REGRA DE TRÊS SIMPLES - GRANDEZAS DIRETA E INVERSAMENTE PROPORCIONAIS - Matemática básica — Transcript

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1. 0:00In this class, you will learn very important content. But why did I speak
2. 0:05so happily? Very important, why are you going to learn? Simple rule of 3 that
3. 0:11is used like this, too much in our daily lives, if you don't use it yet,
4. 0:16let you become an adult and you will see how much it will be used. Let's go?
5. 0:21When I said very important, then you should look at this example that I'm going to read now,
6. 0:36and then you think, wow, it really is used. I don't use it yet, but I've seen someone
7. 0:42in my family using it or I will one day use it too. So an example says the following.
8. 0:48A mother used the leaflet to check the dosage of a medicine she needed to give her son. In it,
9. 0:56the following dosage was recommended. 5 drops for every 2 kg of body weight every
10. 1:058 hours. If the mother correctly administered 30 drops of the medicine to her child every 8 hours,
11. 1:13then the body mass is? So, guys, how am I going to carry out the strategy,
12. 1:22how am I going to develop the strategy to resolve this issue? So see that I already brought it here
13. 1:27separately for you. What are the quantities involved in this exercise? And another thing that
14. 1:34is very important when reading the statement and this is a 2012 Enem question. So, when reading the statement,
15. 1:42what should you do? You must already be highlighting, right? Highlighting the
16. 1:48important information that will help in developing a strategy. So, as you can see, the
17. 1:53quantities involved in this exercise are body mass and number of drops, the dosage of the
18. 2:02medicine that is administered. The first thing I advise students to do when carrying out a
19. 2:07rule of 3 exercise is to identify the relationship between these quantities. If these
20. 2:16quantities are directly proportional or if they are inversely proportional, and how do I do
21. 2:24that? I do it using arrows, right? The arrows, oh, so let's think about it like this, the greater the
22. 2:32person's body mass, what happens to the amount of medication they have to take?
23. 2:38Number of drops will increase. O. So see that I like working with arrows today,
24. 2:46Gis, but if I say it like this, the smaller the body mass, what happens to the number
25. 2:52of drops? The number of drops a person will take is smaller. So you were able to see
26. 2:57that in my speech either the 2 arrows went up because my question, the more mass,
27. 3:02the more drops of medicine or the less mass, the fewer drops of medicine, regardless of the way I
28. 3:08asked, they are both in the same direction. And therefore, when they are in the same direction,
29. 3:15I have quantities that are directly proportional quantities, which I say GDP, okay,
30. 3:23for short, directly proportional quantities. Then, after I have identified whether these quantities
31. 3:30are directly or inversely proportional, then I go there and put the number, but say, why do
32. 3:36you put the number, only then should you ask why it is better for us to analyze
33. 3:41what the quantities are? ? Because from the moment I put the number here, the student may
34. 3:46start to get confused. Wow, but that's the number. Then it turned into this. So that's why I
35. 3:50don't put the number. Firstly, I identify how these quantities are related. Now let's get
36. 3:55to the numbers, so, body mass, guys, what is body mass? body mass is how much
37. 4:01does a person weigh? But we don't say the weight, right people? It's body mass, who hasn't been to the
38. 4:07pharmacy and stood on the scales to weigh, weighing is to see the body mass we have, let's talk
39. 4:13straight, okay? So, the recommendation written on the leaflet was that you should administer 5 drops of a
40. 4:20certain medication for every 2 kg of body weight, right? Imagine if you don't read the leaflet
41. 4:28and then take the wrong dosage of the medicine? It's not possible, right, guys? You have to pay close attention. So, what
42. 4:34do I want to discover there? The statement says that if the mother then correctly administered 30 drops, where
43. 4:41do I put 30 here, or here? Here, right, guys? So, she administered correctly, 30 drops.
