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## 7th grade (Eureka Math/EngageNY)

### Unit 2: Lesson 2

Topic B: Multiplication and division of integers and rational numbers- Why a negative times a negative is a positive
- Why a negative times a negative makes sense
- Signs of expressions
- Multiplying positive & negative numbers
- Dividing positive and negative numbers
- Multiplying negative numbers
- Dividing negative numbers
- One-step equations with negatives (multiply & divide)
- Multiplying negative numbers review
- Dividing negative numbers review
- Rewriting decimals as fractions: 2.75
- Write decimals as fractions
- Rewriting decimals as fractions challenge
- Fraction to decimal: 11/25
- Worked example: Converting a fraction (7/8) to a decimal
- Fraction to decimal with rounding
- Converting fractions to decimals
- Multiplying positive and negative fractions
- Multiplying positive and negative fractions
- Dividing negative fractions
- Dividing positive and negative fractions
- Negative signs in fractions
- Negative signs in fractions
- Negative signs in fractions (with variables)
- Dividing mixed numbers
- Dividing mixed numbers with negatives
- Simplifying complex fractions
- Expressions with rational numbers
- Simplify complex fractions
- Equivalent expressions with negative numbers (multiplication and division)
- Equivalent expressions with negative numbers (multiplication and division)
- Why dividing by zero is undefined
- Dividing by zero

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# Simplifying complex fractions

Learn how to take complex looking fractions and make them much, much simpler.

## Want to join the conversation?

- Why can't you swap the reciprocal fractions when multiplying?

When you turn the division problem into a multiplication by transforming the fraction on the right into the reciprocal of the fraction on the left, why can't you switch them around and make the fraction on top or on the left the reciprocal of the fraction on the right?(6 votes)- It is kind of like saying 9 divided by 3, why cant we switch the numbers around and say 3 divided by 9. You can, but these two ways mean different things and you will get different answers. Hope this helps :)(7 votes)

- how do we simplify normal fractions tho(7 votes)
- It's defo a tricky thing to see until you get it like i just did lol but there's 2 ways you simplify fractions, first is the one where you Simplify by finding the Greatest Common Factor (GCF) for the top and bottom numbers of your answer then divide them both by it.

Then the other is where you Simplify an improper fraction into a mixed number by dividing the numerator (top number) by the denominator (bottom number), and you'll get a number with a remainder so you write the number as your whole number then write the remainder next to it, draw a line under it and write the original denominator of the fraction you just simplified under it.

Well you need to use the GCF one for just Proper Fractions and then the one changing it into a mixed fraction for any improper fractions.

Why? because from numbers 100 and above it becomes too hard and takes too long to keep writing all the common factors for it but just to give it a process to follow people just choose to use GFC for only proper fractions and change it into a mixed fraction only for improper fractions.

For bigger Proper Fractions say... 110/200 you just have to look at the numbers and ask yourself What number goes both into 110 and 200? well look at the last 2 numbers first so clearly... 10 will go into both 110 and 200 so divide both by 10 to simplify it to the smallest possible fraction :) eventually you'll then just become good at looking at the numbers than having to keep writing the common factors.(1 vote)

- from1:37to2:36, Sal explains how to simplify 2/2/3. However, I could reason differently. I could simplify the 2/2, resulting in 1, and end up with 1/3. Their are other ways to get 1/3 too. I could break all the fractions to get 2÷2÷3, which I think could be 3 or 1/3 depending on how I look at it. How do I know which way I should do?(6 votes)
- How do u put the time he said it in the video in your question/ comment?? I need help plz!(1 vote)

- So how would you do something like 1 / 1/2? Would it just be 1/2?(2 votes)
- if you mean (1/1)/2 then yes because 1/1 is 1 and that leaves 1/2.

If you meant 1/(1/2) then the answer is different:

with the last expression you are dividing 1 by 1/2, or in other words you are asking how many times does 1/2 fit into 1? Because we are dealing with very small numbers you can just count halves until you reach 1, in this case 2 halves go into 1 so your answer is 2. If you take a different approach that will work with any number you can use the rule that something divided by something else is the same as multiplying by its reciprocal. So 1/(1/2) = 1 x 2/1 = 2

hope it helped :)(4 votes)

- At4:15why did he flip 3/7?(2 votes)
- Because that's what you when a fraction is being divided. If you want to multiply it, then flip the denominator.(4 votes)

- I get how to simplify, but do you guys have anything that could help me solve the complex fractions. All I can find is simplifying complex fractions. I just want to solve them.(2 votes)
- Well you simplify like this...

for example 4/5 / 5/6 can be written as 4/5 divided by 5/6 so the answer is 24/25 and simplify fractions is the same as solving it.

