Mathematics · Grades 6–9
Ratios, proportions and misleading comparisons
A part-to-part ratio is not the same as a part-to-whole fraction.
Understand the idea
Identify the quantities
A part-to-part ratio is not the same as a part-to-whole fraction.
Use units
A rate compares quantities with stated units; cancel units only when appropriate.
Keep the baseline
Percentage change uses the original value as the reference.
Worked examples
A bag has 2 green beads for every 3 yellow beads. What fraction of all beads is green?
The total ratio is 2 + 3 = 5 parts.
2/5
A model uses 4 cm for 12 m. How many metres correspond to 7 cm?
12/4 = 3 m per cm; 7 × 3 = 21.
21
Try it yourself
Which table describes a direct proportion?
- x: 1,2,3; y: 4,8,12
- x: 1,2,3; y: 4,5,6
- x: 1,2,3; y: 2,4,7
- x: 1,2,3; y: 6,6,6
A price changes from 50 to 65 units. Find the percentage increase.
A price rises by 20% and then falls by 20%. Does it return to the original price? Explain.
Five identical pens cost 7.50 units. What is the cost of eight at the same rate?
Answers and marking notes
Answers and marking notes
- x: 1,2,3; y: 4,8,12
The ratio y/x is always 4.
- 30
15/50 × 100 = 30%.
- 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.
- 12
7.50/5 × 8 = 12.
Preview material · independent educational review required. Grade bands are approximate, not official curriculum alignment.