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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: 7 6/9 - 3 2/5

We can subtract two mixed numbers, by converting them to improper fractions. First, multiply the whole number by the denominator and add the numerator to get the improper fraction. Find a common denominator and adjust the numerators accordingly. Subtract the two improper fractions, and simplify the result if possible. Finally, convert the improper fraction back to a mixed number if desired. Created by Sal Khan.

## Want to join the conversation?

- Why do we need to add and subtract fractions?(91 votes)
- Well, suppose your cooking, and you need, say, 2/3 of a cup of sugar. What if your only doing half of a recipe? You need to chop 2/3 in half. Or if your doing 2 times the recipe. You need to double 2/3. This is only one example, there are lots of others.(102 votes)

- If you have a whole number minus a fraction for example 3 - 2 2/3 how do you do this(18 votes)
- Think of the numbers as improper fractions. For ex: 9/3 - 8/3 = 1/3.

That way all you have to do is subtract the numerators.(14 votes)

- Why the minus sign for 3-2/5? I still don't get it.(15 votes)
- Do you know about negative numbers? If you, then please realize - 1 (or minus one) is also a -1 (negative one).(14 votes)

- this is hard I can't do some problems with this even though he explained it 😪😪😪😯😯😥😥 so can someone explain it much more simpilaier or easier to me?(10 votes)
- Okay, Error.

For example:

12 3/4 - 7 4/5 = ?

Here, find the LCM of both the denominators.

4 and 5's LCM is 20, so it should be 12 ?/20 - 7 ?/20.

Here, multiply both numerators by the number you multiplied the denominator to get to 20.

Since you multiplied 4 against 5, which is 20, multiply 3 against 5, the answer to which is 12 15/20.

Since you multiplied 5 against 4, which is 20, multiply 4 against 5, the answer to which is 7 16/20.

Now, subtract the numbers.

Here, you need to borrow 1 from 12.

Borrow it, and add 20/20 to 15. You now have 12 35/20. Subtract 7 16/20 from it.

12 35/20 - 7 16/20 = 5 19/20.

Voilá! You're done!

#QED

Hope this helps, Error.(19 votes)

- why is fractions so important?(6 votes)
- Fractions will become important when you get older. For example, if you are baking, you have to know what 1/2 is or 1/4.(10 votes)

- hello i nee lots of help i dont know how to add fractions if anyone noews the answer can someone pleaes3e tell me sporry my kat is walkijg over ny jkeayboard so i cant ytype very well its quite an issue yes. sorry for speaking bad francais i am not familiar with argentina.(5 votes)
- Well first do 1/2+1/2 the denominator stays the same so add the 1+1 that’s 2 so the answer for that is 2/2 also known as a whole aka 1

1/3+1/5 to find a common denominator multiply the denominator that’s 15 so for 1/3 u multiply 3x5 to be 15 so u do 1x5 for the numerator for 1/5 you do 5x3 to be 15 so do 1x3 for numerator to find that. Add them up and u got your answer.

I hoped this helped srry if it’s late and long!(6 votes)

- when do we usually use the add and subtract fraction in real life?

😕😕😕(6 votes)- In the previous lessons, you learned that a fraction is part of a whole. Fractions show how much you have of something, like 1/2 of a tank of gas or 1/3 of a cup of water. In real life, you might need to add or subtract fractions. For example, have you ever walked 1/2 of a mile to work and then walked another 1/2 mile back?(5 votes)

- What happens if the first number is negative and you are subtracting them? Do you have to do something different?(3 votes)
- Yes you do. Example: -1/2 - 3/4

Since the fractions have the same sign, we add (follow me here). 1/2 = 2/4, and what is 2/4 + 3/4? 5/4, or 1 1/4.

Now, since we started with two negatives, make your answer negative.

-1/2 - 3/4 = - 1 1/4(10 votes)

- why do we need to find the common number and then either add or subtract. Why not divied and multilpy(5 votes)
- To multiply or divide, you do not need to do that. To multiply two fractions multiply their numerators and denominators. I know that this sounds confusing but it is true. Dividing fractions is harder. It requires taking the reciprocal of the second fraction and then multiplying.(0 votes)

- Why do you first use plus and than minus?(3 votes)

## Video transcript

Let's try to evaluate 7
and 6/9 minus 3 and 2/5. So like always, I like to
separate out the whole number parts from the fractional parts. This is the same thing as 7
plus 6/9 minus 3 minus 2/5. And the reason why I'm
saying minus 3 minus 2/5 is this is the same thing
as minus 3 plus 2/5. And so you distribute
the negative sign. You're subtracting a 3, and
then you're subtracting the 2/5. And so now we can worry
about the whole number parts, 7 minus 3. Well, 7 minus 3 is
going to give us 4. So that's going to give us 4. And then we're going
to have 6/9 minus 2/5. So let me think about
what 6/9 minus 2/5 are. 6/9 minus 2/5, well,
we're going to have to find a common denominator. So this is going to
be the same thing. And I think the least
common multiple of 9 and 5 is going to be 45. Literally, you then multiply. They have no common factors. So it's going to be over 45. To go from 9 to 45, I
have to multiply by 5. So I'm going to have to
multiply the numerator by 5. So 6 times 5 is 30. Then I'm going to subtract. To go from 5 to 45, I
had to multiply by 9. So I have to multiply
the numerator by 9 if I don't want to
change the value. So 2 times 9 is 18. And 30/45 minus 18/45 is
going to be something over 45. 30 minus 18 is 12. If I subtract these two
fractions right over here, I get 12/45. So it's 4 plus 12/45. Or if we wanted to write
it as a mixed number, this is equal to 4 and 12/45. But we're not done yet. We can simplify this further. 12 and 45 have common factors. They're both divisible by 3. Actually, they're both
divisible by-- well, I think we can divide
more after that. So let's see. If we divide the numerator by
3 and the denominator by 3, we end up with 4. And 12 divided by 3 is 4. And 45 divided by 3 is 15. 4 and 4/15. And actually, we're done. These two can't be
simplified anymore. 4 and 4/15.