What is Percentage

The word percent means one part in a hundred.

Percentage is a number or ratio as a fraction of 100. The number of a percentage is always followed by a percent symbol (%). Below are examples of percentages:

`5%,10%,33 1/3%``,67.5%,100% `

Percentage is applied in different fields. It is commonly used in accounting and finance such as interest rates, profits, sales and taxation. A number of schools and universities used percentages to express the grades of the students. Probabilities, nutrition facts and downloading process are represented by percentages.


Terms to remember

Fraction ratio between two nonzero integers.Ex. 1/2
Ratio relationship between two numbers. Ex. 1:2
Mixed Number a whole number and a proper fraction. Ex. 1 2/3
Proper Fraction a fraction having a numerator which is less than the denominator. Ex. 3/4
Quantity a number representing an amount or value
Distinguish identify differences between two or more subjects.

Calculating the Percentage


The percentage is the result when a specific number is multiplied by a percent. Most of the time, percentages are smaller than the number since a percentage is a portion of a number or quantity. But there are cases that the percentage is greater than the number. This would happen if the percent is greater than 100%.

In short, a percentage is a certain percent of a number.

Most of the time, the quantity is followed by the phrase "percent of".

For example;

70% of 50 is 35.

In this statement, 50 is the quantity, 35 is the percentage and 70% is the percent.

Example 3:
 24
Explanation:

40 is the percent.

60 is the quantity.

Percentage is the required quantity.

Multiplying the number by the percent;

`60 ` x `40% = 60` x `40/100 = 2400/100 = 24`

Therefore, 40% of 60 is 24.

Example 4:
 27
Explanation:

75 is the percent.

36 is the quantity.

Multiplying the number by the percent;

`36` x `75% = 36` x `75/100 = 2700/100 = 27`

Therefore, 27 is 75% of 36.


Calculating the Percent


In finding the percent of a number, divide the percentage by the quantity then multiply the product by 100. Put a percent symbol (%) after the final product.

If the percentage is greater than the quantity, this means that the percent is greater than 100%. The percent is a factor of increase in the value of the quantity.

Example 5:
 25%
Explanation:

18 is the percentage.

72 is the quantity.

Percent is asked.

Dividing the percentage by the quantity;

`18/72 = 0.25`

Multiplying the product by 100 and place a percent symbol (%) after;

0.25 x 100 = 25%

Therefore, 18 is 25% of 72.

Example 6:
 80%
Explanation:

12 is the percentage

15 is the quantity.

Percent is asked.

Dividing the percentage by the quantity;

`12/15 = 0.8`

Multiplying the product by 100 and place a percent symbol (%) after;

0.8 x 100 = 80%

Therefore, 12 is 80% of 15.

Example 7:
 200%
Explanation:

100 is the percentage

50 is the quantity.

Percent is asked.

Dividing the percentage by the quantity;

`100/50 = 2`

Multiplying the product by 100 and place a percent symbol (%) after;

2 x 100 = 200%

Therefore, 100 is 200% of 50.


Converting Percent to Decimal


In getting percentages, it is necessary to convert the percent into decimal form before multiplying it to the quantity.

Here are the steps in converting percent to decimal:

1. Neglect the percent symbol (%).

2. Move the decimal point two places to the left.

Example 8:
 0.1
Explanation:

Neglect the percent symbol (%) and move the decimal point 2 places to the left.

10% = 0.1

Therefore, 10% is 0.1 in decimal.

Example 9:
 0.0531
Explanation:

Neglect the percent symbol (%) and move the decimal point 2 places to the left.

5.31% = 0.0531

Therefore, 0.0531 is the decimal form of 5.31%.

Example 10:
 4.28
Explanation:

Neglect the percent symbol (%) and move the decimal point 2 places to the left.

428% = 4.28

Therefore, 4.28 is the decimal form of 428%.


Converting Decimal to Percent


It is easy to convert decimals to percents: just move the decimal point two places to the right then place the percent symbol (%) after.

Example 11:
 60.7%
Explanation:

Move the decimal point 2 places to the right and place a percent symbol (%) after.

0.607 = 60.7%

Therefore, 0.607 is 60.7%.

Example 12:
 120.8%
Explanation:

Move the decimal point 2 places to the right and place a percent symbol (%) after.

1.208 = 120.8%

Therefore, 1.208 is 120.8%.


