Hi, I’m Rob.  Welcome to Math Antics.
In this lesson, we’re gonna learn how to add Mixed Numbers.
If you’re not quite sure what Mixed Number are,
then you should definitely watch our video called “Mixed Numbers” first.
As you remember, a Mixed Number is a combination (or sum) of a Whole Number and a Proper Fraction.
And for this lesson, it’s gonna be important to remember that
even though the plus symbol isn’t usually shown between those two parts of a Mixed Number,
they’re being ADDED together.
3 and 1/4 means 3 PLUS 1/4
2 and 5/8 means 2 PLUS 5/8.
Here’s why that’s so important to remember…
Let’s say you’re given a problem
where you need to add the Whole Number 2 to the Mixed Number 3 and 1/4.
If you know that 3 and 1/4 is the same as 3 PLUS 1 /4
then you can see that the problem is really 2 + 3 + 1/4
Well that’s easy… all you have to do is add the 2 and the 3 to get 5
and you’ll have 5 plus 1/4 which is the Mixed Number 5 and 1/4.
So if you need to add a Whole Number to a Mixed Number,
you can just add the Whole Number parts and you’re done!
Okay, but what if you need to add a Mixed Number to a fraction?
…like in the problem: 1 and 3/8 pus 1/8
Again, if you remember that 1 and 3/8 means 1 PLUS 3/8
then you can see that this problem is really 1 + 3/8 + 1/8
That looks pretty easy also.
3/8 and 1/8 are what we call ‘like’ fractions…
they have the same denominator and can be added easily.
3/8 + 1/8 = 4/8
So our answer is simply the Mixed Number 1 and 4/8
Oh, but you might notice the fraction part can be simplified.
4/8 simplifies to 1/2,
so we should write our answer as 1 and 1/2 instead.
It’s not mathematically “wrong” if you don’t simplify a fraction,
but teachers (and tests) usually require you to simplify whenever you can,
so it’s a good habit to get into.
Notice that in each of those examples,
we just added Whole Numbers to Whole Numbers and fractions to fractions.
And it work the same way when adding a Mixed Number to a Mixed Number,
like 2 and 1/5 plus 4 and 2/5
Again, let’s show our Mixed Numbers with the plus signs so we can see the real problem:
2 + 1/5 + 4 + 2/5
Because all of these parts are being added,
and addition has the commutative property,
it really doesn’t matter what order we do the addition in.
That means we can rearrange this problem to make it simpler:
Now we have 2 + 4 + 1/5 + 2/5
Adding the Whole Numbers is easy: 2 + 4 = 6
and adding these ‘like’ fractions is easy too: 1/5 + 2/5 = 3/5
That leaves us with 6 + 3/5 which is the Mixed Number 6 and 3/5.
So when you add Mixed Numbers,
you can just add the Whole Number parts to get the Whole Number of the answer,
and you add the fraction parts to get the fraction part of the answer.
That’s why in a lot of math books,
you’ll see addition of Mixed Numbers written in a stacked form like this.
This is similar to the way you would stack multi-digit numbers up to add them,
and it helps you remember that you can add the fraction parts
and the Whole Number parts in two separate columns
and write your answer below the answer line just like in multi-digit addition.
And do you remember how in multi-digit addition,
if a column of digits added up to 10 or more, you had to “carry” or “re-group” to the next column?
Well, something similar to that can happen when adding Mixed Numbers.
Sometimes adding the fraction parts of two Mixed Numbers
actually effects the Whole Number part of the answer.
To see what I mean by that,
let’s say you hosted a massive pizza party for all your friends…
Hey Man… this is a great party!
You’ve got some really cool friends.
Hey thanks!  You should hang out with us more often.
I think you’d really fit in.
And after the party ended,
you had 1 and 3/8 cheese pizzas left over
and 1 and 5/8 pepperoni pizzas left over.
What’s the total amount of leftover pizza?
Well, we just need to add those two mixed numbers together.
Let’s stack them like I just showed you and add them column by column.
3/8 + 5/8 is 8/8
and 1 + 1 = 2
So, the answer is 2 and 8/8.
Ah, but do you see what happened?
The fraction parts of the two Mixed Numbers combined to form what I call a “Whole Fraction” (8/8)
And we know that 8/8 simplifies to 1.
