Percentage Increase
Learn to calculate and apply percentage increases
1. Understanding Percentage Increase
The Big Idea
When a value goes UP, we have an increase.
The original value is always 100% (the base).
The Formula
Increase = New Value - Original Value
Percentage Increase = (Increase ÷ Original) × 100%
Important: Always divide by the ORIGINAL value, not the new value!
2. Calculating Percentage Increase
Example 1: Prize-Giving Ceremony Medals
At a prize-giving ceremony, a tray with 5 medals was prepared for Class A. Mrs Tan added 2 more medals to the tray for Class B. What is the percentage increase in the number of medals on the tray?
Method 1: Formula
Increase = 7 - 5 = 2 medals
Percentage Increase = (2 ÷ 5) × 100% = 40%
Method 2: Table Method
Percentage Increase
| Number of medals | Percentage | |
|---|---|---|
| 5 | 100% | |
÷ 5 | ÷ 5 | |
| 1 | 20% | |
× 2 | × 2 | |
| 2 | 40% |
Example 2: Buns Sold
Mr Lim sold 80 buns on Monday. On Tuesday, he sold 40 more buns than on Monday. Find the percentage increase in the number of buns sold on Tuesday.
Percentage Increase = (40 ÷ 80) × 100% = 50%
The percentage increase in the number of buns sold on Tuesday was 50%.
3. Finding New Value from Percentage Increase
The Method
Step 1: Calculate the increase: Original × (Percentage ÷ 100)
Step 2: Add to original: New Value = Original + Increase
Example 1: Restaurant Service Charge
A restaurant bill is $85 before service charge. The restaurant adds a 10% service charge. What is the total bill?
Service charge = 10% of $85 = 10/100 × $85 = $8.50
Total bill = $85 + $8.50 = $93.50
Example 2: Town Population Growth
A town had a population of 25,000 people. After new housing was built, the population increased by 8%. What is the new population?
Increase = 8% of 25,000 = 8/100 × 25,000 = 2,000
New population = 25,000 + 2,000 = 27,000
4. Working Back from a Percentage Increase
Key Insight
If you know the amount of the increase and the percentage increase, the amount of the increase is that percentage of the original value. Use it to find 100%. If you know the new value after the increase, it is (100% + percentage increase) of the original.
Example 1: Tennis Racket Price
The price of a tennis racket increased by 20%. The increase was $32. What was the price of the tennis racket after the increase?
Finding the Price After the Increase
| Percentage | Value | |
|---|---|---|
| 20% | $32 | |
× 5 | × 5 | |
| 100% | $160 | |
+20% | +$32 | |
| 120% | $192 |
Another way, finding 1% first:
20% = $32, so 1% = $32 ÷ 20 = $1.60
100% (original) = $1.60 × 100 = $160
Price after increase = $160 + $32 = $192
Example 2: Finding Original from New Value
After a 25% increase, a shirt now costs $75. What was the original price?
Finding Original Price
| Percentage | Value | |
|---|---|---|
| 125% | $75 | |
÷ 5 | ÷ 5 | |
| 25% | $15 | |
× 4 | × 4 | |
| 100% | $60 |
Key Points to Remember
- ✓ Increase = New Value - Original Value
- ✓ % Increase = (Increase ÷ Original) × 100%
- ✓ Always divide by the ORIGINAL value (not the new value)
- ✓ The original value is always 100% (the base)
- ✓ GST, a service charge and interest are examples of percentage increase
- ✓ To find the original from the increase: the amount of the increase is (percentage increase) of the original
- ✓ To find the original from the new value: the new value is (100% + percentage increase) of the original