Reverse Percentages — Multiply & Divide Pathway
Finding the original value
- If you know the new value after a percentage change, work backwards.
- Find what percentage the new value represents.
- Divide by that percentage (as a decimal) to get the original.
- Example: After 20% increase, value is 60. Original = 60 / 1.20 = 50.
Example: A price after 25% off is 45. Find the original.
- Step 1: 25% off means you paid 75%. Multiplier = 0.75.
- Step 2: Original = new price / multiplier.
- Step 3: 45 / 0.75 = 60.
- Answer: The original price was 60.
Your turn
- A price after 10% increase is 55. Find the original.
- 10% increase means multiplier = 1.10.
- Original = 55 / 1.10.
- Answer: 50.
Common Mistakes to Avoid
- Adding the percentage instead of dividing. To find the original, you divide by the multiplier, not add the percentage.
- Using the wrong multiplier. After a 20% increase, the new value is 120% of the original, so divide by 1.20.
Real-Life Example
A coat costs 45 pounds after a 25% discount. The 45 pounds represents 75% of the original price. Original = 45 / 0.75 = 60 pounds.
Extra Support Hints
- Work out what percentage the new value represents of the original.
- Divide the new value by that percentage (as a decimal) to get the original.