Main content

## 7th grade

### Course: 7th grade > Unit 5

Lesson 5: Multiply & divide negative fractions# Dividing mixed numbers

Sal shows us how to change mixed numbers into improper fractions, divide, and then change the answer back to a mixed number. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- What is the reciprocal?(82 votes)
- A reciprocal of a fraction is when you flip the numerator and denominator. Such as the reciprocal of 6/10 is 10/6.(6 votes)

- How do I do an equation like: 5/-8 ÷ 1 3/7, with a negative denominator? Please answer this ASAP, I really need help with this.(4 votes)
- You can always do the signs apart from the numbers. In multiplying and dividing, you count number of negative signs. With 0, 2, 4, 6, ... answer is positive, if 1, 3, 5, 7, ... answer is negative. In your example, you only have 1 negative, so answer is negative then do (5/8)/(1 3/7).(5 votes)

- how would you do this if the mixed number was negative(6 votes)
- Can you show me how to do this problem? 4 1/2 divided by 3? I don't get it.(3 votes)
- 4 1/2 divided by 3 = 9/2 times 1/3 = 3/2 or 1 1/2(1 vote)

- can you please do another vid on how to divide 4 with 1 7/4?(5 votes)
- wait, why is two fourths the same as eight fourths?(2 votes)
- 2/4 is not the same as 8/4 but 4/2 is the same as 8/4(6 votes)

- but how do I divide negative numbers?(3 votes)
- Note: These rules for dividing also apply for multiplication

A negative divided by a negative is a positive

A negative divided by a positive is a negative

A positive divided by a positive is a positive(4 votes)

- A seven and half(7 1/2) tub has only one fifth(1/5) of water.

how many gallons of water is in the tub?

Can anybody solve this problem step by step?(4 votes) - Why do we have to find the reciprocal when dividing fractions or mixed numbers??(4 votes)
- The heck is that black magic at the start(3 votes)

## Video transcript

Divide. Simplify the answer and write
as a mixed number. And we have 2 and 1/4 divided
by 1 and 3/4. So the first thing we want to
do since both of these are mixed numbers is to
convert them both into improper fractions. So let's start with 2 and 1/4. So we're still going to have
4 in the denominator, but instead of 2 and 1/4,
remember, 2 is the same thing as 8/4. So we have 8/4, and then
we have another 1/4. That gives us 9/4. Or another way to come up with
this 9, you take 4 times 2, which is 8, plus 1. That gives you 9. And then the 1 and 3/4,
same process. You're going to have 4 in the
denominator, and then the numerator is going to be 4 times
1, which is 4, plus 3, which is 7. So this is the exact
same problem here. 2 and 1/4 divided by 1 and 3/4
is the same thing as 9/4 divided by 7/4. And we saw in several videos
already that dividing by a fraction is the same thing as
multiplying by its reciprocal. So this is equivalent to-- so
these are all equivalent. This is equivalent to 9/4 times
the reciprocal of this. We're changing the division
operation to a multiplication, and we're taking the reciprocal
of the 7/4. For the reciprocal of 7/4, you
swap the numerator and denominator, or the top
number and the bottom number, and you get 4/7. Now, we could just
multiply these. We could just say this is 9
times 4, which would be 36, over 4 times 7, which is 28,
and then try to put it in lowest terms, or we could do it
right now because it would be simpler. We have a 4 in the numerator. We have a 4 in the denominator,
that'll eventually be in the
denominator, so let's divide our eventual numerators
and our eventual denominators both by 4. So you divide this 4
by 4, you get 1. This 4 by 4, you get 1. So now when you multiply it, you
get 9 times 1, which is 9, over 1 times 7, which is 7. So we have our answer,
but right now, it's an improper fraction. They want us to write it
as a mixed number. And to figure it out as a mixed
number, we can do it in our heads now. I think we've seen this
enough times. We say how many times
does 7 go into 9? Well, it goes into it exactly
one time, but when you take 7 into 9 one time, what do
you have left over? Well, you're going to have
2 left over, right? 7 times 1 is 7, and you're going
to have 2 left over. You need 2 more to get to 9. So you're going to have 2 left
over, so this is 1 and 2/7. And we're done!