Hey, it's Kaeleigh. This lesson is on adding mixed numbers, but using a
different method of improper fractions. Let's get started.
Remember that a mixed number
is a whole number and a fraction combined. Sometimes it's easier to work
with mixed numbers if we rewrite them as improper fractions.
An improper fraction
is a fraction that is top-heavy, or has a bigger number in the numerator than in
the denominator. We can convert mixed numbers to improper fractions pretty
easily, but there are a few steps. So the first step here is we take our whole
number, the big one here, and we multiply it by our denominator here. So in this
case we'd get 2 times 4 is equal to 8 and then we take that number and we add
it to the numerator of our fraction. So it's 3. And then we take our denominator
and it stays the same, so we just move it over here. And now I have 8 plus 3 is 11
and I keep my denominator the same — 4. So my improper fraction 11 over 4 is equal
to the mixed number 2 and 3/4. All right, now let's try using improper fractions
to add mixed numbers. So here I have my whole number 3 plus my mixed number 3
and 1/3. So let's convert our mixed number here to an improper fraction. So,
first, I multiply my whole number by my denominator — 3 times 3. That gives me 9. I
add my numerator — 1 — and I keep my denominator the same. So this is equal to
10 over 3. But, now, if I have my whole number 3, I need to convert that to a
fraction. So I have 3 over 1 and I need 3 in my denominator, so I know I need to
multiply it by 3 over 3 and that's gonna give me 9 over 3. And now I'm adding
these two together. So "9 over 3" plus "10 over 3" gives me ... ?
I check my denominator — they are the same. I can go ahead — I can add my numerators ...
19 over 3. So now my addition is done and I'm going to convert my improper
fraction — remember it's top-heavy — into a mixed number. So I do that by dividing —
remember a fraction just means "division." So 3 goes into 19 how many times? Well, 3
times 6 gives me 18 ... When I subtract those I get a 1. I keep my remainder as a
fraction, so it's 1 over 3. So ... 19/3 is the same as 6 and 1/3. And
there's my answer! Good, let's try one more together.
So in this one I have two mixed numbers: 1 and
2/5 plus 1 and 4/5. So let's go ahead and
convert these mixed numbers to improper fractions, starting with our first one
here: 1 times 5 gives me 5. I add my numerator, which is 2. I keep my
denominator the same. So 5 plus 2 — that gives me 7/5 and now I'm gonna
add 7/5 to whatever this improper fraction is. 1 times 5 gives me
5 ... plus my numerator — that's 4. I keep my denominator the same — that's 5. This gives
me 9/5. So now I have 7/5 plus 9/5, which is equal to ...
Checking my denominators (they are the same) ... 5 goes on the bottom ... and 7
plus 9 gives me 16. But it's top-heavy, so it's an improper
fraction. Let's convert it back to a mixed
number. 5 goes into 16 three times (3 times 5 — that gives me a 15. I subtract these. I
get a 1.) Remainder as a fraction looks like 1/5. So 16/5 is the same as 3
and 1/5. And there's my answer. Good work! So now whenever you have to
add mixed numbers, you can choose how you want to do it —
adding the whole numbers together and then adding the fractions, or converting my
mixed numbers to improper fractions and adding across.
All right! So practice what you've learned by doing the online quizzes. Have
fun and remember to always be clever!