Math Tutor Bob

Multiplying fractions is very easy. Just multiply the top (numerator) and multiply the bottom (denominator) and you have the answer. To explain, consider

                      1⁄4 * 3⁄8

Multiply the numerators ... which is 1*3 = 3

And the denominators ... which is 4*8 = 32

             So     1⁄4 * 3⁄8 = 3⁄32
             

Its rather simple, multiply the numerators (tops) and the denominators (bottoms). And, of course, just like multiplying three integers (say 3*4*2) multiply them one at a time. So, try these and see if you can get the right answer.

     1⁄4 * 3⁄8 = 3⁄32

     3⁄4 * 3⁄5 = 9⁄20
                                                                   
     3⁄5 * 3⁄7 = 9⁄35
                                                                   
     1⁄4 * 5⁄7 = 5⁄28
                                                                   
     3⁄4 * 1⁄2  * 3⁄5  = 9⁄40
                                                                   
     4⁄7 * 2⁄3  * 2⁄3  = 16⁄63
     

Sometimes the final answer is a fraction which needs to be reduced, such as:

        3⁄4 * 4⁄5 = 12⁄20 

Now the fraction

       12⁄20 

can be reduced by cancelling a 4. To explain

 12⁄20  can be written as (4*3)⁄(4*5)

and the two 4s can be cancelled, giving a final answer of

          3⁄5 

Of course this cancellation process at the end could have been avoided if it was recognized early on that 4 could be cancelled in the original problem. That is to say given the original problem,

       3⁄4 * 4⁄5 

The 4 in the denominator of the first fraction and the 4 in the numerator of the second fraction could have been cancelled, thereby giving the final answer much quicker.

A few more with cancelling ...

    2⁄3 * 6⁄7 = 4⁄7  cancel 3 from top and bottom using 3 and 6
        
    2⁄5 * 10⁄11 = 4⁄11  cancel 5 using 5 and 10
        
    4⁄7 * 7⁄8 = 1⁄2  cancel 7 using two 7s and cancel 4 using 4 and 8
        
    1⁄2 * 2⁄3 = 1⁄3  cancel 2 using two 2s
        
    21⁄25 * 5⁄7 = 3⁄5  cancel 7 using 21 and 7 AND cancel 5 using 5 and 25

References multiplication of fractions.

Calculator Soup - has a "fraction calculator" which you can enter your own fractions and then "Calculate" and compare your answer with theirs.

More Examples

Now, lets consider a few more

      43⁄5 *  1⁄2  

To make sure that is clear ... four and three-fifths times one-half.
Well, first we must change the mixed number

      43⁄5 

to an improper fraction. This is

      43⁄5 = 23⁄5

And now carry on with the multiplication of the fractions.

      23⁄5 * 1⁄2 = 23⁄10
        
      Which reduces to  23⁄10 

A useful fraction calculator from one Dad and two Daughters