Percentage Decrease
Learn to calculate and apply percentage decreases
1. Understanding Percentage Decrease
The Big Idea
When a value goes DOWN, we have a decrease.
The original value is always 100% (the base).
The Formula
Decrease = Original Value - New Value
Percentage Decrease = (Decrease ÷ Original) × 100%
Key Relationship: % Remaining = 100% - % Decrease
2. Calculating Percentage Decrease
Example: Chess Club Membership
A chess club had 280 members last year. This year the club has 70 members. Find the percentage decrease in the number of members in the club.
Decrease = 280 - 70 = 210 members
Percentage Decrease = (210 ÷ 280) × 100% = 75%
The percentage decrease in the number of members is 75%.
Another Way: The Table Method
| Number of members | Percentage | |
|---|---|---|
| 280 | 100% | |
÷ 4 | ÷ 4 | |
| 70 | 25% | |
× 3 | × 3 | |
| 210 | 75% |
3. Finding New Value from Percentage Decrease
The Method
Step 1: Calculate the decrease: Original × (Percentage ÷ 100)
Step 2: Subtract from original: New Value = Original - Decrease
Or: New Value = (100% - percentage decrease) of the original. After a 15% decrease, the new value is 85% of the original.
Example 1: Mobile Phone Sales
Mr Tan sold 60 mobile phones in March. His sales decreased by 15% in April. How many mobile phones did he sell in April?
Decrease = 15% of 60 = 15/100 × 60 = 9 phones
April sales = 60 - 9 = 51 phones
Or directly: 85% of 60 = 85/100 × 60 = 51 phones
Example 2: 20% Discount on T-Shirt
The usual price of a T-shirt is $40. How much does the T-shirt cost after a 20% discount?
Discount = 20% of $40 = 20/100 × $40 = $8
Sale Price = $40 - $8 = $32
4. Working Back from a Percentage Decrease
Key Insight
If you know the remaining amount after a decrease, that amount is (100% - percentage decrease) of the original.
If you know the amount of the decrease, that amount is the percentage decrease of the original.
Example 1: Basketball Match Spectators
During a basketball match, some spectators left and the number of spectators decreased by 30% to 210. Find the number of spectators at the start of the match.
Finding Original Number of Spectators
| Percentage | Value | |
|---|---|---|
| 70% | 210 | |
÷ 7 | ÷ 7 | |
| 10% | 30 | |
× 10 | × 10 | |
| 100% | 300 |
100% - 30% = 70% remaining
70% = 210 spectators
10% = 210 ÷ 7 = 30 spectators
100% = 30 × 10 = 300 spectators
Example 2: Devi's Cookies
Devi baked some cookies. She ate 20% of the cookies and gave 1/5 of the remainder to her neighbour. She was left with 96 cookies. How many cookies did she bake?
Finding Total Cookies
| Percentage | Value | |
|---|---|---|
| 64% | 96 | |
÷ 16 | ÷ 16 | |
| 4% | 6 | |
× 25 | × 25 | |
| 100% | 150 |
Example 3: Blouse Price Decrease
The price of a blouse decreased by 25%. The decrease was $9. What was the price of the blouse after the decrease?
Finding the New Price
| Percentage | Value | |
|---|---|---|
| 25% | $9 | |
× 3 | × 3 | |
| 75% | $27 | |
+25% | +$9 | |
| 100% | $36 |
Key Points to Remember
- ✓ Decrease = Original Value - New Value
- ✓ % Decrease = (Decrease ÷ Original) × 100%
- ✓ % Remaining = 100% - % Decrease
- ✓ Always divide by the ORIGINAL value
- ✓ Discount is a common example of percentage decrease
- ✓ To find the original from what remains: the remaining amount is (100% - decrease %) of the original
- ✓ If the amount of the decrease is known: that amount is (percentage decrease) of the original