Converting Percent to Fraction


Sometimes, converting percent to fraction is an easier method to obtain the percentage. Fractions are preferred to be used than decimals if the decimal has many digits. This makes the multiplication more convenient since only factorization is used to simplify the percentage.

Here are the steps in converting percent to fraction:

1. Neglect the percent symbol (%).

2. Divide the percent by 100. If the numerator has digits to the right of the decimal point, move the decimal point until the numerator becomes a whole number. Move the decimal point of the denominator (which is 100) by the same number of decimal places that the decimal point of the numerator has moved.

3. Reduce to lowest terms.

Example 13:
 `4/25`
Explanation:

Neglect the percent symbol (%) and divide the percent by 100.

`16/100`

Reduce to lowest terms.

`16/100 = text(2 x 2 x 2 x 2)/text(2 x 2 x 5 x 5) = text(2 x 2)/text(5 x 5) = 4/25`

Therefore, 16% in fraction form is `4/25`.

Example 14:
 `5/8`
Explanation:

Neglect the percent symbol (%) and divide the percent by 100.

`62.5/100`

Move the decimal point of both the numerator and denominator by 1 decimal place to the right in order to make the numerator a whole number.

`625/1000`

Reduce to lowest terms.

`625/1000 = text(5 x 5 x 5 x 5)/text(2 x 2 x 2 x 5 x 5 x 5) = 5/text(2 x 2 x 2) = 5/8`

Therefore, 62.5% in fraction is `5/8`.

Example 15:
 `8 1/25` or `201/25`
Explanation:

Neglect the percent symbol (%) and divide the percent by 100.

`804/100`

Reduce to lowest terms.

`804/100 = text(2 x 2 x 201)/text(2 x 2 x 5 x 5) = 201/text(5 x 5) = 201/25 or 6 1/25`

Therefore, the fraction form for 804% is `8 1/25` or `201/25`.


Converting Fraction to Percent


In converting fractions to percent, it is easier and convenient to convert the fraction to decimal first then convert decimal to percent after.

Here are the steps in converting fractions to percent:

1. Divide the numerator of the fraction by the denominator. The result is in decimal form.

2. Multiply the decimal form by 100.

3. Place a percent symbol (%) after the last digit of the percent.

In case of mixed numbers;

1. Apply the steps above for the proper fraction of the mixed number only.

2. Multiply the whole number of the mixed fraction by 100.

3. Add the product (whole number multiplied by 100) and the decimal form of the proper fraction.

4. Place a percent symbol (%) after the last digit of the percent.


Example 16:
 60%
Explanation:

Divide the numerator by the denominator.

0.6 5 3.0 0 30 30 0

Multiply the decimal form by 100 and place a percent symbol after the last digit.

0.6 x 100 = 60%

Therefore, `3/5` is 60%.

Example 17:
 225%
Explanation:

Divide the numerator by the denominator.

`2.25 4 9.00 8 10 8 20 20 0`

Multiply the decimal form by 100 and place a percent symbol after the last digit.

2.25 x 100 = 225%

Therefore, `9/4` is 225%.

Example 18:
 112.5%
Explanation:

Divide the numerator of the proper fraction by the denominator.

` 0.125 8 1.000 0 10 8 20 16 40 40 0`

Multiply the decimal form by 100.

0.125 x 100 = 12.5

Multiply the whole number of the mixed number by 100.

1 x 100 = 100

Add the product (whole number multiplied by 100) and the decimal form of the proper fraction.

100 + 12.5 = 112.5%

Therefore, `1 1/8` is 112.5%.


Distinguishing Percent and Percentage


There are some misconceptions upon the usage of the words percent and percentage. The two words have

A percent refers to a specific number.

For example;

Bernadette got 90 percent of the test questions correctly.

She got 90% (percent) in the test.

A percentage is the result when a number is multiplied by a percent. It denotes a portion and mostly described as lower or higher.

For example;

Bernadette got a high percentage in the test.

She got a percentage of 90/100 in the test.

Mostly, the word "percent" comes after a certain number and commonly these numbers are whole or counting numbers. It is not commonly used in sentences since it is always replaced by a percent symbol (%). The word "percentage" comes before a fraction or after an adjective (e.g. high, low, large, small).


Percentage Examples

Example 1:
Example 2:






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