Why do we not need a common denominator in order to multiply two fractions?

Answer 1

Who sez? You need a common denominator to ADD two fractions. To multiply, just do separate operations on the numerator and denominator.

Answer 2

You do not need a common denominator to multiply two fractions.

In essence, you do not even 'need' one to add or subtract them either. We simply find a CD during these manual hand operations to aid the process. By finding a number which is a multiple of both (or more, if more than two fractions are considered) denominators, we have thus found a 'common denominator' which allows us to express both fractions with the same denominator. Hence, we have expressed the operation as something more computationally easier (if doing it by hand).

For example, it is harder to hand-perform 1/6 + 3/4 than the equivalent 4/24 + 18/24. For the latter, all we need to do is add the numerators to reach the answer; i.e 22/24 ~ 11/12.

Another example:
Simplify: 1/12 + 1/3.

Because the denominators are not the same, it is more difficult to hand-compute this question. So we find a common denominator. Easiest method is to of course multiply the denominators, as it is a fact that if c = a x b, where a and b are numbers, then c is an element of the subset of common denominators of those numbers. I.e 12 x 3 = 36 is guaranteed to be a common denominator of 12 and 3.
We then turn this question into the equivalent 3/36 + 12/36. Now that the denominators are the same, all we have to do is the add the numerators, which is much more computationally (and intuitively) easier. I.e the answer is 15/36.

Answer 3

1). Simplify
2) Multiply the numerator
3) Multiply the denominator

Example: 1/2 x 3/4 = 3/8

- - - - - -

Example;

3/5 x 4/8 = 12/40 = 3/10 . . .The common factor is 4

Remember reduce the fraction to lowest terms

Click on the URL below for additional information concerning Multiplying Fractions.

www.math.com/school/subject1/lessons/S1U4L4GL.html

www.math.com/school/subject1/practice/S1U4L4/S1U4L4Pract.html

- - - - -s-

Answer 4

You don't. If you multiply 1/2 by 1/3, you get 1/6. for addition and subtraction, you need to find the common denominator, but multiplication and division are different.

Answer 5

because when we multiply fractions we cross multiply

Answer 6

You only need one too add them. Multiplication is a don't care.