What Is a Proportion?
A proportion states that two ratios are equal: A/B = C/D. This means A × D = B × C (the cross-multiplication rule). If three of the four values are known, you can always solve for the fourth.
The Cross-Multiplication Method
- Write the proportion as two fractions: A/B = C/D
- Cross-multiply: A × D = B × C
- Solve for the unknown variable
Example: If 3 apples cost $1.50, how much do 7 apples cost?
3/1.50 = 7/x → 3x = 7 × 1.50 → 3x = 10.50 → x = $3.50
6 Real-World Proportion Problems Solved
| # | Problem | Setup | Answer |
|---|---|---|---|
| 1 | Recipe scaled up: 2 cups flour for 12 cookies, need 30 cookies | 2/12 = x/30 | 5 cups flour |
| 2 | Map: 1 cm = 25 km, distance on map = 4.5 cm | 1/25 = 4.5/x | 112.5 km |
| 3 | Car: 350 km on 28L, how far on 40L? | 350/28 = x/40 | 500 km |
| 4 | Concrete: 1 bag cement for 6 bags sand, need 42 bags sand | 1/6 = x/42 | 7 bags cement |
| 5 | Currency: $100 = €92, how many euros for $350? | 100/92 = 350/x | €322 |
| 6 | Shadow: 6 ft pole casts 4 ft shadow; tree casts 18 ft shadow | 6/4 = x/18 | 27 ft tree |
When NOT to Use Cross-Multiplication
Cross-multiplication only works for direct proportions (as X increases, Y increases at the same rate). For inverse proportions (as X increases, Y decreases), the relationship is A × B = C × D, not A/B = C/D. Example: 4 workers finish a job in 6 days. How long for 8 workers? 4 × 6 = 8 × x → x = 3 days.
The proportion calculator below solves for any missing value in A:B = C:D — just enter three values and it calculates the fourth instantly.