Finding Percentage of a Quantity A percentage is a number representing a portion of a whole. It is often expressed as a percentage sign (%) followed by a num...
A percentage is a number representing a portion of a whole. It is often expressed as a percentage sign (%) followed by a number between 0 and 100.
To find the percentage of a quantity, we can divide the portion by the whole and multiply the result by 100.
Example: If we have 30 apples and 15 are rotten, the percentage of rotten apples would be 50% (30 ÷ 60 = 0.5).
Formal Definition:
Let x be the portion of the whole. Then the percentage of x is given by:
Properties of Percentage:
Adding percentages with the same base gives the same percentage. For example, 50% + 25% = 75%.
Multiplying a percentage by a number gives the same percentage. For example, 50% × 2 = 100%.
Dividing a number by a percentage gives the same percentage. For example, 60 ÷ 50% = 1.2.
Uses of Percentage:
Percentage is used in various contexts, including:
Calculating discounts and taxes
Comparing prices and costs
Determining the completion rate of a project
Evaluating the effectiveness of a marketing campaign
By understanding the concept and properties of percentages, students can effectively find the percentage of a quantity and apply it to real-world problems