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### Course: Arithmetic (all content) > Unit 5

Lesson 16: Adding and subtracting mixed number with unlike denominators- Adding mixed numbers: 19 3/18 + 18 2/3
- Subtracting mixed numbers: 7 6/9 - 3 2/5
- Add and subtract mixed numbers with unlike denominators (no regrouping)
- Adding mixed numbers with regrouping
- Subtracting mixed numbers with regrouping (unlike denominators)
- Add and subtract mixed numbers with unlike denominators (regrouping)

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# Subtracting mixed numbers with regrouping (unlike denominators)

To subtract mixed numbers, first align the whole numbers and fractions so they can be subtracted separately. If the fractions have different denominators, find a common denominator and convert them accordingly. If the fraction on the bottom is larger, regroup by borrowing from the whole number on top. This will allow you to complete the subtraction.

## Want to join the conversation?

- how did he suddenly change from only having 4/9 to adding 4/9 + 9/9? Where did the 9/9 fraction come from? It's a bit confusing.(33 votes)
- Sal took a whole (9/9) from 17 because if 4/9 minus 6/9 it will be negative. And 17 becomes 16.

16 13/9 is the same thing as 17 4/9. Since if you change 13/9 into a mixed number (1 4/9), then add it to 16, it's 17 4/9.

Hope this helps(14 votes)

- how did you turn the 2/3 into 6/9?(0 votes)
- You can always multiply by 1 and get the same (equivalent) thing. He multiplied by 3/3 which is like a nickname for 1. Multiplying the tops (2*3=6) and the bottoms(3*3=9). The bottoms(denominators) is why we chose the 3/3 version of 1 in the first place. That was the way to get common denominator.(14 votes)

- why do you need to simplify your answer?(7 votes)
- you cant add/subtract if your denomeraters are not the same.like 5/9 and 2/6.they have denomerator of 54 so now it would be 30/54 and 18/54 which would be 48/54.hope it helps!(5 votes)

- What if you need to be simplified? I still don't get simplifying fractions with whole numbers.(3 votes)
- At the end of the problem, if your answer can be simplified, do it!

For example, if you have 5 6/12 , you can automatically see that the "6/12" can be simplified down to 1/2. You don't need to do anything to the 5 because you never simplify the whole number. Your final answer would be 5 1/2

Did this help?(9 votes)

- is there something that can help me understand better?(5 votes)
- I would recommend re-watching the video and doing the practice multiple times to get better.(4 votes)

- Can you just use knowledge in needing to regroup and not cross out the number, but re-write the number?(4 votes)
- ou can always multiply by 1 and get the same (equivalent) thing. He multiplied by 3/3 which is like a nickname for 1. Multiplying the tops (2*3=6) and the bottoms(3*3=9). The bottoms(denominators) is why we chose the 3/3 version of 1 in the first place. That was the way to get common denomina(4 votes)
- Why can we put it as a negative? (4/9 - 6/9)= -2/9 ?(2 votes)
- Because the magnitude of the positive component is fewer than the negative.(2 votes)

- When you subtract 1 3/4 and 3 2/4, how do you subtract the whole numbers?(3 votes)
- You can't subtract 1 3/4 and 3 2/4, you have to do 3 2/4 first because its greater than 1 3/4, so in order to subtract you have to take 1 away from 3, in order to get 4/4 then add that to 2/4, and you can subtract, negative numbers are not stated in this video,(0 votes)

- why did you got 9-9 when it can be 1-1 right is it because the denominator is 9 is that how you got 9-9?(2 votes)
- Well, they are both equivalent because they both equal 1 so you could use either and you can also use 1.(1 vote)

## Video transcript

- [Voiceover] So we have
the expression 17 4/9 minus 12 and 2/3. And I encourage to pause the video and see if you can
figure out what this is. So now let's work through it. So what I'm going to do
is I'm going to rewrite these mixed numbers. So I'm going to write this as 17 and 4/9 minus 12 and 2/3. I'm going to write the
12 right under the 17, and I'm going to write the
2/3 right under the 4/9. Let me make it very clear,
we are subtracting 12 and 2/3 from 17 and 4/9. So the first thing that
we might want to do is we could look at the fraction parts and we might want to start
subtracting until we see, look, we have different denominators here. We have ninths and we have thirds. So the first thing we'd want to do is let's get to a common denominator, and a good common denominator
would be the least common multiple of nine and three. Well, what's that going to be? Well to think about that, I like to start with
a larger number, nine. And say, well, is that divisible by three? Well, yes, it is divisible by three. It is divisible by the other denominator, so this actually is the
least common multiple. If it wasn't, I would keep
taking higher and higher multiples of 9. I would go to 18 and
then I would go to 27, and I would keep going until I found one that's divisible by three. But I didn't have to do that because nine is divisible by three. So I can rewrite both
of these fraction parts in terms of ninths. Now the one on top already is
written in terms of ninths, so I can just rewrite that. 17 and 4/9. And the one on the
bottom, I can write as 12 and some number of ninths. So 2/3 is how many ninths? Well, to go from thirds to ninths I had to multiply by three,
had to multiply by three, so the numerator, I need to
multiply by three as well. Two times three is six. 2/3 is the same thing as 6/9. And now I can try to subtract. But even here, when I try to subtract, I have a larger fraction down here that I'm trying to subtract
from a smaller one. I have 4/9 minus 6/9. So what can I do? Well, be answer is I can regroup. I can take a whole from the 17. Let me do that. So if I take a whole from the 17, that's going to become 16, and then that whole that I just took from, I guess you could say
the whole number place, I can add it to the fraction. Well, a whole is just going to be 9/9. So all I did was I regrouped here. I took 9/9 from 17. 9/9 is one, so I took 9/9
from 17, I'm left with 16, and then I regrouped them and I added them to the fractions place, as
one way to think about it. Well, what's 4/9 plus 9/9? Well, that's going to be 13/9. So this right over here is 13/9. 13/9. It's a very strange way to
write it, but 17 and 4/9 is the same thing as 16
and 13/9, because notice, this is greater than one. This is the same thing as one and 4/9. One and 4/9 plus 16 is
going to be 17 and 4/9. Now why did I do all of this? Well 13/9 is larger than
6/9, so I can subtract. What's 13/9 minus 6/9 going to be? Well, 13 of something,
in this case, ninths, minus six of that same
something is going to be 7/9. Seven, let me write
that in a neutral color. So that's going to be 7/9. 13/9 minus 6/9 is 7/9. And then I can look over
in the whole number place. All I have left a 16 here. 16 minus 12 is four, and I'm done. 17 and 4/9 minus 12 and 2/3 is equal to four and 7/9.