What is a Ratio? Video Lecture | Mathematics (Maths) Class 6

0:0:3: To understand ratios,
0:0:4: you just need to understand the simple story!
0:0:8: Gaurav and Jay used to receive chocolates
0:0:10: from a mysterious magic hand every day.
0:0:14: But the magic hand was a little biased towards Jay.
0:0:17: Every time it gave two chocolates to Gaurav,
0:0:20: it gave three to Jay.
0:0:22: Two to Gaurav and three to Jay.
0:0:25: Nobody knew why!
0:0:27: Of course Jay did not complain.
0:0:30: So the ratio of the number of chocolates Gaurav
0:0:32: got to the number of chocolates Jay got
0:0:34: is written as 2 colon 3.
0:0:37: Or 2 divided by 3.
0:0:40: This can be read as 2 is to 3.
0:0:43: We are basically comparing the number of chocolates.
0:0:46: Gaurav got to the number of chocolates Jay got.
0:0:50: This went on for quite a few days.
0:0:52: So every time the magic hand gave two chocolates to Gaurav
0:0:56: it gave 3 chocolates to Jay.
0:0:59: Now let's count the total number of chocolates each of them have.
0:1:4: Gaurav has 4 and Jay has 6.
0:1:7: The ratio now becomes 4 by 6.
0:1:11: The magic hand again gives Gaurav of 2 chocolates,
0:1:14: and Jay 3 chocolates.
0:1:16: Now the total number of chocolates with Gaurav is 6
0:1:20: and the total number of chocolates with Jay is 9.
0:1:23: So the ratio becomes 6 by 9.
0:1:26: Both these ratios when simplified will give us 2 by 3.
0:1:31: In every case the ratio has remained the same.
0:1:35: What does this mean?
0:1:37: If we multiply 2 with 2 and 3 also with 2
0:1:41: we get 4 by 6.
0:1:43: If we multiply 2 with 3 and 3 with 3, we will get 6 by 9.
0:1:50: And similarly, if you multiply 2 with 4 and 3 with 4,
0:1:54: we will get 8 by 12 which is again equivalent to 2 by 3.
0:2:0: So all the three ratios are equal to 2 by 3.
0:2:4: What does all this mean?
0:2:6: It means that if the ratio of two quantities is 2 by 3,
0:2:10: then the quantities will be multiples of 2
0:2:13: and multiples of 3 respectively
0:2:16: and not necessarily just two and three.
0:2:20: A few students have this confusion
0:2:22: that the ratio of two by three
0:2:24: will mean Gaurav has just two chocolates,
0:2:27: and jay just three chocolates.
0:2:29: If the ratio is 2 by 3
0:2:32: then the quantities will be in the form of 2x and 3x,
0:2:36: where 2x and 3x are multiples of 2 and 3.
0:2:41: So ratio is basically a comparison of quantities.
0:2:45: But there is a bit more to comparison of quantities.
0:2:49: We see that next.