Hi and Welcome to Math Antics.
In the last video we learned how easy it is to add and subtract fractions that have the same bottom number.
We call those ‘like’ fractions.
But often you’ll be asked to add or subtract fractions that have different bottom numbers, or ‘unlike’ fractions.
And we learned that the only way we can do that is to change our fractions so that they DO have the same bottom number.
Alright then… how do we do that? How can we change two ‘unlike’ fractions into two ‘like’ fractions?
How do we get our fractions to have a ‘common denominator’?
The answer is, we need to use equivalent fractions! You remember what equivalent fractions are, right?
They’re fractions that have the same value, but use different top and bottom numbers:
like 1 over 2 and 2 over 4. They both represent one half, but with different numbers.
Well, whenever we have two unlike fractions that we need to add, if we could find equivalent fractions to use instead,
AND if those new equivalent fractions had the SAME bottom numbers as each other, then we’d be all set.
We’d have two ‘like’ fractions and we could add them using our procedure.
Okay, but how do we find equivalent fractions that have a common denominator (or the same bottom number)?
Well, there’s two main ways of doing it.
In this video, we’re only gonna learn the first way of doing it,
and I like to call this way ‘finding the easiest common denominator’.
In the next video, we’ll talk about another method that some of you may have already heard about.
It’s called ‘finding the least common denominator.’
Okay, so how does this ‘easiest common denominator method’ work?
Well, even though this is an easy method, it might sound a little complicated at first.
But don’t worry. It’ll make a lot more sense once you’ve seen a few examples.
In this method, the common denominator is always going to be the product of the bottom numbers.
In other words, it will be number you’d get if you multiplied the bottom numbers together.
Basically, all we’re going to do is take the two different bottom numbers, and make two different ‘whole fractions’ using them.
Then, we’re going to move the ‘whole fraction’ to the opposite sides and multiply them by our ‘unlike’ fractions.
Doing this will give us two new equivalent fractions that will have the same bottom number.
Then we can add or subtract them easily.
Okay, let’s try a couple examples so we can see this method in action.
Let’s add the fractions 2 over 5 and 1 over 3.
These are NOT like fractions because they have different bottom numbers, so we’re going to change them.
And the common denominator we will uses is the product of the bottom numbers: 5 × 3 = 15.
We change them by multiplying each fraction by a ‘whole fraction’.
The first ‘whole fraction’ is going to be 3 over 3, because 3 is the second fraction’s denominator,
and the second ‘whole fraction’ is going to be 5 over 5 because 5 is the first fraction’s denominator.
Next, we multiply starting with our first fraction.
On the top: 3 × 2 = 6
And on the bottom: 3 × 5 = 15.
So our first fraction has become 6 over 15.
Now for the second fraction…
On the top: 1 × 5 = 5
And on the bottom: 3 × 5 = 15.
So our second fraction has become 5 over 15.
Now we just add them using our procedure for adding ‘like’ fractions. We add the top numbers: 6 + 5 = 11.
And then we keep the same bottom number, which is 15.
So that means the answer to 2 over 5, plus 1 over 3, is 11 over 15.
That’s pretty easy, huh? Alright, let’s see one more example of this method.
Let’s add the fractions 7 over 8 and 3 over 10.
Our common denominator for this problem is going to be 80,
because that’s what we get when we multiply the denominators together: 8 × 10 = 80.
We’ll multiply our 7 over 8 by the ‘whole fraction’ 10 over 10.
And we’ll multiply our 3 over 10 by the ‘whole fraction’ 8 over 8.
Then, when we do our multiplication, the 8 times 10 will give us 80 on the bottom of both fractions.
For the top of the first fraction we have: 7 × 10 = 70.
And the top of the second fraction we have: 3 × 8 = 24.
Now that we have ‘like’ fractions, we can just add the top numbers: 70 + 24 = 94.
And keep the bottom number the same: 80
So… 7 over 8, plus 3 over 10, equals 94 over 80.
Some of you see that this answer could be simplified.
Be sure to check out our videos on Mixed Numbers and Simplifying Fractions to see how you could do that for your final answer.
Alright, that’s the first way you can find the common denominator and change your ‘unlike’ fractions into ‘like’ fractions so you can add or subtract them easily.
Remember, practice is really important in math, so be sure to do the exercises for this section so you really get the hang of it.
After that, check out the next video and I’ll show you how to use a different method to find what we call the Least Common Denominator.
Thanks for watching and I’ll see you next time.
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