If you’re reading this, I’m going to assume a basic level of math skills: addition, subtraction, multiplication and division. This is for you who are trying to learn fractional math next. Multiplying fractions is actually the easiest of the functions you can do with fractions. I’d advise starting with multiplying, then dividing, adding and then subtracting, in that order. Unlike with whole numbers, adding and subtracting are more complicated than multiplying and dividing when it comes to fractions.
The very first thing you need to know how to do is simplify a fraction. This is actually very, very easy. It just means to reduce to the smallest possible form. Let’s say you have a fraction like 4/8. 4/8 is not in its simplest form.
That’s because both the top number (called a numerator) and the bottom number (called a denominator) are divisible by several numbers. If the only whole number they’re both divisible by is 1, then it’s in its simplest form, and you don’t need to simplify.
However, if they share other numbers that they’re both divisible by, then you should divide both by the largest of those that you know. So with 4/8, both 4 and 8 are divisible by 1, 2, and 4. That means to reduce 4/8, you need to divide both the numerator and denominator by 4. 4/4 = 1, and 8/4 = 2. That means that 4/8 reduces to 1/2, which is its simplest form.
Multiplying fractions is just like multiplying whole numbers, with a few additional steps. First, you always multiply the numerators together and then the denominators together. That gives you the answer, but you need to simplify afterward. The more simple the fraction, the easier it is to work with. And the whole point of math is to be usable. If you’re learning to work with fractions, chances are, you’re going to be using the results in some way.
Let’s try some examples.
4/3 * 7/8 = ?
Just like regular multiplication, but numerators together and denominators together, so it turns into 4*7 / 3*8, which is:
This is very clearly not simplified. Assuming we don’t know anything other than the fact that 2 will go into both the numerator and the denominator, we’ll divide both by 2, giving us:
Also not simplest form available, since 2 goes into both of those numbers as well. We’ll divide both by 2 again, and get:
This is great. It is the smallest form we can get. If you were going to be using the fraction with other fractions after this, you could leave it like that. However, this is not an acceptable final answer, because the numerator is larger than the denominator. So, take the subtract the highest multiple of the denominator from the numerator, divide the number you subtracted by the numerator, and place it as a whole number before the fraction. In this case, 6 goes into 7 a total of 1 time, with 1 left over, which means that you are left with:
1 and 1/6
So next example:
5/9 * 6/12 = ?
Just do it again. Multiply the numerators together and you get 30. Multiply the denominators together and you get 108. So it’s:
And we know we can get this into a more simple form. Let’s just divide by 2.
This is divisible by three. (There’s a trick to know when something is divisible by three by adding the digits together to get a smaller number. If their sum is divisible by three, the number is also divisible by three) So lets divide by three.
This is the simplest possible form of this fraction, so you’re done!
Here’s some problems to try on your own:
1/3 * 1/7 = ?
3/4 * 5/6 = ?
1/2 * 9/11 = ?
1/6 * 5/7 = ?
1/6 * 6/1 = ?
3/4 * 4/3 = ?
7/8 * 16/14 = ?
If you’d like, ask me, and I’ll leave the answers to any of these in the comments.