 = 15

Y = 15

So 10% of 150 is 15

Double check your answer with the original question: What is 10% of 150? Multiply 0.10 * 150 = 15

Sources: PinterPandai, Omni Calculator

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