Kung Fu Fractions


>>Professor Perez: Hey! This is Professor Perez from Saddleback College. Today, we’re going to do
something called Kung-Fu fractions. Actually, it’s called clearing
the fractions, but, some of the students call it
Kung-Fu, so, I guess we’ll use that. Anyway, let’s see what Charlie’s
up to, he says he loves to Kung-Fu. He better be ready to go! Hey, quit fooling around over there, sit down! All right, anyway, let’s get started here. Let’s get started with some Kung-Fu-ing now. Now, before you start Kung-Fu-ing,
you have to know what you’re doing, so we’re going to explain what
it is first, and then we’re going to do some Kung-Fu, or clearing fractions. All right, Charlie, pay attention, right there! 4 times 3 fourths. Let me walk you through this first one, Charlie. Notice, we’re going to take the 4, and write
it as a fraction, 4 over 1, times 3 fourths. And notice, the 4’s will reduce, right? They both become 1’s because they’re
divisible by 4, and notice, on top, when we multiply straight across the
top and straight across the bottom, we end up with 3 over 1, which is what, Charlie?>>Charlie: 3.>>Professor Perez: 3. So, really, 4 times 3 fourths ends up being
a whole number, there’s no more fraction. And so it was cleared, or Kung-Fu’d. Now watch this, Charlie. 8 times 3 fourths. Now notice here, we have 8 over 1 times 3 over
4, and Charlie, we can reduce the 8 and the 4. How does that reduce?>>Charlie: 2 over 1.>>Professor Perez: 2 over 1. And notice, the denominator is going
to be 1, and numerator will be 6, just like that, and so our answer is 6. Again, we have a whole number,
the fractions cleared out. We’ll do one more here with 12. 12 times 3 fourths, we write it
as 12 over 1 times 3 fourths. The 12 over 4 reduces by 3 over 1, and
now, on the top, we end up with a 9, and on the bottom a 1, and
again, a nice whole number. So notice here, with all these fractions,
those denominators divide evenly into those whole numbers being
multiplied to the fraction. And when that happens, that’s
when you can Kung-Fu. Okay, go ahead Charlie!>>Charlie: Hi-yah!>>Professor Perez: All right,
calm down over there! Okay, so, let’s kind of review
what we just did here. 4 times 3 fourths. Notice, the 4’s cancel out, 4 goes
into 4 1 time, and 1 times 3 is 3. There’s our answer there. That was the first one. In the second one, 8 times 3 fourths, you can
just simply think, 4 goes into 8 2 times, right? That’s how it reduces and
then 2 times 3 is that 6. Now we’re starting to clear fractions a lot
more efficiently, this is called Kung-Fu. All right, 12 times 3 fourths, Charlie. 4 goes into 12 how many times?>>Charlie: 3 times.>>Professor Perez: 3, and 3 times 9 is?>>Charlie: What?>>Professor Perez: 9…That’s right. 3 times 3 is 9, okay. All right, so, now, like I said, before
you start Kung-Fu-ing, you need to know and understand what your doing, so,
Charlie, can we Kung-Fu this one?>>Charlie: Yes, Hwah!!!>>Professor Perez: No, Charlie,
you just got beat up! See, you have to know what you are doing. You have to know when and
when you cannot use Kung-Fu. Because otherwise, I’m going
to Kung-Fu your grade! All right, Charlie. No, you can’t Kung-Fu this one, so,
we’ll write it 5 over 1 times 3 fourths, because the 4 doesn’t reduce with that 5, right? And so you just multiply straight
across the top and straight across the bottom, and notice, we get 15 over 4. The fraction did not go away. All right, how about this one, Charlie?>>Charlie: Yes! Hi-Yah!>>Professor Perez: No, you
cannot Kung-Fu this one, Charlie. 9 does not go into 3. It will reduce, but not the way you’re thinking. Watch. Let’s write 3 as a
fraction, 3 over 1 times 2 over 9. And notice, the 3 and the 9
will reduce, but notice Charlie, you do not have a 1 on the bottom this time. So on the top, you have 1 times 2 which
is 2, and on the bottom, 1 times 3 is 3. It did not reduce, right…it did
not come out to be a whole number. So be very careful. All right, Charlie, let’s see
if you get this one right.>>Charlie: Yes!>>Professor Perez: All right, that’s better.>>Charlie: Uh-huh.>>Professor Perez: Because the 3 will
divide evenly into that 15, right? Okay, so the 15 over 3 reduces to 5 over 1. We have a 1 in the denominator, so we
can disregard it, and 5 times 1 is what?>>Charlie: 20.>>Professor Perez: 20. Very nice there, Charlie. All right, let’s try this one. 8 times 7 halves. Yes, because 8 over 2 reduces to 4 over 1. 4 times 7 is 28, over 1, which is 28. Very nice. Let’s do 12 times 5 fourths. Yes or no, Charlie?>>Charlie: Yes!>>Professor Perez: All right. Now, the 12 over 4 reduces to?>>Charlie: 3 over 1.>>Professor Perez: 3 over 1. 3 times 5 is?>>Charlie: 15.>>Professor Perez: 15 over 1 which is just 15. Very nice. Now, 12 times 7 thirds, Charlie?>>Charlie: 3 goes into 12, 4 times. 4 times 7…28.>>Professor Perez: Very nice there Charlie. That is true. Now, I know you’re all thinking, well, it
doesn’t always work out where you have a number in front that’s going to be
divisible by that denominator. Well, that’s true, so, let’s look at an
application of Kung-Fu fractions here. Now, 2 thirds plus 3 fourths, Charlie. We can’t add them together because
they do not have the same denominator. Well, what is the LCD here?>>Charlie: 12.>>Professor Perez: 12. That’s right. Now, we’re going to apply some Kung-Fu to this. Watch. Now, remember, Charlie, 1 times
anything doesn’t change anything, right? It’s still itself. So, we’re going to take that 1 and
we’re going to rewrite it as 12 over 12, which is our LCD, right? Our LCD is 12, so we’re using the
LCD to rewrite the 1 as 12 over 12. And now, what we’re going to do, Charlie,
is we’re going to take that numerator which is a 12, and we’re going to distribute
into the parenthesis just like this, right? And now, don’t forget, outside,
we still have the 1 twelfth. All right. Now, here we go. We can start Kung-Fu-ing, Charlie. What’s 12 times 2 thirds, Charlie?>>Charlie: 8.>>Professor Perez: That’ll be 8, that’s right. Just like that. Now, how about 12 times 3
fourths, Charlie, what do you get?>>Charlie: 9.>>Professor Perez: That’s 9, that’s
right, because the 12 and the 4 reduce to 3 over 1, and you’re left with a 9 on top. And now, notice, all you have to do, is add
the 8 plus 9, which is 17, and don’t forget, since you’ve got the 1 twelfth outside, 17 is 17 over 1 times 1 twelfth,
is 17 over 12, and that’s it. Kung-Fu! All right, here we go Charlie, so…Let’s do another one,
let’s step it up a bit. Don’t get scared! We’re just going to use that LCD, watch. All right, Charlie, what is the LCD here? Now, think about this one.>>Charlie: 18.>>Professor Perez: Very nice there,
Charlie, that was a tough one. Now, again, remember, if we multiply
anything by 1, it doesn’t change it. So we’re going to rewrite that 1 in the front of
the parenthesis as an 18 over 18 and we’re going to distribute that numerator
18 into the parenthesis. Just like that. And don’t forget, outside, we
still have the 1 eighteenth. And now, here we go, we can Kung-Fu. Okay, Charlie. 18 times 8 over 9. 9 goes into 18 how many times, Charlie?>>Charlie: 2.>>Professor Perez: 2. That’s right. And 2 times 8 is 16. Let’s go to the next one. 3 goes into 18 how many times?>>Charlie: 6.>>Professor Perez: And 6 times 2?>>Charlie: 12.>>Professor Perez: Very nice. We go to the next one. 2 goes into 18 how many times, Charlie?>>Charlie: 9.>>Professor Perez: That’s right. And 9 times 1 is 9. And the last one, 6 goes into 18…>>Charlie: 3 times.>>Professor Perez: And 3
times 5 is 15, there you go. So now we just have arithmetic. Now, in the parenthesis, Charlie, you just
have to do 16 plus 12 subtract 9 subtract 15. All right, Charlie, start working on it. This is a tough one. Oh, he’s working hard. Let’s not distract him. All right, Charlie, time’s up. What did you get?>>Charlie: 4.>>Professor Perez: 4, very nice! And don’t forget, we have the eighteenth,
1 over 18 outside, so bring that in. Our answer is 4 over 18 which
does reduce to what, Charlie?>>Charlie: 2 ninths.>>Professor Perez: 2 over 9. Very nice there, Charlie! That was some good Kung-Fu here! Now, as you practice, you’ll get
better and more efficient at it. So, let’s just take a look really quickly
how a black belt would do this, watch. The same problem, 2 thirds plus 3 fourths. Pay attention, Charlie. They see that the LCD is 12,
and this is what they do. 3 goes into 12 4 times, 4 times 2 is 8. And then, 4 goes into 12
3 times, 3 times 3 is 9. And so it’s 8 plus 9 over
12, which is 17 over 12. There you go. Very efficient here! Looks like you’re cheating, huh? Well anyway, let’s do one more. Bring it home. 8 ninths, LCD is 18, here we go. 9 goes into 18 2, 2 times 8 is 16. 3 goes into 18, 6. 6 times 2 is 12. 2 goes into 18, 9. 9 times 1 is 9. 6 goes into 18, 3 times, 3 times 5 is 15. There we go. All over 18. And do your arithmetic, it’s 4
over 18 which reduces to 2 ninths. Kung-Fu. Anyway, we’ll see you all again soon!>>Charlie: Hi-yah!

7 thoughts on “Kung Fu Fractions

  1. Do you have a video on Chains Of Operations in fractions (e.g. -2/3 + 5/2 x -2 3/5 -[-1 2/5 + 2 1/10 / 5 5/6]=? I also need a lot of please Q: A painter needs 35 1/3 liters of paint to cover 12 1/6 walls. If each liter of paint costs $5 1/2, how much will it cost him to paint 10 walls?

  2. @themomo6710 These problems are a little above the level I am currently working on but I'll eventulaay get there. My main main faculty website has some materials that you may find useful.

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