Adding Mixed Numbers

U02_L3_T1_we3 Adding Mixed Numbers

Add and simplify the answer and
write as a mixed number.

So we have two mixed
numbers here.

We have a whole number part
and a fraction part.

We need to add them.

Now, there's two ways
to do this.

You could convert both of these
into improper fractions,

then add them, and then
convert that back

into a mixed number.

Or you could just look at this
and say, well, you know what?

17 and 2/9 is the exact same
thing as 17 plus 2/9, and then

5 and 1/9 is the exact same
thing as 5 plus 1/9, so 17 and 2/9

plus 5 and 1/9 is the same
thing as 17 plus

2/9 plus 5 plus 1/9.

These two statements are
completely equivalent.

And we know that when you're
just adding a bunch of

numbers, it doesn't matter what
order you do it in, so

you can swap the order.

So you could say that this is
the same thing as 17 plus 5

plus 2/9 plus 1/9.

And we could do this
in any order.

And we know what 17 plus 5 is.

We've done that before.

17 plus 5 is 22, so that
part right there is 22.

So we have 22 plus-- now
what is 2/9 plus 1/9?

Well, they have the same
denominator, so it's going to

be over 9, and then you
add the numerators.

2 plus 1 is 3.

So it's 22 plus 3/9, but
this can be simplified.

Both the numerator and
the denominator are

divisible by 3.

Divide the numerator
by 3, you get 1.

Divide the denominator
by 3, you get 3.

So this is 22 plus 1/3, which is
the exact same thing as 22

and-- let me write it in that
other blue color-- which is

the exact same thing
as 22 and 1/3.