The Complete Guide to Ratios and Proportions
By Arshi Khan, Founder of Just4Marketing · Last reviewed October 2026
A ratio compares two quantities, and a proportion sets two ratios equal to each other. This guide covers how to simplify a ratio to its lowest terms and how cross-multiplication solves for a missing value in an equivalent ratio.
What is a ratio and why does it matter?
A ratio expresses how two quantities relate to each other in size — for example, a recipe calling for a 2:1 ratio of flour to water means twice as much flour as water, regardless of how large the batch is. Ratios are used constantly in cooking, mixing solutions, scaling maps and models, and financial ratios like debt-to-income.
Two ratios are equivalent, or proportional, if one can be obtained from the other by multiplying or dividing both terms by the same number — 2:1 and 6:3 describe the exact same relationship. That equivalence is what makes it possible to solve for an unknown value: if you know three of the four numbers in A:B = C:D, cross- multiplication finds the fourth.
Solving A:B = C:D for a missing term
| Missing value | Formula | Example |
|---|---|---|
| C | C = (A × D) ÷ B | 4:8 = C:20 → C = (4 × 20) ÷ 8 = 10 |
| D | D = (B × C) ÷ A | 4:8 = 5:D → D = (8 × 5) ÷ 4 = 10 |
| A | A = (B × C) ÷ D | A:8 = 10:20 → A = (8 × 10) ÷ 20 = 4 |
| B | B = (A × D) ÷ C | 4:B = 10:20 → B = (4 × 20) ÷ 10 = 8 |
Tips for working with ratios
Keep the order consistent
A:B = C:D means A relates to B the same way C relates to D. Reversing the order on one side (B:A = C:D) changes the entire relationship.
Simplify before comparing two ratios
It's much easier to tell whether 6:9 and 10:15 are equivalent once both are simplified — they both reduce to 2:3.
Units must match on each side
A ratio comparing minutes to minutes, or dollars to dollars, is straightforward — mixing units (like minutes to dollars) requires converting to a common unit first.
A ratio of 0 in either term can't be simplified further by division
If one term is 0, the greatest common divisor calculation still works, but a ratio like 0:5 has no equivalent 'simpler' form beyond itself.
Frequently asked questions
How do you simplify a ratio like 8:12?
Divide both terms by their greatest common divisor (GCD). The GCD of 8 and 12 is 4, so dividing both by 4 gives the simplified ratio 2:3.
How do you solve for a missing value in a proportion?
Use cross-multiplication. For A:B = C:D with C unknown, C = (A × D) ÷ B. For example, if 4:8 = C:20, then C = (4 × 20) ÷ 8 = 10.
What's the difference between a ratio and a fraction?
A ratio compares two separate quantities (like 3 cups of flour to 1 cup of sugar), while a fraction represents a part of a single whole. In practice, a ratio A:B can be treated like the fraction A/B for simplification purposes.
Can a ratio have more than two terms?
Yes — a ratio like 2:3:5 compares three or more quantities at once, and is simplified the same way, by dividing every term by the greatest common divisor shared across all of them.