In this video, we’re gonna to learn the basics about how to add fractions.
Now a lot of math books will teach you how to add fractions before they teach you how to multiply them,
but here at Math Antics, we think you should learn the other way around.
You remember how easy it is to multiply fractions, right?
You just multiply the top numbers together, and you multiply the bottom numbers together, and you have your answer.
So, you might be wondering, “Well… can’t we just do that with addition too?”
“Can’t we just add the top numbers together and add the bottoms together and get our answer?”
Well alright, let’s try it and see…. but I’ve got a bad feeling about this!
Let’s try adding 1/2 to 1/2
So if we added the top numbers, we’d get 2
And if we added the bottom numbers, we’d get 4
But… well that can’t be right!, because 2 over 4 simplifies to one-half.
And if you add one-half and one-half, you should get a whole …not a half!
[Alarm sound] Uh Oh! We must have broke some sort of math rule! I’m outta here!!
Okay, here’s what we did wrong.
It turns out that there’s some important math rules called ‘Order of Operations’
that say you have to do multiplication and division BEFORE you do addition and subtraction.
Now because fractions are just division problems, if you just added the top numbers and added the bottom numbers,
you'd be breaking those rules because you’d be doing the addition before the division.
So, what are we gonna do instead?
Well fortunately, there’s a trick that lets us work around the Order of Operations rules and add fractions without dividing.
But there’s a catch. It only works for fractions that have the same bottom numbers.
The trick is, if fractions have the same bottom numbers,
we can add them by just adding the top numbers together and keeping the same bottom number in our answer.
For example, to add one-half and one-half, we just add the top numbers; and 1 and 1 gives us 2.
But we DON’T add the bottom numbers. We just use the same bottom number in the answer, which is 2.
So, 2 over 2 is a whole fraction. And that makes sense because if you add one-half and one-half, you get a whole!
Let’s see a few more examples. …like this one: 5 over 16 plus 2 over 16.
Again, since the bottom numbers are the same, it’s easy to add these fractions.
All we do is add the top numbers together: 5 plus 2 equals 7, and that’s the top number of our answer.
Then we just keep 16 as the bottom number of our answer.
So, 5 over 16, plus 2 over 16, equals 7 over 16. Pretty easy, huh?
But what about subtracting fractions? Does that work the same way?
Yep, if the bottoms numbers are the same, all you have to do is subtract the top numbers and keep the same bottom number in your answer.
Here’s an example of subtracting fractions with the same bottom numbers: 5 over 9 minus 2 over 9.
First we subtract the top numbers: 5 minus 2 equals 3.
Then we just write the same bottom number in our answer: 9
So, 5 over 9, minus 2 over 9, is 3 over 9.
Yep, adding and subtracting fractions with the same bottom numbers is easy.
And there’s a special name for problems like this. It’s called “Adding or Subtracting ‘Like’ Fractions.”
A teacher once told me that they’re called ‘like’ fractions because the bottom numbers are the same, (or ‘alike’)
but I think it’s because they secretly like each other.
Just kidding. But seriously, ‘like’ fractions are easy to add with the trick we just learned,
but what happens if you want to add two ‘unlike’ fractions?
What do you do if you have fractions with DIFFERENT bottom numbers?
Unfortunately, the only way we can add ‘unlike’ fractions without doing the division first, is to change them so that they DO have the same bottom numbers.
In other words, we need to change our ‘unlike’ fractions into ‘like’ fractions so we can just use our trick.
In math language, that’s called “finding a common denominator”.
Now remember that a ‘denominator’ is just a fancy math word for the bottom number of a fraction.
And ‘common’ just means that they’re the same.
So, how do we find a common denominator so that we can add or subtract ‘unlike’ fractions?
That’s what we’re gonna learn in the next video.
But before you move on, be sure to do the exercises for this section.
Learn more at www.mathantics.com