What Is a Proportion?
A proportion is a statement that two ratios are equal.
2/3 = 4/6 is a proportion. It says: the ratio 2 to 3 is the same as the ratio 4 to 6.
Solving proportions
When one value is unknown, you can solve using cross-multiplication:
2/3 = x/12
Cross-multiply: 2 × 12 = 3 × x → 24 = 3x → x = 8
Check: 2/3 = 8/12. Simplify 8/12 = 2/3. ✓
Why proportions matter
Proportions solve real problems:
- Recipes: "If 2 cups of flour makes 12 cookies, how much for 36 cookies?" → 2/12 = x/36 → x = 6 cups
- Maps: "1 inch = 50 miles. 3.5 inches = ?" → 1/50 = 3.5/x → x = 175 miles
- Unit rates: Finding the cost per item, speed per hour, etc.
- Scale drawings: Maintaining consistent ratios between drawing and reality
Proportional vs. non-proportional
Two quantities are proportional when their ratio is constant:
| x | y | y/x |
|---|---|---|
| 2 | 6 | 3 |
| 4 | 12 | 3 |
| 5 | 15 | 3 |
y/x is always 3, so y = 3x. This is proportional.
If y/x varies (3, 3.5, 4...), the relationship is not proportional.
Related concepts
- Ratios and Proportions teaching guide
- What is a ratio?
- Equivalent fractions: proportions are equivalent fraction pairs