How to Multiply Fractions

Why can't everything in life be as easy as multiplying fractions? To multiply two fractions, just do the following: Multiply the two numerators (top numbers) to get the numerator of the answer; multiply the two denominators (bottom numbers) to get the denominator of the answer.

When you multiply two proper fractions, the answer is always a proper fraction, so you won't have to change it to a mixed number, but you may have to reduce it.

Before you multiply, see whether you can cancel out common factors that appear in both the numerator and denominator. (This process is similar to reducing a fraction.) When you cancel out all common factors before you multiply, you get an answer that's already reduced to lowest terms.

Sample questions

1. Multiply 2/5 by 4/9.

   

   Multiply the two numerators (top numbers) to get the numerator of the answer. Then multiply the two denominators (bottom numbers) to get the denominator of the answer:

   

   In this case, you don’t have to reduce the answer.

2. Find

   
   

   Before you multiply, notice that the numerator 4 and the denominator 8 are both even. So, divide both of these numbers by 2 just as you would when reducing a fraction:

   

   Now the numerator 2 and the denominator 4 are both even, so repeat this process:

   

   At this point, neither numerator has a common factor with either denominator, so you’re ready to multiply. Multiply the two numerators to get the numerator of the answer. Then multiply the two denominators to get the denominator of the answer:

   

   Because you canceled all common factors before multiplying, this answer is in lowest terms.

Practice questions

1. Multiply 2/3 by 7/9.

2. Find

   

3. Multiply 2/9 by 3/10.

4. Figure out

   

Following are answers to the practice questions:

1. 

2. 

   Multiply the numerator by the numerator and the denominator by the denominator:

   

   The numerator and denominator are both even, so both can be reduced by a factor of 2:

   

3. 

   Begin by canceling out common factors. The numerator 2 and the denominator 10 are both even, so divide both by 2:

   

   Next, the numerator 3 and the denominator 9 are both divisible by 3, so divide both by 3:

   

   Now multiply straight across:

   

   Because you canceled out all common factors before multiplying, this answer is already reduced.

4. 

   Start by canceling out common factors. The numbers 14 and 8 are both divisible by 2, and 9 and 15 are divisible by 3:

   

   Now multiply: