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