How to simplify and solve ratios
A ratio compares two quantities. To simplify one, divide both sides by their greatest common factor. To solve a proportion, where two ratios are equal, cross-multiply to find the missing value. This calculator does both: it reduces a ratio to its simplest form and solves for an unknown term.
Worked example
The ratio 8:12 simplifies to 2:3, because both divide by 4. To solve 8:12 = 4:?, cross-multiply to find the missing value is 6.
Common uses
Ratios appear in recipes, scale models, mixing fuel or paint, maps and finance. Simplifying makes them easier to read, and solving proportions lets you scale a recipe or drawing up or down.
Frequently asked questions
How do I simplify a ratio?
Divide both numbers by their greatest common factor. For 8:12, both divide by 4, giving 2:3.
How do I solve a proportion?
Set the two ratios equal and cross-multiply. For 8:12 = 4:x, multiply across to find x = 6.
How do I scale a recipe?
Put the original amount as A, the total as B, and your new amount as C to find the matching quantity x.
Can ratios have decimals?
Yes, though simplification works best with whole numbers. Multiply both terms to clear decimals first if needed.
What is a proportion?
A proportion is a statement that two ratios are equal, like 1:2 = 3:6.