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Multiplying Fractions
By Francesca on November 30, 1998:

HOW DO YOU MULTIPLY FRACTIONS?

By Simon Munday (sjm78) on November 30, 1998:

Dear Francesca,

This is actually quite easy, but I'll start with a couple of simple examples. First of all, how do you multiply a fraction by an integer (a normal number)? You just multiply the top of the fraction (the numerator) by the integer and leave the bottom of the fraction (the denominator) as it is, for example:


3×  1
2
 =  3×1
2
 =  3
2

7×  3
4
 =  7×3
4
 =  21
4

What do you do when you divide a fraction by an integer? You leave the numerator as it is and multiply the denominator by the integer, for example:
 1
2
 ¸3 =  1
2×3
 =  1
6

 3
4
 ¸7 =  3
4×7
 =  3
28

Now when you multiply two fractions, you can split the process into two bits. First, you multiply the first fraction by the numerator of the second, (which you know how to do because the numerator is just an integer), and then you divide the result of that by the denominator of the second fraction (which you also know how to do). For example,

 1
2
 ×  3
4
 =  1×3
2
 ¸4 =  3
2
 ¸4 =  3
2×4
 =  3
8

Now in the first part of the process, you don't change the denominator, and in the second, you don't change the numerator, so you can do the two things at the same time to get the same result, for example,

 1
2
 ×  3
4
 =  1×3
2×4
 =  3
8

So, in other words, the rule is simply
 a
b
 ×  c
d
 =  a×c
b×d
where a/b and c/d are any fractions you want.

I hope you followed this. If not, the last bit is all you need to know in order to multiply any fraction