Percentage Calculations
Apply percentages to real-life situations — find what percentage one number is of another, calculate a percentage of an amount, and work out percentage increases and decreases.
Finding a Percentage of an Amount
To find a percentage of an amount, convert the percentage to a decimal (divide by 100) then multiply, OR use the fraction method.
Decimal Method
Find 35% of $240
35% = 35 ÷ 100 = 0.35
0.35 × $240 = $84
Build-Up Method
Find 35% of $240
10% of $240 = $24
30% = 3 × $24 = $72
5% = half of 10% = $12
35% = $72 + $12 = $84
Bar Model: 35% of $240
What Percentage Is One Number of Another?
To express one number as a percentage of another: write it as a fraction, then multiply by 100.
Formula: (Part ÷ Whole) × 100 = Percentage
16 out of 20
(16 ÷ 20) × 100
= 80%
9 out of 25
(9 ÷ 25) × 100
= 36%
$15 out of $60
(15 ÷ 60) × 100
= 25%
Percentage Increase and Decrease
Percentage Increase
A jumper costs $60. The price increases by 15%. What is the new price?
Step 1: Find 15% of $60
0.15 × $60 = $9
Step 2: Add to original
$60 + $9 = $69
Percentage Decrease
A bike costs $320. It is on sale with 20% off. What is the sale price?
Step 1: Find 20% of $320
0.20 × $320 = $64
Step 2: Subtract from original
$320 − $64 = $256
Key Vocabulary
Percentage of an Amount
Finding a fractional part of a whole, expressed as a percentage. E.g. 30% of $50 = $15.
Percentage Increase
When a value grows by a percentage of the original. Calculate the increase and add it on.
Percentage Decrease
When a value falls by a percentage of the original. Calculate the decrease and subtract it.
Discount
A reduction in price, often expressed as a percentage off the original price. Common in sales.
Worked Examples
Find 45% of $360.
Step 1: Convert: 45% = 0.45
Step 2: Multiply: 0.45 × $360 = $162
Answer: 45% of $360 = $162
Mia scored 18 out of 24 on a test. What percentage did she score?
Step 1: Write as a fraction: 18/24
Step 2: Divide: 18 ÷ 24 = 0.75
Step 3: Multiply by 100: 0.75 × 100 = 75%
Answer: Mia scored 75%.
A shop reduces a $120 bag by 25%. What is the sale price?
Step 1: Find 25% of $120. 0.25 × $120 = $30
Step 2: Subtract: $120 − $30 = $90
Answer: The sale price is $90.
Knowledge Check
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Key Concepts Summary
- ●To find a percentage of an amount: convert % to decimal (÷100), then multiply.
- ●To express one number as a percentage of another: (part ÷ whole) × 100.
- ●Percentage increase: calculate the percentage amount, then add to the original.
- ●Percentage decrease: calculate the percentage amount, then subtract from the original.
- ●The build-up method (using 10% and 5% blocks) is a useful mental strategy.