Practice interactively simplifying 2 and 3 number ratios.

Equivalent Ratios

Generate and simplify ratios

Generate a two or three number ratio and then convert it to simplest form.
Use the *Integers*, *Decimals* and
*Fractions* buttons to choose the properties you wish.
When the ratio is set to fractions, you may choose any of *Proper*, *Improper* or
*Mixed*.

Enter the operations you wish to perform in the input boxes below the numbers, making sure you keep the ratio equivalent by entering the same operation for each number. Alternatively, enter the new equivalent ratio values directly.

This activity supports calculating and understanding equivalent ratios
by enforcing:

- Application of the same operation to all numbers in the ratio,
- Recognition and factoring of common divisors.

It is interesting to consider that because mathematics as studied by Pythagoras and his followers was motivated by geometry, their understanding of number was based on measurement, and thus all numbers were essentially understood as ratios. (This is also why irrational numbers caused them such concern — see the story about the unfortunate Hippasus.) This Pythagorean understanding makes an interesting contrast with the more familiar and modern conception of numbers in terms of ordering and the number line.

Enter a ratio to simplify: