Welcome to the presentation

on multiplying fractions. Well, I think today you’ll be

very happy because you’ll find out that this is one of the few

times where multiplying something is easier than adding

it, I think, or subtracting it for that matter. And if you don’t believe me,

let’s do some problems. Let’s start with 1/2 times 1/2. So when you multiply fractions

it’s very straightforward. It’s essentially just two

separate multiplication problems. You multiply the numerators,

so you get 1 times 1. And you multiply the

denominators, 2 times 2. 1 times 1 is 1. 2 times 2 is 4. So 1/2 times 1/2

is equal to 1/4. That makes sense. That’s like saying 1/2 of 1/2

is 1/4, which makes sense. What if we had

negative numbers? Well, if I had 1/2 times

negative 1/2 — and when you have a negative fraction it’s

good ascribe the negative number. I tend to ascribe the negative

number to the numerator — negative 1 over 2. You realize that negative

1/2 is the same thing as negative 1 over 2. Hopefully that make sense. So 1/2 times negative 1/2,

that’s just the same thing as 1 times negative 1 over 2 times

2, which equals negative 1 over 4, which is the same

thing as negative 1/4. What if I had different

denominators, and when you’re adding and subtracting

fractions that tends to make things difficult. Well, it’s not necessarily

the case here. If I had 2/3 times 1/2, just

multiply the numerators, 2 times 1, and you multiply

that denominators 3 times 2. So you get 2 times 1

is 2, 3 times 2 is 6. And 2 over 6 we know from

equivalent fractions is the same thing as 1/3. That was an

interesting problem. Let’s do it again and I want to

show you a little trick here. So, 2 over 3 times 1/2 — as

we said, any multiplication problem you just multiply the

numerators, multiply the denominators and you

have your answer. But sometimes there’s a little

trick here where you can divide the numerators and the

denominators by a number, because you know that this is

going to be the same thing as 2 times 1 over 3 times 2. Which is the same thing — I’m

just switching the order on top — as 1 times 2 over 3 times 2. All I did is I switched the

order on top, because you can multiply in either direction. And that’s the same thing

as 1/3 times 2 over 2. Well that’s just is 1/3 times

1, which is equal to 1/3. And why did I do that? Well I want to show you that

these 2s, these 2s, all I did is switch the order, but at

all times we had 1, 2 in the numerator raider and I had

1, 2 in the denominator. If I wanted to, and this is

kind of a trick for doing multiplication really fast so

you don’t have to reduce the final fraction too much,

you get 2/3 times 1/3 — 2/3 times 1/2, sorry. You say I have a 2 in the

numerator, 2 in the denominator, let me divide them

both by 2, that equals 1/3. Just a fast trick. I hope I didn’t confuse you. Let’s do a couple of more

problems, and I’ll do it both with the trick

and without the trick. What if I had 3/7

times 2 over 5. Well, multiply the

numerators, 3 times 2 is 6. 7 times 5 is 35. That’s it. Let’s do some negative numbers. If I had negative 3 over 4

times 2 over 11, well, that’s negative 6 over 44, which

is the same thing as negative 3 over 22. And we could have done that

cross-dividing trick here. Let’s do it again

with the cross–. Times 2 over 11. We say oh, well 2 and 4,

they’re both divisible by 2, so let’s divide them both by 2. So 2 becomes 1, 4 becomes

2, and then our answer becomes minus 3 over 22. Negative 3 times

1 is minus is 3. 2 times 11 is 22. Do another one right here. If I had negative 2/5 times

minus 2/5, well, that just is equal to negative 2 times

negative 2 is positive 4. It’s 5 times 5 is 25. 4 over 25. And that’s, just remember, a

negative times a negative is a positive, which makes sense. Let’s just do a couple

more problems since we have a lot of time. But I think you probably

got this by now. You’re probably realizing that

multiplying fractions is a lot easier than adding or

subtracting them, hopefully. I guess it’s not a bad thing if

you find adding or subtracting fractions easy as well. Let’s do — I’m just

making up numbers now — 2/9 times 18 over 2. Well here we could, well, we

have a 2 in the numerator and a 2 in the denominator. Let’s divide them both by

2, so they both become 1. And we have an 18 in

the numerator and a 9 in the denominator. Well they both are divisible

by 9, so let’s divide them both by 9. So 9 becomes a 1, and

the 18 becomes a 2. So you have 1 times 2 over 1

times 1, well, that just equals 2 over 1 which equals 2. That was pretty

straightforward. We could have done it, I guess

you could call it the hard way, if we said 2 times 2

over 9 times 18 over 2. 2 times 18 is 36. 9 times 2 is 18. And 36 divided by 18, and we

can see 18 goes into 36 two times, that also equals 2. Either way is fine. If you don’t feel comfortable

doing this trick right now, you don’t have to. All that does is you won’t end

up with huge numbers in your product that you’ll have to

figure out if they can be reduced further. Let’s do two more problems. Minus 5 over 7 times 1 over 3. Minus 5 times 1 is minus 5. 7 over 3 is 21. That’s it. Let me do one with the

little trick I showed you. Say I had 15, and here I think

you’ll see why that trick is useful, over 21

times 14 over 5. Well clearly, if we multiply

this out we end up with pretty big numbers. I think 220 one 105 and

you have to reduce those. It becomes a big mess. But we can see that 15 and

5 are both divisible by 5. So let’s divide them both by 5. So 15 divided by 5 is 3. 5 divided by 5 is 1. 14 and 21, they’re

both divisible by 7. 14 divided by 7 is 2. 21 divided by 7 is 3. So we got 3 times 2 is 6 over 3

times 1 is 3, which equals 2. That’s the same thing

as what I said before. If we had multiplied 15

times 14 that would have been 210 I think. Yeah, 15 times 14 is 210. And 21 times 5 would have been

105, and you would have to say, I guess in this case it’s kind

of obvious, that 210 is 2 times 105 and you would have

gotten 2 as well. So hopefully I didn’t

confuse you too much with that last problem. But I hope you realize

multiplication’s pretty straightforward. You just multiply the

numerators, you multiply the denominators, and then if you

have to reduce you reduce, but you’re pretty much done. I think you’re ready now to try

the multiplication module, and I hope you have fun.

what do you look like khan? i learn so much from you

16 people can't multiply

thannkkkk yooou.

