Evaluate three and three-fifths divided by six giving the answer in its simplest form.
In order to divide a mixed fraction or mixed number by a whole number, we firstly need to convert it into a top-heavy or improper fraction. To do this, we multiply the whole number by the denominator and then add the numerator. In this case, we’re multiplying the integer by the denominator to work out how many fifths there are in three whole ones. Three multiplied by five is 15, and adding three to this gives us 18. The mixed number three and three-fifths is equivalent to the improper fraction eighteen-fifths. We need to divide eighteen-fifths by six. As 18 divided by six is equal to three, eighteen-fifths divided by six is equal to three-fifths.
An alternative method to solve this calculation would be using the acronym KCF. We keep the first fraction the same. We change the division sign to a multiplication sign. We then flip or find the reciprocal of the second number. As six is the same as six over one, its reciprocal is one-sixth. Six and 18 have a common factor of six, so we can cross cancel. We are left with three-fifths multiplied by one. Once again, this is equal to three-fifths. Three and three-fifths divided by six is three-fifths.