Evaluate three and one-third divided by 10, giving the answer in its simplest form.
In order to divide a mixed number or mixed fraction by a whole number, we firstly need to convert it into an improper or top-heavy fraction. We do this by multiplying the whole number by the denominator and then adding the numerator. Three multiplied by three is equal to nine. Adding one to this gives us 10. This means that three and one-third is the same as the improper fraction ten-thirds.
We could also have shown this pictorially. One whole one is equal to three-thirds. This means that three is equal to nine-thirds. As we have three and one-third, this is equivalent to ten-thirds. We need to divide ten-thirds by 10. As 10 divided by 10 is equal to one, ten-thirds divided by 10 is equal to one-third.
Three and one-third divided by 10 in its simplest form is one-third. This is also clear from the diagram. If we were splitting the ten-thirds between 10 people, each person would have one-third.