Percentage - Formula, Conversions & Practice Questions

The reading material provided on this page for 'Percentage' is specifically designed for students in grades 5 to 12. So, let's begin!

Percentage

A percentage is a way to express a number as a fraction of 100. It is often denoted using the symbol " %". If we have to calculate the percent of a number, divide the number by the whole and multiply by 100.

Percentage Formula

To calculate the percentage of a number, we can also use the following formula:
Percentage = (Part/Whole) x 100
where, "Part" is the number we want to find the percentage of, and "Whole" is the total value.

Example: What is 20% of 50?

Solution: Percentage = (Part/Whole) x 100
Let Part = x, Whole = 50, Percentage = 20%
20% = (x/50) x 100
20/100 = x/50
0.2 = x/50
x = 0.2 x 50
x = 10

Therefore, 20% of 50 is 10.

Another way to solve:

> 20% of 50
= (20/100) x 50
= 0.20 x 50
= 10

Some more Examples -

1. What is 25% of 80?

Answer: 25% of 80 is (25/100) x 80 = 20.

2. If a store offers a 20% discount on a $50 item, how much will the item cost?

Answer: The discount on the item will be 20% of $50, which is $10. So, the item will cost $50 - $10 = $40.

3. If a person earns $50,000 per year and receives a 5% raise, what will their new salary be?

Answer: The raise is 5% of $50,000, which is $2,500.
So, the person's new salary will be $50,000 + $2,500 = $52,500

4. If a recipe calls for 2 cups of sugar for every 5 cups of flour, what percentage of the recipe is sugar?

Answer: The total ratio of sugar to flour is 2:5.
To convert this to a percentage, we add the two numbers together to get 2 + 5 = 7
Then we divide 2 by 7 and multiply by 100 to get the percentage: (2/7) x 100 = 28.57%
So, 28.57% of the recipe is sugar.

5. If a person scores 70 out of 100 on a test, what percentage did they score?

Answer: To find the percentage, we divide the score by the total possible points and multiply by 100: (70/100) x 100 = 70%.
So, the person scored 70%.

Conversion from Percentage to Fraction

The conversion of a percent to a fraction is very simple and convenient.

To convert a percentage to a fraction, follow these steps:
1. Remove the percent symbol (%).
2. Divide the percentage by 100.
3. Simplify the resulting fraction, if possible.

For example, let's convert 25% to a fraction:
= 25/100
= 1/4
Therefore, 25% is equal to 1/4 as a fraction.

Conversion from Fraction to Percentage

To represent a fraction as a percentage, we can multiply the fraction by 100.
(m/n) x 100
Where m/n is a fraction value.

Example:
if we have the fraction 3/4, we can convert it to a percentage as follows:
3/4 x 100 = 75%
So, 3/4 is equivalent to 75%.

Conversion from Mixed Number Percent to Fraction

Example: Consider 12¹⁄₂%.

> Step 1: Convert it into an improper fraction. 12¹⁄₂%
> Step 2: Drop the percent symbol %, multiplying by 1/100. So, 25/2 % = (25/2) × (1/100) = 25/200.
> Step 3: Reduce it to the lowest form, i.e., 25/200 = 1/8.

Conversion from Decimal Percent to Fraction

Example: Consider the percentage value of 7.5%.

Percentage Increase

When comparing the increase in a quantity over a period of time, we first find the difference between the original value and the increased value. We then use this difference to find the relative increase against the original value and express it in terms of percentage.

The formula for percentage increase is given:

Percentage Decrease

When comparing the decrease in a quantity over a period of time, we first find the difference between the original value and the decreased value. We then use this difference to find the relative decrease against the original value and express it in the form of a percentage.

The formula for percentage decrease is given: