Reducing Fractions Examples

Reduce  to its lowest terms.

It's pretty easy to see that both numbers are divisible by 5, so let's start there. You can fit 5 into 30 a grand total of 6 times, and 45 divided by 5 is 9. So our new fraction is . But hold the phone! (We're speaking figuratively—you can put the phone down now.) Each of those numbers is divisible by 3. Do our thing one more time and we're left with , which can no longer be reduced. Not without a hacksaw, anyway.

Reduce  to its lowest terms.

We've got a couple of even numbers here, so clearly 2 will divide both the numerator and denominator. We start by reducing this fraction to , but we've still got two even numbers, so we do it again. Now we've got . There are no natural numbers (except 1) that divide 30 and 23, so the fraction  is in lowest terms.