44. 4:48How many kilograms does the child weigh then? That's not what you're asking,
45. 4:52Ah, but Gis, there's a time every 8 hours, but the time won't change, right people,
46. 4:58because it's an indication of how often you can take the medicine, so leave it he
47. 5:02for there. And now what do I do? I've already included the magnitudes. I have already identified the relationship between
48. 5:09the quantities, I have put the respective values ​​ready and now we will see when we have
49. 5:15the quantities they are. Directly proportional, I do cross multiplication. Multiplication
50. 5:22in x, so you won't have to solve all the rule exercises and multiply the cross,
51. 5:27which isn't, okay? In this case I will do it, because it is directly proportional, so
52. 5:33I multiply 2 by 30, 2 by 30, is equal to 60, right? And then I divide it by what's left, because then
53. 5:43I would multiply the 5 by the unknown value, but then I like to explain it directly. So I always
54. 5:48multiply the 2 values ​​here and then I divide by what's left. So that means I
55. 5:54divide by 5, 60 ÷ 5, I can take 6 which gives 1, 1 × 5, 5, one remains, then I reduce the zero to 10, then I
56. 6:05do 2, 2 × 5= 10, zero remainder , let's cut the last one here, right? So what does it mean? This
57. 6:12means that this child whose mother gave 30 drops had 12 kg of body mass.
58. 6:21Gis is what I learned, my teacher said, look, I should multiply then, 2 by
59. 6:2730, look how you must have learned, so I'm going to write it here in the corner, look, pay close attention,
60. 6:32look, it's like this , 2 to 5 there, here is 30 and then generally you must have learned with x here, right
61. 6:41? So, how do you do it? Multiply x times 5 which gives 5 x equal to 2 × 30 which is 60, and then do
62. 6:51X= 60 divided because here you are multiplying then divide by 5, which will end up in 12. But I
63. 7:00prefer to do it first without the Put the question mark, which is the unknown value
64. 7:06and without putting together a little equation I like to do it straight, I always multiply the values ​​that exist
65. 7:12here diagonally, as the students say, ok and divide by what is left, it will always work out
66. 7:18like this right when they are directly proportional quantities, it will always multiply diagonally,
67. 7:24so that's good and another way wow, how many ways you could do it too, look here,
68. 7:31look. From 5 to 30. What happened here from 5 to 30? It wasn't multiplied by 6. So,
69. 7:40as the magnitudes are directly proportional here I could do it quickly, look, I multiplied it
70. 7:46by 6, 2 × 6 which gave 12. That's how quick people can do it. When they are directly
71. 7:51proportional, it's a breeze. But what if it were, conversely, you would multiply on one side and
72. 7:57do the inverse operation on the other and divide, it would also work like this, without calculating all
73. 8:02this, okay? So, mark the techniques that we did to solve this little rule,
74. 8:09when it is directly proportional and now let's move on to another exercise, shall we? The director
75. 8:15of a school hired a team of 6 people for 40 days to fix the roof of the
76. 8:22school where she works. However, worried about possible delays, she decided to hire 2 more
77. 8:31people, considering that all professionals have the same efficiency. So, what was the deadline
78. 8:39for completing this work? So see, in this question, what are the great things that I have already written here to
79. 8:46make your life easier. The magnitudes in this situation, then, are quantity of people and time,
80. 8:53right? To work, then time like I'm going to start doing this exercise the way
81. 8:59I told you, which is very easy. We are going to identify what the relationship is between the quantities,
82. 9:04so let's think, if I increase the number of people there carrying out the work, in this case by changing
83. 9:12the school's roof, what happens over time? time decreases, remembering that the statement
84. 9:19said that people have the same efficiency, right? That will maintain this efficiency. So,
85. 9:23the more people working, the less time they will spend. So, the greater the number of
86. 9:31people, the shorter the time. Just like if you asked like this, because sometimes students
87. 9:36get confused. I ask, starting with bigger or smaller, it doesn't matter, now let's ask the question,
88. 9:42how many fewer people work there on my site? What will happen longer
89. 9:49will take longer, will take longer, so it will be bigger. So you saw the less people,
90. 9:54oops, the more time on the opposite side of me, the less people, the more time or more people, the less
91. 10:01time. How did you manage to notice that the arrows are in opposite directions?
