Evaluate six and five-sixths times eight.
Six and five-sixths is a mixed number. Eight is a whole number. This is multiplying a mixed number by a whole number. To solve this problem, we’ll need to first convert the mixed number to an improper fraction. So we’ll take our mixed number, six and five-sixths, and turn it into an improper fraction.
Our first step is to multiply the whole number, six, by the denominator, also six. We take that value and we add the five, already in the numerator. Then we make all of this the new numerator with the same denominator, six.
What we have now is six times six plus five over six. Six times six is 36. Put that plus five over six. 36 plus five equals 41. We keep the denominator of six and we have forty-one sixths. This is an improper fraction. We can take this improper fraction and multiply it by our whole number, eight.
41 sixths times eight. We can write the whole number eight as a fraction over one. From there we multiply the numerators, 41 times eight equals 328. After that, we multiply six times one. We multiply both of the denominators together. Six times one equals six.
We have 328 over six and we know that this is an improper fraction. We want our final answer to be in the form of a mixed number. How do we take 328 over six and turn it into a mixed number? We use division. We put 328 inside the division box and keep the six on the outside.
How many times does six go into 32? Five times. Six times five equals 30. We subtract, 32 minus 30 equals two. Bring down the next digit. Ask the question how many times does six go into 28. It can go four times. Four times six equals 24. Then we subtract, 28 minus 24 equals four.
That gives us 54 with a remainder of four. We take our remainder of four and we put that over the six we were using for division. 54 and four-sixths. There is one last thing we need to notice though. This four-sixths is not reduced all the way. If we divide the numerator and the denominator by two, we can simplify this part of our fraction.
Four divided by two equals two. Six divided by two equals three. We keep the whole number 54 and we add the reduced fraction, two-thirds. Six and five-sixths times eight equals 54 and two-thirds.