Ratios & Percentages
What is a Ratio?
A ratio compares two or more quantities and shows how much of one thing there is compared to another.
If there are 3 apples and 5 oranges, the ratio of apples to oranges is 3:5 (read as "3 to 5").
Ratios can be written three ways: 3:5 Β· 3/5 Β· "3 to 5"
Simplifying Ratios
Like fractions, ratios can be simplified by dividing both numbers by their GCF.
15:25 β GCF is 5 β 15Γ·5 : 25Γ·5 = 3:5
12:8 β GCF is 4 β 3:2
Dividing a Quantity in a Ratio
Share Β£40 between two people in the ratio 3:2. Total parts = 3 + 2 = 5 Each part = Β£40 Γ· 5 = Β£8 Person A gets: 3 Γ Β£8 = Β£24 Person B gets: 2 Γ Β£8 = Β£16
Proportions
A proportion states that two ratios are equal.
2/3 = 4/6 β these are in proportion
To check if two ratios are proportional: cross multiply.
2/3 = ?/6 β 2 Γ 6 = 3 Γ ? β 12 = 3? β ? = 4 β
Percentages
A percentage is a ratio out of 100. The symbol is %.
45% means 45 out of 100, or 45/100, or 0.45
Converting between forms:
| Form | Example |
|---|---|
| Fraction β % | 3/4 = 0.75 = 75% |
| Decimal β % | 0.6 Γ 100 = 60% |
| % β decimal | 35% Γ· 100 = 0.35 |
Finding a percentage of a quantity:
What is 30% of 200? = 30/100 Γ 200 = 0.30 Γ 200 = 60
Finding the percentage one number is of another:
18 is what % of 72? = (18 Γ· 72) Γ 100 = 0.25 Γ 100 = 25%
Percentage Increase and Decrease
Increase 80 by 15%: 15% of 80 = 0.15 Γ 80 = 12 β New value = 80 + 12 = 92
Decrease 120 by 20%: 20% of 120 = 24 β New value = 120 β 24 = 96