>> Adding mixed numbers is similar to adding fractions except we'll be adding fractions
as well as the whole numbers but we do have to be careful when we add the fraction parts
that the fraction is not an improper fraction.
We can't express an answer as a mixed number when the fraction is improper.
So I think it's helpful to write this vertically to begin with so we have 2 4/15 plus 3 1/6.
The first step in this type of problem is to obtain a common denominator
and hopefully the least common denominator using our denominators of 15 and 6.
So the least common denominator is going to be the least common multiple of 15
and 6 which is the smallest number that is divisible by 15 and 6.
That would be 30.
So we want to write both of these fractions with a denominator of 30
so multiply this first fraction by 2/2.
Notice how 2/2 is like multiplying by 1.
And if we multiply 6 by 5 and the numerator
by 5 notice how both fractions will have a denominator of 30.
So let's go ahead and rewrite this.
We're going to have the whole number is 2 and this is going to be 8/30
and here we're going to have 3 5/30.
Now it's important to remember that we are adding so we'll start by adding the fractions.
Again, notice how we have a common denominator so the denominator is going
to stay 30 and we'll add the numerators.
Eight plus 5 is 13 and now we'll add the whole numbers.
Two plus 3 is equal to 5.
We have a sum of 5 13/30.
A couple of things to check.
Notice that this is a proper fraction meaning the numerator is less than the denominator
and also that this fraction is not simplified.
Thirteen's a prime number, therefore the numerator
and denominator do not have any common factors.
Let's take a look at a second example.
Again the first step is to write this vertically so we have 5 3/4 plus 8 5/6.
The next step is to determine the least common denominator using 4 and 6.
We could always multiply 4 and 6 to get 24 and use 24 as a common denominator
but the least common denominator would actually be 12.
Twelve is the smallest number that is a multiple of both 4 and 6.
So we can multiply 3/4 by 3/3.
We'll multiply 5/6 by 2/2.
Again notice how both denominators are now equal to 12.
So here we're going to have 5 and this will be 9/12.
Here we'll have 8 10/12.
So now we'll go ahead and add starting with the fractions.
Again we have a common denominator so we'll add the numerators, 9 plus 10 is equal to 19
and here we have 5 plus 8 which is equal to 13.
So this is the correct value of our sum but it's not in the correct form.
We can't leave a mixed number or the fraction part is an improper fraction.
So what we're going to do now is take 19/12 and write it as a mixed number.
To do that we'll divide 19 by 12.
There's one 12 in 19 with a remainder of 7.
So that tells us that 19/12 is equal to 1 and 7/12.
So what we're going to do is take our whole number 13
and add the mixed number for 19/12 which was 1 7/12.
So our sum in the correct form is going to be 14 7/12.
So this is the main thing you have to watch out for when adding mixed numbers.
When we have the fraction parts, if the fraction is an improper fraction, we have to convert it
to a mixed number and then add it to the whole number. ------------------------------721d2d98087b--