Use this http://www.wikihow.com/Simplify-Complex-Fractions(2 votes)

- For 2x 3/2 why didn't he change 2 to 2/1?(1 vote)
- Because it's not needed. It's an easy problem, doable with mental math.(4 votes)

- This math is my greatest foe. It's really Hard.(3 votes)
- Ill give you an idea about how to do it, I dont think its that effective though. It'll take time to understand

Lets say...

27/54

1. Find which times table both numbers occur in: 9

2. What does 9 need to be multiplied with to get to 27/54: 3 and 6

3. The answer is 3/6.

Wait...

4. WE NEED TO SIMPIFY IT FURTHER. I dont know how to use the first part of the strategy on this part(I think the fraction is not applicable due to the numbers being tool small) but let me know if you do. When you think about 3/6 its obviously going to remind you of A HALF. AND A HALF IS WRITTEN AS 1/2

5. The answer to simplifying 27/54 IS 1/2. Finally we're done!

PS: This took me 24 minutes to type: I had to adjust the numbers and put in variables(1 vote)

- how do you do the simplify fraction work?(2 votes)
- i am very confused with this.(2 votes)

## Video transcript

- What I hope to do in this video is emphasize the relation, the connection, between fractions and division and then using that knowledge to help us simplify some
hairy looking fractions. So, let's say, let's just
do a little bit of a review. So, if I say two divided
by, two divided by three, two divided by three,
I could write this as, I could write this as two over three. Two divided by, two divided by three. So, this expression here,
sometimes we might say, "Hey, this is 2/3. Think
of it as a fraction." But you can also view this
as two divided by three. So, if we went the other way around. If someone were to write four over, actually, let me just do
it in a different color, if someone were to say four, 4/9, four, four over nine,
we could interpret this, this could be interpreted
as four divided by nine. Four divided by nine. In fact, if we wanted
to, if wanted to convert this into a decimal that's
exactly what we would do. We would calculate what
four divided by nine is. We would divide nine into four. Four divided by nine. So, this is all review. So, let's just use this knowledge and I'll think more complex fractions. So, if someone were to say, actually, let me just take
this example right over here, if someone were to say two over, instead of saying two over three. If they said two over, I don't know, let me say two over 2/3. Two over 2/3. Well, what
would this simplify to? Well, we could go the other way around. This is the same thing
as two divided by 2/3. So, let's write it like that. This is the same thing as two divided by, two divided by
2/3, two divided by 2/3, which is the same thing as, dividing by a fraction's the same thing as multiplying by its reciprocal. So, this is going to be the same thing as two times, two times
the reciprocal of 2/3, which is, we swap the
denominator and the numerator, two times three over two. So, two times three halves, if I have three halves twice, well, that's just going to be equal to, that's going to be equal to six halves, and six halves, you can view that as, well, two halves is a whole, so this is gonna be three wholes. Or you can say six divided by two. Well, that's just gonna be equal to three. You can view it either way. And then that is equal to three. Let's do a few more of these. And let's keep making them a
little bit more complicated. Just let me get some good practice. And like always, pause the video. You should get excited when
you see one of these things. And pause the video and see
if you can do it on your own. All right, let's do
something really interesting. Let's say negative 16 over nine over, over, I'll do this in a tan color, over, let's say, three over seven. What is this? Can you simplify
this complex fraction? Can you simplify this
expression over here? Well, once again, we can view this as negative 16/9 divided by 3/7. So, this could be rewritten as, and I can write it either
as negative 16 over 9 or I could rewrite it as negative 16/9. So, I can put the negative
in front of the whole, in front of the whole fraction like that, or I could say that it's
negative 16 over nine, or I can even write this as
negative 16 over negative nine. Those would all be equivalent. But right now I'm writing at negative 16/9 and I am going to now divide, we can interpret this complex fraction as dividing it by 3/7. Dividing by 3/7. And so, this is going to be equal to, this is going to be
equal to negative 16/9, negative 16 over nine. Actually, let me just rewrite
it as negative 16 over nine. Negative 16 over nine just
to show that we can do it. Times the reciprocal of this. So, times 7/3. I just swap the numerator
and the denominator. Times, do that same brown color, times, times 7/3, and now
what am I going to get? In the numerator, I have
negative 16 times seven. Let me think about it. 10 times seven is 70. Six times seven is 42. 70 plus 42 is 112. So, this, so this part right over here, this part right over here
would be negative 112. Negative 112 over nine times three. Nine times three is 20,
nine times three is 27. And there you have it. You can view this as negative 112 over 27 or you can put the negative up front and you can say, "Hey, this is hinting "as negative 112, 112/27." 112/27 and just to make
everything come full circle you can view this as
negative 112 divided by 27 or negative 112/27. Either way.