Multiplying fractions is actually one of the simplest operations to perform on two fractions. In order to multiply two fractions together, all you have to do is multiply the numerators, and then multiply the denominators. Lets look at the following problem:
We multiply the numerators: 4 x 3 = 12. We then multiply the denominators: 5 x 4 = 20 to get our result of 12/20.
We then need to make sure we reduce our answer (
See Reducing Fractions). Since 12 and 20 our both divisible by 4 we can reduce our answer to 3/5.
Reducing Before Multiplication
When dealing with multiplication of fractions, you can actually do some reducing before even performing multiplication. when you have a multiplication of fractions problem, you can simplify the problem by rewriting it with all of the numerator terms on the top and all of the denominator terms on the bottom as seen below:
Since there is a 4 in the numerator and a 4 in the denominator, we can look at that as a the fraction 4/4 which can be simplified to 1/1.
We can now multiply 1 x 3 = 3 and 5 x 1 = 1 to get the same result of 3/5.
The numbers do not necessarily have to match to reduce before multiplying, lets change the problem to 4/5 x 3/2. You can see we now have 4 in the numerator and 2 in the denominator. Since they both have a common factor of 2 we can divide both numbers by 2 and replace them with the result as seen below.
We multiply 2 x 3 = 6 and 5 x 1 = 5 to get 6/5 which is equivalent to 1 and 1/5.