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What is a Ratio? Video Lecture | Mathematics (Maths) Class 6
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FAQs on What is a Ratio? Video Lecture - Mathematics (Maths) Class 6
| 1. What is a ratio? |  |
Ans. A ratio is a mathematical comparison between two quantities or numbers. It shows the relationship or proportion between the two quantities.
| 2. How is a ratio expressed? | |
Ans. A ratio is expressed in the form of a fraction or using a colon (:). For example, a ratio of 2:3 or 2/3 represents that the first quantity is 2 and the second quantity is 3.
| 3. Can a ratio be simplified? | |
Ans. Yes, a ratio can be simplified just like a fraction. If both the terms of the ratio have a common factor, it can be divided by that factor to simplify the ratio.
| 4. How can ratios be used in real-life situations? | |
Ans. Ratios are used in various real-life situations like cooking recipes, mixing ingredients, financial analysis, and comparing quantities. For example, a recipe may require a ratio of 2 cups of flour to 1 cup of sugar.
| 5. What is the difference between a ratio and a proportion? | |
Ans. A ratio compares two quantities, whereas a proportion compares two equal ratios. In a proportion, the cross-products of the ratios are equal. For example, if the ratio of boys to girls is 3:2, and the ratio of men to women is also 3:2, then it can be said that the two ratios are in proportion.
Text Transcript from Video
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.
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.
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Nov 16, 2024 Last updated |
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