00:00Now, let's move on to our second topic: what is proportion?
00:03A proportion is defined as the equality of two or more ratios.
00:27Friends, we said that two or more ratios are equal.
00:29Well, for example, I could show this symbolically.
00:31A divided by B equals C divided by D, which equals K, folks.
00:36What is this K?
00:38K is the constant of proportionality, folks.
00:45These ratios, my friends, must be equal to a constant of proportionality.
00:50They are all equal, the constant of proportionality.
00:53In other words, its coefficient, or proportionality coefficient.
01:00Friends, A divided by B equals C divided by D, which also equals K, so this is a binary proportion.
01:11What are B and C here, friends?
01:18They are the inner parts of proportion.
01:22The inner aspects of proportion.
01:26And B and C are friends too.
01:29A and D are the outsides of the proportionality equation.
01:40After learning this, friends, A divided by B equals C divided by D, which also equals E divided by F, for example.
01:49If this is equal to K, then friends, that's your constant of proportionality.
01:53What is this?
01:53It is a three-pronged proportion.
01:54We can create more of these.
02:00Let's give an example right away.
02:11Friends, if 15 divided by 5 equals, then 9 divided by 3 also equals, and minus 12 divided by minus 4 also equals...
02:22And if that equals K, then what is our K? Let's check.
02:28So, what is 15 divided by 5, guys?
02:303.
02:30What is 9 divided by 3?
02:323.
02:32What is minus 12 divided by minus 4?
02:34That equals 3.
02:36So, our K here is the constant of proportionality, and it is equal to 3.
02:40This is what we call a three-pronged proportion.
02:43There's one more thing I'd like to mention, if you'll allow me.
02:50We said A divided by B equals C divided by D.
02:53We can also demonstrate this in the following way, friends.
02:55A divided by B equals C divided by D, which equals K.
03:06And let's show it in a three-part format, friends.
03:10A divided by C, look, these are what we're getting, folks.
03:14A divided by C divided by E is equal to B divided by D divided by F.
03:25Our proportions can be shown.
03:32After dividing it, I'll try to take another sample, if you'll allow me.
03:37Let's improve our examples.
03:40Let's say minus 3, divided by 4, divided by 8.
03:45I'm dividing it symbolically.
03:47Actually, this indicates a proportion.
03:50Minus 6, divided by 8, divided by 16.
03:54In this situation
03:58Let's ask for our constant of proportionality.
04:00Let's say the constant of proportionality is...
04:04Now, how were we going to write this, guys?
04:07Minus 3 divided by minus 6, right guys?
04:09Where did we write this?
04:10As we wrote here.
04:12Minus 3 divided by minus 6.
04:15It's equal to 4 divided by 8.
04:18It's also equal to that.
04:20It's equal to 8 divided by 16.
04:22And that's equal to that.
04:23It was K.
04:24Look, what is minus 3 divided by minus 6, guys?
04:261 divided by 2.
04:27What is 4 divided by 8, guys?
04:29Isn't 1 equal to 2?
04:31Yes.
04:31What is 8 divided by 16, guys?
04:331 is equal to 2.
04:34They are equivalent.
04:35Then our K is equal.
04:37We say it's 1 divided by 2.
04:39That's our constant of proportionality.
04:40Let's give another example.
04:46Let A divided by B be 3 divided by 5.
04:51I feel it, guys.
04:524 times A, minus 2 times B, divided by 3 times A, plus B.
05:04I say let's find the ratio.
05:06So, what is A divided by B, guys?
05:09It's 3 divided by 5.
05:10If you write each side as K times K times, the proportionality constant will be different.
05:14I expanded this with K.
05:16If my result is 3/5, then it's actually a multiple of 3/5.
05:20Yes.
05:20Then our A.
05:223K.
05:24And our B.
05:26Wouldn't 5K be okay?
05:27Yes.
05:27Multiples of 3.
05:28This would be a multiple of 5.
05:29Let's immediately substitute 4, a, minus 2, divided by 3, plus B.
05:334 times A, minus 2 times B, divided by 3 times A, plus B.
05:39This is equal to...
05:404 x 3K.
05:41So, 3 times K.
05:43Minus 2 times 5K.
05:44So, 5 times K.
05:46Section.
05:473 times 3K.
05:51Plus 5K.
05:54When we write it, friends, it's 4 times 12K.
05:59Minus 10K.
06:01Right, guys?
06:012 times 5 is 10.
06:023 times 9, plus 5, equals 14K.
06:073 times 9, yes folks.
06:13So right here we say 2K divided by 14K.
06:16It's also equal to that.
06:17The K's will be simplified, folks.
06:192 simplifies to 14.
06:20We find it to be 1/7.
06:22Our rate.
06:23Thank you for watching.
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