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第十一课Adding and Subtracting Fractions
In this video,we’re gonna learn the basics about how to add fractions. A lot of math books will teach you how to add fractions before they teach you how to multiply them. But here,we think you should learn the other way around.
You remember how easy it is to multiply fractions. You just multiply the top numbers together and the bottom numbers together and you have your answer.
So you might be wondering can we just do that with the addition too. Can we just add the top numbers together and add the bottom numbers together and get our answer.
That can’t be right. We broke some of the math rules.
Here’s what we did wrong. It turns out that some important math rules called “order of operations” that say that 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 nubmers and added the bottom numbers,you’ll be breaking those rules because you’re doing the addition before the division.
So what are we gonna do instead?
Fortunately there’s a trick that let’s us work around all the operation rules and add fractions without dividing. But it only works for fractions that have the same bottom numbers.
The trick is, if the fractions have the same bottom numbers,you can add them by just addign the top nubmers 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 but we don’t add the bottom numbers.We just use the same bottom number in the answer.
Let’s see a few more examples,like this one:five over sixteen plus two over sixteen. Again since the bottom numbers are the same, it’s easy to add these fractions. All we do is to add the top nubmers together. Five plus two equals seven and that’s the top number of our answer. Then we just keep sixteen as the bottom answer of our answer.
But what about subtracting fractions,is that work the same way?
Yep,if the bottom numbers are the same,all you have to do is to subtract the top numbers and keep the same bottom number in your answer.
Here’s an example of subtracting fractions with the same bottom number:five over nine minus two over nine.
First we subtract the top numbers. Five minus two equals three. Then we just write the same bottom number in our answer.
Yep,adding and subtracting fractions with the same bottom number is easy. And there’s a special name for problem like this.It’s called “adding or subtracting like fractions”.
Like fractions are easy to add with the trick we just learned.
But what happens if you wanna 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 fracitons into like fractions so we can just use our trick. In math language,that’s called “finding the common denominator”.