92. 10:07another and, for this reason, we are working with inversely proportional quantities. The jeep
93. 10:15and then we remember the jeep and that car, right? And that little
94. 10:19jeep, it goes straight, right? Nothing, right? Let's think like this,
95. 10:23so it goes straight, so in this case I won't do the cross multiplication like in the
96. 10:29previous example. And yes, I'm going to do a straight multiplication remembering the Jeep,
97. 10:34okay? And then we go to our next step, which is to put the numbers here in their respective
98. 10:40magnitudes, what is the number of people so we had 6 people who were working
99. 10:48and they would carry out this work for 40 days. Remembering that time is given in days here,
100. 10:54okay? So, what happened? The director was worried and decided to hire
101. 11:002 more people. So I'm not going to come here and put the number 2, because it's not just 2,
102. 11:06she added 2. So we have a total of 8 people, 8 people will carry out this
103. 11:13work in how many days? And now we can analyze, Ah, if the number of people increased,
104. 11:20the number of days will decrease, right? So let's think about the answer and then, as I told you,
105. 11:26when quantities are inversely proportional, we will multiply straight. Who do I multiply
106. 11:32with who now, the 2 straight numbers here, oh 6 times 40, remember in the other example, I didn't multiply
107. 11:39diagonally because that was cross multiplication. Here it is straight, so it will be 6 × 40. I do 6 × 4 =
108. 11:4824 so 24 and then add the zero, so it becomes 6 × 40 = 240 and then I divide this result by the
109. 11:58number left here, which in this case will be 8, okay? So always like this, multiply the rectum and divide
110. 12:05by what is left. If there were 8 here, I would divide it by the number that was here, that depends, no
111. 12:10problem, where is it? You will always divide and 240 ÷ 8. I take 24, which is 3, 3 × 8= 24
112. 12:20then there is 0 and 0 below this zero here goes zero in the key. So it means that these 8 people
113. 12:31will do it, they will complete this work in 30 days oh, okay, do it like this, I think it's the
114. 12:39quickest way possible, Gis, but I want to do the one that does it with the X the same you did in the other
115. 12:45example, so let's go, we'll take 6 times 40 which will be equal to 240 equals 8 times the
116. 12:57X that you would put here, right? And 8 times X is going to be 8 x now, what am I going to do? This 8
117. 13:05is not multiplying, so it will be divided on the other side, so it will be 240 ÷ 8, which
118. 13:14will be the value of x, which we already discovered that this value is 30. There is also another way that
119. 13:20you should have learned, because I learned this way, which is to do what? Which is to keep the first here
120. 13:26and invert the second, and then cross-multiply, but as I'm here to make your life easier
121. 13:34and not harder, right? It's not that difficult, guys, but let's do it a quicker way, right? And
122. 13:39doing this way here, which I think is the simplest of all, not even this way with x, and then
123. 13:44the student sees x and will start thinking about it, Gis, I don't know, do it directly, people, put a question there and it's the
124. 13:50same X thing and do it straight and that's it. Look how fast it is, and then you're asking because
125. 13:56production was the first thing that asked when I started doing the exercise.
126. 13:59Is it possible to do it like the little arrow from here to here, what did I do from 6 to 8 from
127. 14:076 to 8? If we analyze it, it was multiplied by 4/3, so it ends up being more difficult in this
128. 14:16case to do because you saw that other one there? It was a whole number, wasn't it? So it was quick,
129. 14:20here it was 4/3 and how I identified that it was 4/3 because I did 8 ÷ 6 oh, 8 ÷ 6 if
130. 14:30we simplify it gives 4/3. So I know it was 4/3, so now, if I multiply, oops,
131. 14:39multiply not here I multiplied, right? By 4/3. And then, as we are working,
132. 14:46with inversely proportional quantities here, I don't multiply by 4/3, but rather, I divide by 4/3,
133. 14:53so it will be 40 ÷ 4/3, then I apply the Ping pong method, it will be 40 times 3 which is 120,
134. 15:06and here in the case where there is no one, I put 1, 1 × 4= 4 and 120 ÷ 4 gives us 30. So you can
135. 15:17see how many possibilities I am giving you to solve in the exercise, but I still say this
136. 15:23one, which I did first of all, is the simplest possible, real people. After
137. 15:28I learned how to do it, I never did it again, but then it's up to you, okay? I'm
138. 15:34Showing here a way for you to rock. In your activities and if you enjoyed today's class.
139. 15:39Ah, give Gis a thumbs up in today's class, it's a really nice thumbs up. And subscribe to the channel,
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142. 15:55your activities and exams, because I will help you, people do it, recommending the videos. And
143. 16:01speaking of recommending videos, see that here I only did 2 examples, there are more classes on the channel
144. 16:07about the simple rule of 3. There are also classes, in case you are confused about magnitudes, about ratio
145. 16:15and proportion, and also about the compound rule of 3, because here it is simple, but we also have about
146. 16:22compound and how you will find these classes so you can ask more questions,
147. 16:26Go to the description of this video below. And there are all these classes, I will leave all the links
148. 16:33clearly so you can go there and watch all these classes, so don't forget to share
149. 16:39this class here, look. Summary class, let's put it that way, but I said so much, didn't I? But it was a
150. 16:44summary, okay guys, so time to say goodbye, enough talking Gis, goodbye and see you next class...