>> Welcome to a quick lesson on adding mixed numbers.
Here are the steps we'll follow.
Number 1; we know that when we add or subtract fractions,
we must first obtain a common denominator.
Then we're going to go ahead and add the fractions and the whole numbers together.
And then if the sum has an improper fraction, we'll have to convert it to a mixed number
and then add it to the whole number.
And then of course, we'll simplify the fraction if possible.
Let's go and take a look at a few examples.
The first thing I recommend is write this in vertical form.
So, we have 4 and 1/4, plus 2 and 2/3.
So, notice right away we do not have a common denominator, but we have a nominator
of 4 here and a nominator of 3 here.
Our LCD or least common denominator would be 12, so we're going to multiply this fraction by 4
in the denominator and 4 in the numerator.
This will give us a 12 in the denominator.
And to have a 12 here, we'll have to multiply both the top and the bottom by 3.
This is going to give us 4 and 3/12 and this will be 2 and 8/12.
Now that we have a common denominator, we can go ahead and add these together.
We'll start by adding the fractions and then we'll add the whole numbers.
So, 3/12 plus 8/12, remember we just add the numerators, so 3 plus 8 would give us 11/12
and then 4 plus 2 would give us 6.
Our sum is 6 and 11/12.
Notice 11/12 is not improper and it does not simplify and therefore we're done.
Now, unfortunately, many of the problems don't turn out this nice, so let's go
and take a look at another example.
Again, we'll start by writing this in vertical form.
So, we have 1 and 4/5, plus 2 and 11/15.
So, the first thing we should notice is we do not have a common denominator,
but we could convert this to 15th's by multiplying both the top and bottom by 3
and then we would have a common denominator.
So, we'll start by doing that.
That's going to give us 1 and 12/15.
I'm going to leave this fraction the same, 2 and 11/15.
Now I'll go ahead and add the fractions and notice that again,
our denominator stays the same, our numerator is going to be 12 plus 11 that will be 23/15.
And then we have 1 plus 2 that would be 3.
Now, we can't leave our answer like this because 23/15 is an improper fraction.
So, we need to convert this improper fraction to a mixed number and then add it to 3.
Let's go ahead and do that.
Remember, the procedure for that is to perform long division.
We'll take 23 and divide by 15.
There's 1, 15 and 23 the remainder is 8, so that tells us that 23/15 is the same as 1 and 8/15.
So, we'll go ahead and rewrite this as 1 and 8/15.
So, we're going to have 3 plus 1 and 8/15.
Well, 1 plus 3 is going to give us 4, so our final sum will be 4 and 8/15.
So, this is the 1 thing that we have to be careful about when we add mixed numbers.
When we add the fraction part after obtaining a common denominator,
if this part here is an improper fraction, we have to convert it to a mixed number,
as we did here and then add it to the whole number.
So, 1 plus 3 gave us 4 and 8/15.
Let's go and try 1 more of these.
Let's put this in vertical form.
So, we have 3 and 7/8, plus 2 and 5/6.
Now, if we have a hard time finding a common denominator,
remember we can always just multiply these together, 8 times 6 would be 48.
We could use 48 as a common denominator, but 24 would be the least common denominator.
So, we'll go ahead and multiply this fraction by 3 over 3 that will give us 24,
multiply this fraction by 4 over 4 that will give us 24 as well.
So, here we have 3 and 21/24 and here we have 2 and 20/24.
Let's go ahead and add the fractions together.
The denominator stays the same.
The numerator is going to be 21 plus 20 and that will be 41 and 3 plus 2 will give us 5.
Again, we're not done because this is an improper fraction, so we need to convert this
to a mixed number and then add it to 5.
So, 41 divided by 24 is going to be 1.
It's going to give us a remainder of 17.
So, that tells us that 41/24 is the same as 1 and 17/24.
Let's go ahead and write that over here.
We have 5 plus 1 and 17/24.
So, our final sum will be 6 and 17/24.
Now, we should always check to make sure this fraction doesn't simplify
and 17 is a prime number, so it doesn't, but we should always check that.
Okay, that's going to do it for this video.
I hope you found this helpful.
Thank you for watching. ------------------------------4df85dc3b8b4--