So having 2 + 8/8 is the same as having 2 + 1 which is 3.
We added two Mixed Numbers together and ended up with the Whole Number 3.
And our leftover pizza shows us that we got the answer right.
Here’s another example that shows how the fraction parts
can effect the Whole Number part of the answer when adding Mixed Numbers:
1 and 3/7 plus 2 and 5/7
This time we’ll use the commutative property to rearrange the addition
and then we add the whole number parts: 1 + 2 = 3.
And then we’ll add the fraction parts: 3/7 + 5/7 = 8/7.
So the answer we get is 3 and 8/7
But do you notice something funny about the fraction part of that answer?
It’s an Improper Fraction which means its value is greater than 1.
And it’s really bad form to leave an Improper Fraction in a Mixed Number like this
because, as we saw in the last video,
the Improper Fraction ITSELF can be converted into a Mixed Number.
8/7 contains a ”Whole Fraction” that we can simplify out of it…
it’s the same as 7/7 + 1/7 And since 7/7 equals 1,
that gives us the Mixed Number 1 and 1/7
So just like in the last example,
we can add that extra 1 to the Whole Number part of our answer which gives us 4 and 1/7.
That’s a much less confusing answer than 3 and 8/7,
which almost sounds like it’s less than 4
but it’s actually MORE than 4.
Are you getting it so far?
Adding Mixed Numbers is pretty easy when you realize that
you can just add the whole number parts and fraction parts separately
and then just watch for cases where the fraction parts add up to more than 1.
But there are cases where adding Mixed Numbers can get a little bit tougher.
All of the examples we’ve seen so far had fraction parts that were ‘like’ fractions.
But what if you had to add two Mixed Numbers with ‘unlike’ fractions?
…like this problem:  1 and 1/2 plus 2 and 1/4
If we re-arrange the problem as usual,
we see that the Whole Numbers are still easy to add: 1 + 2 = 3
But the fractions have different denominators.
We can’t add them until we change them so that the bottom numbers are the same.
We cover how to change fractions so that they have the same bottom number (or a “common denominator”)
in other videos that you may want to watch if the steps I’m about to do seem new to you.
4 is a multiple of 2, so 4 is going to be a good choice for a common denominator.
To change 1/2 into fourths, we will multiply it by the “Whole Fraction” 2/2.
On the top we have 1 times 2 which is 2,
and on the bottom we have 2 times 2 which is 4, just like we want.
So now we have 2/4 + 1/4 which equals 3/4.
That means the answer to this problem is 3 and 3/4.
That wasn’t so bad after all.
Let’s try one more example where we need to change ‘unlike’ fractions
into ‘like’ fractions in order to add the Mixed Numbers:
3 and 2/3 plus 4 and 3/4
After re-arranging the parts,
we see that we need to add 3 and 4 which is 7,
and we also need to add 2/3 and 3/4.
Since these are ‘unlike’ fractions we need to change them.
3 and 4 are not multiples of each other,
so it looks like using the “Easiest Common Denominator” will be our best option here.
3 x 4 = 12 so that will be our new denominator.
To convert 2/3 we multiply it by 4/4 which gives us the new equivalent fraction 8/12
To convert 3/4 we need to multiply it by 3/3 which gives us the new equivalent fraction 9/12
Now that we have ‘like’ fractions we can add them easily:
8/12 + 9/12 = 17/12
That gives us 7 and 17/12 as our answer.
But once again, the fraction part is Improper,
so we have to simplify it because its value is greater than 1.
17/12 is the same as 12/12 + 5/12
Which is the mixed Number 1 and 5/12
We need to add that 1 to our Whole Number part.
7 + 1 = 8
Which means our final answer is 8 and 5/12
Alright,  that should give you a pretty good idea of how to add Mixed Numbers.
You can add the Whole Number parts and the fractions parts separately.
But the fraction part of the answer may effect the Whole Number part if its value is 1 or greater.
And remember, if the fraction parts have different denominators,
you’ll need to change them to have a common denominator before you can add them.
With complicated arithmetic like this,
it’s important to practice what you’ve learned so it’ll really make sense.
So be sure to try some exercise problems on your own.
As always, thanks for watching Math Antics and I’ll see ya next time.
Learn more at www.mathantics.com
