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Ratios, fractions and percentages
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Results are often described as ratios, fractions or percentages. You need to calculate and convert between them.
Fractions and percentages
A fraction shows part of a whole: 18 out of 24 participants helped = 1824 = 34 (divide top and bottom by 6).
A percentage is a fraction out of 100: percentage = (part ÷ whole) × 100.
18 ÷ 24 × 100 = 75%.
To find a percentage of a number: 30% of 60 = 0.3 × 60 = 18.
A percentage is a fraction out of 100: percentage = (part ÷ whole) × 100.
18 ÷ 24 × 100 = 75%.
To find a percentage of a number: 30% of 60 = 0.3 × 60 = 18.
Ratios
A ratio compares one part with another part, written with a colon.
If 30 participants were female and 20 were male, the ratio female : male = 30 : 20 = 3 : 2 (divide both by 10).
Ratios can be turned into fractions of the whole: 3 : 2 means 35 were female and 25 were male.
If 30 participants were female and 20 were male, the ratio female : male = 30 : 20 = 3 : 2 (divide both by 10).
Ratios can be turned into fractions of the whole: 3 : 2 means 35 were female and 25 were male.
Percentage change
Percentage change = (change ÷ original) × 100.
Example: aggressive acts fell from 40 before a programme to 30 after.
Change = 40 - 30 = 10. 10 ÷ 40 × 100 = 25% decrease.
Always divide by the original (starting) value.
Example: aggressive acts fell from 40 before a programme to 30 after.
Change = 40 - 30 = 10. 10 ÷ 40 × 100 = 25% decrease.
Always divide by the original (starting) value.
In a study, 45 out of 60 participants conformed. What percentage is this?
- Percentage = part ÷ whole × 100.
- 45 ÷ 60 = 0.75; 0.75 × 100 = 75.
Answer: 75%
Percentage = part ÷ whole × 100. Simplify fractions and ratios by dividing by a common factor. A ratio compares parts; 3 : 2 means 3/5 and 2/5 of the whole. Percentage change = change ÷ original × 100.
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