Simplifying Ratios

Each question gives a ratio and two blanks: 64 : 80 = ___ : ___. Reducing it means finding the largest number that divides both sides and dividing by it - one operation on the pair, not two separate ones.

Every ratio on the sheet has a common factor bigger than one. A pair that is already in lowest terms has nothing to do, and a page of those is a page of no questions, so the generator builds each one from its own answer.

Frequently asked questions

How do you simplify a ratio?

Find the greatest common factor of the two numbers and divide both by it. For 64 : 80 the common factor is 16, giving 4 : 5. It is the same operation as reducing a fraction.

Why is the answer two blanks?

Because a ratio is a pair. Unlike every other answer on this site, a simplified ratio is not one value - 4 : 5 only means something as both numbers together.

Do I have to fully simplify?

Yes. 32 : 40 is an equivalent ratio to 64 : 80 but it is not in lowest terms; the answer key gives the fully reduced pair.

What if the numbers share no factor?

That does not happen on these sheets. Every question is built from a reduced pair multiplied up, so there is always something to find.