What is Adding and Subtracting Percentages?
Adding and subtracting percentages is a fundamental mathematical operation where you combine multiple percentage values to get a total. This is useful in many real-world scenarios like calculating total discounts, combined interest rates, or aggregate growth rates.
How to Add and Subtract Percentages
The process is straightforward: simply add or subtract the percentage values directly.
For addition:
[\text{Total} = \text{Percentage 1} + \text{Percentage 2} + \text{Percentage 3} + ...]
For subtraction:
[\text{Result} = \text{Percentage 1} - \text{Percentage 2}]
Or equivalently, add a negative percentage:
[\text{Result} = \text{Percentage 1} + (-\text{Percentage 2})]
Calculation Examples
Example 1: Adding Percentages
Suppose you want to add 25% and 30% together:
[25 + 30 = 55%]
Example 2: Subtracting Percentages
If you have 75% and want to subtract 20%:
[75 - 20 = 55%]
Or using the calculator, enter 75 in the first field and -20 in the second field.
Example 3: Multiple Percentages
Adding 10%, 15%, and 25% together:
[10 + 15 + 25 = 50%]
Quick Reference Table
| Percentage 1 | Percentage 2 | Operation | Result |
|---|---|---|---|
| 25% | 30% | Addition | 55% |
| 75% | 20% | Subtraction | 55% |
| 10% | 15% | Addition | 25% |
| 100% | 25% | Subtraction | 75% |
Understanding Percentage Difference
While adding and subtracting percentages is a direct operation, percentage difference is a related but distinct concept. Percentage difference measures the relative change between two values:
[\text{Percentage Difference} = \frac{\text{Larger Number} - \text{Smaller Number}}{\text{Smaller Number}} \times 100]
Where:
- Larger Number is the bigger of the two values you're comparing.
- Smaller Number is the smaller of the two values you're comparing.
Percentage Difference Example
If a gadget was $40 last month and is now $70:
- Find the difference: $70 - $40 = $30
- Divide by the smaller number: 30/40 = 0.75
- Multiply by 100: 0.75 x 100 = 75%
The price increased by 75%.
Practical Applications
Understanding how to add and subtract percentages helps you:
- Calculate combined discounts during sales
- Determine total tax rates from multiple sources
- Combine interest rates or yields
- Analyze cumulative growth or decline
- Compare budget allocations