Ratio Generator
Generates a random ratio in the form a:b, with each part independently drawn from 1 to 20 and left unsimplified rather than reduced automatically — because a ratio already in lowest terms gives a simplification exercise nothing to do, and a little over a third of independently drawn pairs share a common factor.
What this generator does
Produces a ratio in the a:b form, for maths practice on scaling, proportion and simplification.
How to use this tool
- Press generate for a random ratio.
Worked examples
- Format
- 4:16, 4:18 and 9:6 — three consecutive draws, all of which happen to simplify
Common use cases
- Ratio-recognition practice
- Placeholder ratio data
- A starting point for a ratio simplification exercise
How this generator works
Two whole numbers are drawn independently from 1 to 20 and written as a:b, without being simplified. Leaving them unsimplified is the point: 6:8 and 3:4 describe the same proportion, and a ratio drawn already in lowest terms would never give anyone the chance to notice that. Of the 400 possible pairs, 145 share a common factor, so simplification practice has something to work on in a little over one draw in three.
Limitations and good to know
- The two parts are independent, so 4:4 and other equal pairs come up — a ratio of one to one is a legitimate ratio, not a fault.
- Neither part is ever zero, because a ratio with a zero part cannot be simplified or scaled and is not a useful exercise.
- Both parts stay within 1 to 20. Larger ratios exist, but past twenty the arithmetic stops being mental and the exercise becomes a different one.
Related generators
- Ratio Question GeneratorRatio questions built to order — simplifying, sharing an amount, working back from one share or from the difference.
- Random Fraction Range GeneratorA random fraction with numerator and denominator each up to 20.
- Random Signed Decimal GeneratorA random decimal between −100 and 100, positive or negative.