percentages' increase and decrease

Percentage Calculations

🧮To increase or decrease a number by a percentage, calculate the percentage amount and then add or subtract it from the original number.

📊The multiplier method simplifies percentage changes by using 1 plus/minus the decimal form of the percentage as a multiplier (e.g., 1.4 for 40% increase, 0.7 for 30% decrease).

Practical Tips

🔢For decreases less than 10%, divide the percentage by 100 first to avoid mistakes (e.g., 3% becomes 0.03, so use 0.97 as the multiplier).

💡Convert percentages to decimals for easier calculations (e.g., 12% becomes 0.12).

Application

💼Apply these methods to solve real-world problems like calculating discounts (e.g., 12% off 142 pounds) or adjusting quantities (e.g., increasing 120 by 30%).

Percentage Calculation Techniques

1. To calculate a percentage increase, add 1 + (percentage as decimal) to get the multiplier, then multiply by the original number.

2. For percentage decrease, subtract the percentage as decimal from 1 to get the multiplier, then multiply by the original number.

Special Cases

3. Be cautious with percentage changes less than 10% and greater than 100%, applying the same multiplier method but adjusting the decimal accordingly.

4. For percentage changes over 100%, convert the percentage to a number greater than 1 before adding it to 1 for the multiplier.

Alternative Methods

5. The decimal technique involves converting the percentage to a decimal by dividing by 100, then multiplying by the original number for the change amount.

6. Conceptualize the original number as 1 and the percentage as a decimal to simplify calculations and avoid common errors.

Percentage Calculations

🧮Q: How do you calculate a percentage increase using the multiplier method?
A: Think of the original number as 1, convert the percentage to a decimal, add 1 + decimal to get the multiplier, then multiply by the original number (e.g., 120 * (1 + 0.3) = 156 for a 30% increase).

📉Q: What's the process for calculating a percentage decrease?
A: Treat the original number as 1, convert the percentage to a decimal, subtract the decimal from 1 to get the multiplier, then multiply by the original number (e.g., 80 * (1 - 0.25) = 60 for a 25% decrease).

Special Cases

🔍Q: How do you handle percentage changes less than 10%?
A: Pay extra attention to the decimal place, converting the percentage to a small decimal (e.g., 3% becomes 0.03), then use the standard multiplier method (42 * (1 - 0.03) = 40.74 for a 3% decrease).

💯Q: What's the approach for percentage changes greater than 100%?
A: Convert the percentage to a decimal greater than 1 (e.g., 250% becomes 2.5), add 1 to get the multiplier, then multiply (16 * (1 + 2.5) = 56 for a 250% increase).

Alternative Techniques

🔢Q: What's the decimal technique for percentage calculations?
A: Convert the percentage to a decimal by dividing by 100, then multiply this decimal by the original number to find the change, and add or subtract from the original (e.g., 120 * (30/100) = 36, so 120 + 36 = 156 for a 30% increase).

🧠Q: How can you simplify percentage calculations mentally?
A: Think of percentages and original numbers as decimals, combine them using addition or subtraction to create a multiplier, then apply this to the original number (e.g., 1 + 0.4 = 1.4 multiplier for a 40% increase, so 210 * 1.4 = 294).

To calculate a 40% decrease, you would use a multiplier of 0.6, which represents the remaining 60% of the original value. Hence, for the same original amount of 210, the calculation would be 210 * 0.6 = 126.