01 Key Concepts
What is a Proportion
An equation of the form a/b = c/d, stating two ratios are equal.
Cross Multiplication
In a/b = c/d, cross multiply to get a x d = b x c, then solve for the unknown.
Direct Proportion
As one quantity increases, the other increases at the same rate (y = kx).
Inverse Proportion
As one quantity increases, the other decreases proportionally (xy = k, a constant).
Unit Rate Method
Find the value for one unit first, then scale up or down to find the value needed.
03 Key Formulas
- If a/b = c/d, then a x d = b x c
04 Solved Examples
Example 1 Solve for x: 3/4 = x/20.
- Cross multiply: 3 x 20 = 4 x x.
- 60 = 4x.
- Divide both sides by 4.
Answer: x = 15
Example 2 If 5 pens cost $10, how much do 8 pens cost (direct proportion)?
- Find the unit rate: $10 ÷ 5 = $2 per pen.
- Multiply by 8: 2 x 8.
Answer: $16
Example 3 4 workers finish a job in 6 days. How many days would 8 workers take (inverse proportion)?
- Since work is fixed, workers x days = constant: 4 x 6 = 24.
- With 8 workers: 24 ÷ 8.
Answer: 3 days
05 Practice Questions
1Solve for x: 2/5 = x/25.
x = 10
2If 3 apples cost $6, how much do 7 apples cost?
$14
3Solve for x: x/4 = 9/12.
x = 3
46 workers complete a task in 10 days. How long would 3 workers take?
20 days
5Is 'more workers, less time' a direct or inverse proportion?
Inverse proportion
📄 Proportion — Downloadable Worksheet
10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.