Fractions are so hard, I did not know how to do them for 7 years. Until I saw this video. My teachers are idiots who can not teach! Thumbs up if you agree.xD

awesome

I LOVE you! You saved me!

Thank you.You helped me very much.

Yes he is

Me too

K i watched dis vid 4 STAAR test which istomorrow n lets c wat i get!!!

God I hate fractions, bu thanks this helped me!

I don't get it? how does 2/9 x 18/2 = 2?

you confused me….

helps so much ๐

helps

thumbs up if you watch it right now ๐

Most teachers are just there to collect pension lol. In my experience its worse in the catholic school systems…or at least the ones I've been in. Switched to public and had no idea what they where doing.

I hate math but i always use vids like this to help with homework thanks kahnacademy keep up the good work

How many times does 3 go into 6?

2 X

I saw on a quiz: 35 1/4 x 18. How do I work that out

WOW THANKS MAN the way teacher gave us the technique was so long

thanks sir!you're the best!

this dude is awesome. can he teach me how to do science??? i stink at science!!!

my teacher showed me this video

you are the best thank you for teaching me this

My teacher did not teach me the negitave

thx

years of school still doesn't compare to this 8 minute video

Thank you so much sal. I'm in 8th grade, and I completely flunked all my classes. But thanks to your videos, I'm a straight A+ student, and my goal is to get my college degree in physics, join the air force and become a pilot.

In mathematics there are two questions to each method 1. How is it done? 2. why is the method right? You say multiplication is easier than addition. I don't agree with that. In my opinion It is harder to answer the second question in case of multiplying fractions than adding fractions and if one is not able to to answer the second question, they have no idea why the method is right and it makes no sense for them to use the method at all, it is much simpler and faster to use a calculator.

I just want to thank you what you are doing is really good for the school

This guy is the Bob Ross of mathematics

Good luck with your dream:) I'm rootin for ya.

@3:10 I'm in 10th grade and I didn't even know that, thank you.

thank s

Same here. Godspeed.

Likewise! Sounds like we need a revolution in the educational system. We must have kids leaving elementary school as mini einsteins

I'm starting college and I forgot about that so don't feel bad, watching these really brings you back up to speed

Hi Sal, question, how come negative * negative is a positive? Thank you.

How do you know so much math?

Whole *

Thx. Im gonna pass my math test tomorrow!!!!!!!!!

Thank you so much you saved my honor roll

Thanks for teaching me how to do fractions

I think it would be smart if u put institutions to write

this was awesome!!!!!!!!!! I copyed ย everything in my notebook. I hope I get it right inmy state test!!!!!!

u r the best

this was made in 07

you can make me understand math in 10 min while my teacher can't even do it it in 1 week

Finals are coming so i gotta study

how do you know when to stop going when you get the last fraction?

great video

Khan for president

This is really gonna help me for the M.A.P. tests this year. I really wanna get a good score so I can get into advanced math. This will certainly help!

This is a good way to show it

do you think im ready for my test? here are some questions:

10 x 83 + 8 – 24 = 814

are you going to do it with whole numbers?

This is a real good tutorial, your practically the best at math

I wish multiplying fractions was as easy as adding and subtracting them. Fuck math

to all the peaple that say its good "NERD!!" ย ย

yea i know i spelled that bad

still you nerds!

thanks for helping me i got 100 percent!!!!

thanks im on this is class in math switch. its a good use for me .

omg argh frustrating!!!! I HATE MATH

'/:o

Curse teachers love khan ! ……..Is khan a teacher ?! Then sorry teachers ๐

WHY MRS. JESTER WHY!!!!!!!!

multiplying is supposed to be easy. its not

(ใฅ๏ฝกโโฟโฟโ๏ฝก)ใฅ best learning video

I like how u broke it up for my son

struggling ๐ข

anything times neg 1 would be equal to neg 1?

boring

I got a 100 on my test;) ๐

what website is he using?(to draw)

I didn't really understand the way my math teacher was teaching me how to do this but this video really helped and made things very easy thank you!

4×1/4=

v good job

old vid

Finally,,,,,someone shows how to get the math, by doing the math…..All instructors should follow this guys

Thank you so much, my teacher couldn't explain it too well

thumbs up!

good way to help

Tricks r 4 kids.

sal , one thing i have noticed in your videos is that as awesome and helpful your lessons are , you sometime tend to complicate things more then they need to be and it makes student more confused .

WOW SOOOO OLD XD

THE YEAR I WAS BORN AND BEFORE APRIL WHEN I WAS BORN XD

.o. …..Omg

I bet this stuff is fall asleep easy for this man. Probably like teaching a baby it's first word.

I used to hate fraction but now they're kinda simple thanks

1 problem made me understand COMPLETELY….. and my mom says school is good for me…….

When do you know to devide the answer and leave it the way it is like the -5/21 compared to the 210/205 turning into 2? Is it whenever you can devide it or a specific rule?

Cool ._.

How is 2ร3= 3 lol

#khanforprez

UUUUUMMMMM

why

I love math

I think that this is a very good tutorial and everyone in the world should watch it and listen, learn, and use it to get better grades ๐๐๐ท๐ค๐ฅ๐ง

๐๐๐๐๐๐๐