00:00Hello everyone. Now we are on the fourth part of our topic on proportions: the properties of proportions.
00:05Let's write, guys.
00:07A divided by B equals C divided by D. That also equals E divided by F. That also equals
00:14Let's say that when K is equal to the constant of proportionality, then it is in proportionality.
00:21Our first property. Because the ratio A to B is equal to K, friends.
00:27Our A equals B times K.
00:30And C divided by D equals. Since K is the constant of proportionality, our C equals D times K.
00:38Since our ratio E divided by F is equal to the constant of proportionality K, our E is equal to F times K.
00:48Let's move on to our second feature, folks.
00:51Our second property is that A divided by B equals C divided by D.
00:57We say "but" and "only." This means that it's mutually reinforcing and mutually reinforcing, folks.
01:02A plus minus B divided by B equals B. What does that mean, folks?
01:08C plus minus D divided by D equals.
01:12What does this mean?
01:13A divided by B equals C divided by D. Friends, it says "if and only if".
01:19A plus B divided by B equals C plus D divided by D.
01:24Or, A minus B divided by B equals C minus D divided by D.
01:29Sometimes they write it using an abbreviation.
01:32Both positive and negative forms.
01:34Our third characteristic is friends.
01:36M and P must be non-zero.
01:44A divided by B equals.
01:47C divided by D. That equals...
01:49If K is equal to our proportionality constant.
01:52What's going to happen, guys?
01:54What is N times A plus minus P times C divided by N times B plus, guys?
02:05Minus P times D.
02:07It's also equal.
02:08It is K.
02:09So what does this mean, guys?
02:12We used N as the numerator and denominator for our ratio A divided by B.
02:17N multiplied by plus or minus the numerators was generally C divided by D, friends.
02:22What happens when we multiply the numerator and denominator by P and the coefficient P?
02:28When we add 1 to the numerator and 1 to the denominator, our proportion still equals K.
02:33Our rate.
02:35Now let's move on to our fourth feature, folks.
02:39Let's consider a number N.
02:41R is the number.
02:42Let's say it's about to happen.
02:45A to the power of N divided by B to the power of N.
02:48That's also equal to that, friends.
02:49What is C to the power of N divided by...?
02:53D above N.
02:54It's also equal.
02:55E to the power of N divided by F to the power of N.
02:58It's also equal.
02:59It is K to the power of N.
03:00All of these will be useful in the questions, guys.
03:04And our fifth and final feature, friends.
03:07Here's a more abbreviated form.
03:09A divided by B equals C divided by D.
03:12That's equal to E divided by F.
03:14If that is equal to K.
03:17But that's all we can say, friends.
03:19Write the sum of these three in the numerator.
03:23When we write the denominator as B plus D plus F, we still say that it is equal to our proportionality constant K.
03:30Pin or string?
03:30Altyazı i völlig próximo,
03:30Thank you.
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