What a ratio tells you
A ratio compares quantities of the same kind. "3:2" says that for every 3 of the first thing there are 2 of the second, whether those are cups of flour, liters of paint or students per teacher. Ratios stay true when every term is multiplied or divided by the same number, which is why 6:4, 3:2 and 1.5:1 all describe the same mix.
Four things this calculator does
- Simplify: reduces any list of terms to the smallest whole numbers by dividing by their greatest common factor. The GCF calculator shows how that factor is found.
- Solve A:B = C:D: leave one box blank and the missing term is found by cross-multiplication, the same rule used in the proportion calculator.
- Scale: set one term to a new value and every other term changes in step. This is how you turn a 4-serving recipe into 10 servings, or a 16:9 screen width into a height.
- Divide a total: share an amount of money, time or material in a given ratio.
Worked examples
Mixing two-stroke fuel at 50:1. One gallon is 128 fluid ounces, so the oil needed is 128 ÷ 50 = 2.56 oz per gallon.
Screen dimensions. A 16:9 image that must be 1,200 pixels wide needs a height of 1,200 × 9 ÷ 16 = 675 pixels.
Splitting a bill. Three roommates split $2,400 rent in the ratio of their room sizes, 5:4:3. That is 12 shares of $200, so they pay $1,000, $800 and $600.
Common mistakes
- Mixing units: convert to the same unit before writing the ratio (2 ft : 6 in is 24:6, i.e. 4:1, not 2:6).
- Swapping the order: 3:2 and 2:3 are different mixes. Keep the terms in the order the question names them.
- Adding instead of multiplying when scaling: doubling 3:2 gives 6:4, not 5:4.
Frequently asked questions
How do you simplify a ratio?
Divide every term by their greatest common factor. For 12:18 the GCF is 6, so the ratio simplifies to 2:3. If the terms are decimals, first multiply them all by the same power of ten to make whole numbers.
How do you solve a ratio with a missing number?
Write it as a proportion, A/B = C/D, and cross-multiply. For 2:3 = 10:x, 2x = 30, so x = 15.
What is the difference between a ratio and a fraction?
A fraction compares a part to a whole. A ratio can compare a part to another part, such as 2 cups flour to 1 cup sugar. The ratio 2:1 means flour is 2/3 of the mix.
How do I split money in a ratio?
Add the ratio terms to get the number of shares, divide the total by that number, then multiply by each term. $900 in the ratio 2:3:4 is 9 shares of $100, so $200, $300 and $400.
Can a ratio have more than two terms?
Yes. Concrete mixes such as 1:2:3 (cement:sand:gravel) and paint tints often use three or more. The simplify and split tools accept as many terms as you need.
Sources and official references
- Ratios, rates and percentages (Grade 6 math) – Khan Academy
Last reviewed October 10, 2026. Results are estimates for planning; see our disclaimer.
