A bag has 2 green beads for every 3 yellow beads. What fraction of all beads is green?
Answer and explanation
2/5
The total ratio is 2 + 3 = 5 parts.
Subjects
Percentages
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Sample exercises
A model uses 4 cm for 12 m. How many metres correspond to 7 cm?
Answer and explanation
21
12/4 = 3 m per cm; 7 × 3 = 21.
Which table describes a direct proportion?
- x: 1,2,3; y: 6,6,6
- x: 1,2,3; y: 2,4,7
- x: 1,2,3; y: 4,8,12
- x: 1,2,3; y: 4,5,6
Answer and explanation
x: 1,2,3; y: 4,8,12
The ratio y/x is always 4.
A price changes from 50 to 65 units. Find the percentage increase.
Answer and explanation
30
15/50 × 100 = 30%.
A price rises by 20% and then falls by 20%. Does it return to the original price? Explain.
Answer and explanation
No. The multipliers give 1.2 × 0.8 = 0.96, so it ends 4% below the original.
The second percentage uses the increased amount as its baseline.
Five identical pens cost 7.50 units. What is the cost of eight at the same rate?
Answer and explanation
12
7.50/5 × 8 = 12.
Study notes
Percentages as fractions
Percent means per hundred. Simplify the resulting fraction.
Grades 5–7Find the original whole
Divide by the percentage as a decimal, not by the whole-number percent.
Grades 6–9Successive percentage changes
Apply each percentage to the value at that stage.
Grades 7–10Repeated percentage growth
Use the decimal growth rate; assume the same rate each period.
Grades 9–12Percentages · Formula sheet
Rules, conditions and small examples in one printable reference.
Grades 5–5Percentages · Formula sheet
Rules, conditions and small examples in one printable reference.
Grades 6–8Percentages · Formula sheet
Rules, conditions and small examples in one printable reference.
Grades 9–10Percentages · Formula sheet
Rules, conditions and small examples in one printable reference.
Grades 11–12Percentages and proportions
A focused reference to use alongside your practice.
Grades 5–9Ratios, proportions and misleading comparisons
A part-to-part ratio is not the same as a part-to-whole fraction.
Grades 6–9Ratios, proportions and misleading comparisons · Revision card
A part-to-part ratio is not the same as a part-to-whole fraction.
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