Decimals & Percentages
Convert between fractions, decimals and percentages, and apply percentages to real-world problems like discounts and price increases.
Converting Between Fractions, Decimals & Percentages
Fractions, decimals and percentages are three ways of representing the same value. Being able to convert between them fluently is a core Year 7 skill.
| Fraction | Decimal | Percentage |
|---|---|---|
| 1⁄2 | 0.5 | 50% |
| 1⁄4 | 0.25 | 25% |
| 3⁄4 | 0.75 | 75% |
| 1⁄5 | 0.2 | 20% |
| 1⁄10 | 0.1 | 10% |
Conversion rules:
- Fraction to Decimal: Divide the numerator by the denominator. 3⁄4 = 3 ÷ 4 = 0.75
- Decimal to Percentage: Multiply by 100. 0.75 × 100 = 75%
- Percentage to Decimal: Divide by 100. 35% ÷ 100 = 0.35
Finding a Percentage of an Amount
To find a percentage of an amount, convert the percentage to a decimal and multiply.
Formula
Percentage of Amount = (Percentage ÷ 100) × Amount
Example: 30% of $150
0.30 × $150 = $45
Example: 15% of 80 kg
0.15 × 80 = 12 kg
Percentage Increase & Decrease
Percentage change is used everywhere — from sale discounts to price rises. These are the two key formulas:
Percentage Increase
New price = Original × (1 + rate)
A $200 jacket increases by 10%:
$200 × 1.10 = $220
Percentage Decrease
New price = Original × (1 − rate)
A $200 jacket is discounted by 25%:
$200 × 0.75 = $150
Key Vocabulary
Percentage
A number expressed as a fraction of 100. The symbol % means "per cent" (per hundred). 45% = 45⁄100.
Decimal
A number that uses a decimal point to show values less than one. Each place to the right is ten times smaller.
Percentage Increase
Adding a percentage of the original amount to itself. Multiply by (1 + rate). For 20% increase, multiply by 1.20.
Percentage Decrease
Subtracting a percentage from the original amount. Multiply by (1 − rate). For 15% decrease, multiply by 0.85.
Worked Examples
Convert 0.45 to a percentage and a fraction.
Decimal to Percentage: 0.45 × 100 = 45%
Decimal to Fraction: 0.45 = 45⁄100 = 9⁄20 (HCF is 5)
Find 35% of $240.
Step 1: Convert 35% to a decimal: 35 ÷ 100 = 0.35
Step 2: Multiply: 0.35 × $240 = $84
A $80 pair of shoes is discounted by 20%. What is the sale price?
Step 1: 20% decrease means multiply by (1 − 0.20) = 0.80
Step 2: $80 × 0.80 = $64
The sale price is $64.
Knowledge Check
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Key Concepts Summary
- ●Convert decimal to percentage by multiplying by 100; convert percentage to decimal by dividing by 100.
- ●To find a percentage of an amount, convert to a decimal and multiply by the amount.
- ●Percentage increase: Multiply original by (1 + rate). For 15% increase, use multiplier 1.15.
- ●Percentage decrease: Multiply original by (1 − rate). For 20% decrease, use multiplier 0.80.
- ●Fractions, decimals and percentages all represent the same value in different forms.