What is a Percentage?
A percentage is a way of expressing a number as a part of 100. The word cent comes from the Latin word centum. So percent means “per one hundred”. % symbol is used to denote the percentage. Percentages can be represented with a numerical value followed by the percent symbol (%).
It is a ratio, fraction, or portion of a whole which is represented as 100. It helps us easily compare amounts. For example, if you score 80% on a test, it means you got 80 out of 100 points.
Why do we use Percentages?
Percentages are everywhere! They are used to:
- Compare scores, in tests or games.
- Show discounts while shopping.
- Represent data in surveys or polls.
- Track changes, like growth or loss in money.
Understanding Percentages
Visualizing percentages can be easy and fun using squares. Draw a large square and divide it into 100 smaller equal squares. This represents 100% of the square.
50% : Shade 50 of the 100 squares. Half of the square is colored, showing 50%.
25% : Shade 25 of the 100 squares. A quarter of the square is colored, representing 25%.
75% : Shade 75 of the 100 squares. This shows that three-quarters of the square is colored, which is 75%.
Fractions, Decimals and Percentages
A percent can be written as a fraction or a decimal.
20% (20 per 100) is written as 20 with the denominator 100 ($\frac{20}{100}$).
In the decimal system, hundredth is ($\frac{1}{100}$). 20% is written as 20 hundredths (0.20)
20% = $\frac{20}{100}$ = 0.20
Converting Percentage to Fraction
We can convert the % to a fraction by dividing the given number by 100, and then simplifying it to its lower terms.
Steps:
- Write the percentage as the numerator (without the % sign).
- Set the denominator as 100.
- Simplify the fraction if necessary.
Example:
Convert 75% to a fraction.
75% = $\frac{75}{100}$ = $\frac{3}{4}$
Converting Fraction to Percentage
We can convert a fraction to percentage by multiplying the given fraction by 100. If the denominator has any common factor with 100, simplify by cancelling out the common factors and add % to the result.
Example:
Convert $\frac{1}{4}$ to percentage.
$\frac{1}{4}$ x 100
4 and 100 have common factors. Cancelling out 4 in the denominator and 100, we get
1 x 25 = 25%
Converting Percentage to Decimal
We can convert the % to a decimal value by just moving the decimal point two places to the left of the given number.
Example:
Convert 6% to a decimal number
6% = 0.06
Convert 16% to a decimal number
6% = 0.16
Converting Decimal to Percentage
Decimals can be written as percentages by moving the decimal point two places to the right.
Example:
0.23 = 23%
1.5 = 150%
Finding Percentage of a Number
Percentage of a Number=$\frac{Percentage}{100}$×Number
Method 1:
- Convert the percentage to a decimal by dividing it by 100.
- Multiply the decimal by the number you’re finding the percentage of.
To find 30% of 150, convert 30% into a decimal.
$\frac{30}{100}$ = 0.3
Multiply by 150.
0.3 x 150 = 45
So, 30% of 150 is 45.
Method 2:
- Multiply the percentage by the number you want to find the percentage of. Divide the result by 100.
Percentage of a Number=$\frac{Percentage X Number}{100}$
- Simplify by cancelling out the common factors. Look for common factors in the numerator (percentage multiplied by the number) and the denominator (100). Cancel out these common factors and then do the final division.
Example 1: Let’s find 25% of 160 using this method.
25% of 160 = $\frac{25}{100}$x160
25 and 100 have 25 as the common factor. On simplifying,
$\frac{25}{100}$ = $\frac{1}{4}$
25% of 160 = $\frac{25}{100}$x160 = $\frac{1}{4}$x160 = 40
Example 2: Let’s find 32% of 50.
32% of 50 = $\frac{32}{100}$50
50 and 100 have a common factor 50. Canceling it out,
32% of 50 = $\frac{32}{100}$ x 50 = $\frac{32}{2}$ = 16
Here’s a quick way of solving the above problem. 32% indicates 32 for every 100. So, for 50, it would be half of that. Half of 32 is 16.
Special Percentages
To find 50% of a number – just halve it! 50% is 50 per 100, which is half of the original.
- 50% of 40 = 20
To find 25% of a number, quarter it (or divide by 4).
- 25% of 120 = $\frac{120}{4}$ = 30
To find 75% of a number, quarter it then multiply by 3. 75% is the same as three-fourths or three-quarters.
- 75% of 120 = $\frac{3}{4}$ x 120 = 90
To find 10% of a number, divide it by 10. This is equivalent to shifting the decimal point one place to the left. 10% is the same as one-tenth.
- 10% of 250 = $\frac{1}{10}$ x 250 = 25
To find 30%, you divide by 10 and multiply by 3. 30% is the same as three-tenth.
- 30% of 90 = $\frac{3}{10}$ x 90 = 27
To find 70%, divide by 10 and multiply by 7.
- 70% of 60 = $\frac{7}{10}$ x 60 = 42
To find 1% of a number, divide it by 100, which is equivalent to shifting the decimal point two places to the left.
- 1% of 25 = $\frac{1}{100}$ x 25 = 0.01 x 25 = 0.25
Percentages Greater than Whole
Percentages are often thought of as parts of a whole, but they can also be greater than a whole. They are percentages greater than 100. This occurs when a value exceeds the original whole value. It occurs commonly when you’re working with amounts that are more than the original. This concept is especially useful in scenarios involving growth, increases, and comparisons.
- If 100% represents the original, 200% of something means it’s double the original (or 2 times the whole).
- 150% of something means it’s 1.5 times the original (or 50% more than the whole).
Example:
If a town had 500 people and the population grew to 1000, the population is now 200% of the original value.
If a showroom sold 500 cars last month and 750 cars this month, the present sales is 150% of the previous value.
How to Calculate Percentage of a Whole
To find what percentage a number is of the whole:
- Divide the part by the whole.
- Multiply the result by 100.
- Add the % symbol.
Percentage=$\frac{Part}{Whole}$×100
Practice Quiz on Percentages
FAQs on Percentages
To calculate a percentage of a number, multiply the number by the percentage and divide by 100. For example, 20% of 50 is (20 × 50) ÷ 100 = 10.
To convert a fraction into a percentage, divide the numerator by the denominator, then multiply the result by 100. For example, 3/4 as a percentage is (3 ÷ 4) × 100 = 75%.
To convert a decimal into a percentage, multiply the decimal by 100 and add the “%” symbol. For example, to convert 0.32 to a percentage, 0.32 x 100 = 32%.
Percentages are used in various real-life situations, like calculating discounts, interest rates, grades, and statistics.
- 10%: Divide the number by 10.
- 50%: Divide the number by 2.
- 25%: Divide the number by 4.
- 75%: Multiply by 0.75 or calculate 50% and 25% and add them.
Yes, percentages can be greater than 100 when the part exceeds the whole. For example, if you score 120 out of 100 on a test (due to extra credit), your percentage would be 120%.