Calculate five-sixths divided by five 12ths. Give your answer in its simplest form.
When dividing fractions, we’re actually going to multiply by the second fraction’s reciprocal. So we keep our first fraction of five-sixths. But instead of dividing, we will represent this by multiplying by the second fraction’s reciprocal. So a reciprocal is where we flip the fraction. So instead of five 12ths, we have 12 fifths.
Now, before we begin multiplying, we’re supposed to have our answer in its simplest form. So if we wanted to, we could go ahead and reduce at this next step or multiply our numbers together and reduce at the end. So let’s go ahead and multiply our numbers and reduce at the end. And then we’ll come back and look at the other route.
So when multiplying fractions, we multiply the numerators together, so five and 12. And now, we multiply the denominators together, six and five. So as we said before, we can either multiply these numbers together and then simplify or we can simplify right here. So let’s go ahead and multiply. Five times 12 is 60 and six times five is 30. And 60 over 30 or 60 divided by 30 is equal to two or we could write two over one. So this would be our final answer.
Now as we said before, we could have reduced at this step. So we could simplify one number on the numerator with one number on the denominator and then repeat the process until there’s nothing left to simplify. So the five on the numerator can cancel with the five on the denominator. So now, repeating the process again, is there another set that can simplify? Well, six and 12. Six goes into itself once and six goes into 12 twice.
It should also be noted that when we said that the fives cancel, we could also think of it as five goes into five once and then once again five goes into five once. So on the numerator, we had one times two. And on the denominator, we had one times one and one times two is two. And one times one is one. So two over one is equal to our final answer, which is two. So our answer in its simplest form would be two.