Multiplying and Dividing Fractions

Multiplying Fractions

When we multiply fractions, we multiply the numerators and then the denominators. Then you need to write the answer in lowest terms. You can also reduce the fractions and eliminate common factors before you multiply. This is a better method when you’re using large numbers. For example, when multiplying I can simplify the fractions before I multiply.

Multiplying Mixed Numbers

When you multiply mixed numbers, they need to be written as improper fractions. Then follow the process of multiplying and change it back to a mixed number if necessary.


For example:

multiplying mixed numbers.gif
two and a half times three and two thirds equals five halves times eleven thirds

Notice how I changed the mixed numbers to improper fractions. This will make multiplying the fractions easier! Now let’s discuss dividing fractions.

Division of Fractions


Before we can talk about dividing, we need to define a reciprocal. The reciprocal of a fraction is found by switching the numerator and denominator.


Dividing Fractions

When you divide fractions, you’ll take the reciprocal of the divisor and change the problem to a multiplication problem.

Here’s the general formula:

A over B divided by C over D equals A over B times D over C

Dividing Mixed Numbers

When dividing mixed numbers, the same rules apply. Change the mixed numbers to improper fractions and then follow the rules for division.



  1. two thirds times one fourth
  2. one half divided by five sixths
  3. eight twelfths times nine tenths
  4. ten fourteenths divided by thirty-five
  5. fourteen times eight twenty-first
  6. sixteen divided by forty-eight forty-ninths
  7. four and one fourth times three and seven eighths
  8. twelve and three fourths divided by two and a half
  9. five and three fifths times one and two fifths
  10. eight and one fourth divided by four and one eighth