Multiplying fractions (old)

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.

100 thoughts on “Multiplying fractions (old)

  1. 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

  2. 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.

  3. 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.

  4. 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.

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

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

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

  8. 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!

  9. 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!

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

  11. 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 .

  12. 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?

  13. 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 🍔🍟🎷🐤🥓🧀

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