Simplifying Ratios
Free printable simplifying ratios worksheets. Reduce a ratio to lowest terms, with an answer key. Every pair has a common factor to find.
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.
What this worksheet covers
- Write a ratio in lowest terms
- Divide both parts of a ratio by their greatest common factor
Common Core standards
- 6.RP.A.1 Understand the concept of a ratio and use ratio language.
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.