Calculate two-fifths times three-fourths, giving your answer in its simplest form.
When multiplying fractions, we take the numerators — the numbers on the top — and we multiply them together. So we will have two times three on our numerator. And then, on the bottom, our denominators, we multiply those together. So we have five times four.
Now, one thing to keep in mind is we’re supposed to put our answer in simplest form. So we can either reduce here or we can go ahead and multiply our numbers and then reduce at the end. Let’s go ahead and multiply first, get an answer, reduce. And we will show the other way where we could have reduced right here.
So two times three is six and five times four is 20. Now, six 20ths reduces to three 10ths. This is because the largest number that goes into six and 20 will be two. And six divided by two is three and 20 divided by two is 10. So our final answer is three 10ths.
Now, let’s go back to this step because we actually could have reduced right here. So any numbers on the top can simplify or cancel with any numbers on the bottom. So we have two and three on the top and five and four on the bottom. So are there a pair of numbers that can simplify, where one number is on the top and one is on the bottom.
Two and four, two goes into itself one time and two goes into four two times. So on the numerator, we have one times three. And on the denominator, we have five times two. Now, since we already reduced, when we multiply, this should be your final answer. So on the numerator, one times three is three and five times two is 10. And three 10ths is indeed the correct answer. So again, our final answer will be three 10ths.