Hi guys, have you already learned that the simple rule of three is used to solve problem situations involving two quantities and in this class you will learn how to solve the rule of three compotes which involve more than two quantities , so you have doubts and want to learn more about this content? Come with me. .
. So welcome to my channel, I'm Gis and in this class you will learn how to solve the compound rule of three, do you know why it's called the compound rule of three, it gets its name folks because it involves more than two magnitudes in the simple rule of three class, you saw that it is called the simple rule of three because it only has two magnitudes, ok, so before starting the class, I'm going to make that request for you, subscribe to the Gis channel, if you don't Subscribe and leave me a thumbs up, ok? So what guidance do I give to the student when he starts to solve a problem situation, first identify in the statement what the quantities are, oh Gis, but how am I going to be able to know when solving it that everything is mixed up in a test for example in an activity like I will identify if it is a simple rule of three or will be composed of the number of quantities involved, if there are two quantities simple rule of three if there are more than two compound rules of three then let's see if what is announced he brought.
Working for 5 days, two seamstresses produce 60 towels, well, just reading up to the point, right, I can already identify which quantities are involved and if you didn't attend the class on magnitude that I explained about units of measurement, I also invite you to go back there to attend this class, so the magnitudes here let's highlight I have 5 days, 2 seamstresses and 60 towels so here is the 5 days it is indicating that the magnitude time so let's write here I have then the magnitude time which is given in day until what day is the unit of measurement I have the quantity of seamstresses o quantity of seamstresses ok because I counted, right? quantities involved, which is why the compound rule of three, now we need to identify in which quantity our unknown, our unknown term will be, because unlike the simple rule of three, I only compared the two quantities and I was able to identify if they were directly or inversely proportional here in the rule of three compounds before making this comparison I need to identify where the known term is because based on this magnitude I will make the comparisons, I always make the comparison two by two so I'll start here differently there of the rule of three here I will start by placing the values to identify where the known term is. So I have here 5 days, 2 seamstresses produce 60 towels, ok and how many towels I could have also thought about, right, that would be our unknown here in the towels quantity of towels so it is the unknown term that I need to find out I will put a question mark so the quantity of towels in question, 3 seamstresses working at the same pace as the others produced so in 2 days, well guys, so now what do you have to know ?
if they are directly or inversely proportional quantities and then I will have to compare the quantity of towels with the quantity of seamstress, right to also identify if they are directly or inversely proportional quantities so look here how many more towels I am not looking at the values, ok To ask the question, I'm just thinking about the quantities, the more towels I want to produce, what will happen over time, the more time I'm going to spend, so the more towels I'm going to produce, the more time I'm going to spend, so notice that the little arrows are in the same sense, okay, so it means that comparing the quantity of towels with time, these two quantities are directly proportional quantities, okay, I'm going to write here the quantity of towels and time and they are gdp, directly proportional quantities, okay, and now what do I need? compare now I need to compare the number of towels with the number of seamstresses , okay, if I increase the number of towels they will only remain in the same direction as the arrow, what will happen with the number of seamstresses, will I need more seamstresses, right? You could ask, the more seamstresses I have, the more towels I can produce, the more seamstresses, the more towels, so notice that the two boxes are also in the same direction, so the number of seamstresses increases the quantity of towels too, so the towels and the seamstresses are also quantities directly, not the towels, the seamstresses, the quantity of towels and the quantity of seamstresses are quantities directly proportional, beauty, I identified how am I going to resolve this situation now, people?
Let's see how you do it now, so you will always start with the quantity, which is the unknown term, so it will be set up like this, oh 60. Do you remember from the ratio class that what is ratio is when I have a comparison between two quantities, then the quantity of seamstress I'm going to write here a ratio 60 is for the known term, then 60 is for the unknown term as well as now here on this second side I'm going to have to write the multiplication of the other two ratios like so what is the ratio here of the time to time ratio is 5 to 2, 5 to 2 then I'm going to multiply by the ratio formed here in magnitude the number of seamstresses which will be 2 to 3, you see I put it in the same order as it was 5 to 2, 2 to 3 so here I wrote the reasons corresponding to the quantities I have here, so mark this one and now we're going to need a little space to solve this one, shall we? Look guys, so to remember this ratio here 60 for the unknown term means the ratio between the quantity of towels, 5 to 2 is the ratio relating to time, the magnitude of time and 2 to 3 is the ratio relating to the quantity of seamstresses, so remember- If first I must make a comparison between the quantities, always the one that has an unknown value with the other and then with the third, right, I always do two by two and then I identify if they are directly proportional quantities, ok, then the next step is to write In the account, I will always put the unknown value here first, right, the first ratio and then the other one, the others that are left, the other two, regardless of how much there is, I will multiply between them, then do the multiplication, so here it became a multiplication of fractions how to multiply fractions I must multiply numerator with numerator denominator with denominator so here it will be 60 is for the unknown term which is who I'm looking for and on this side I will multiply 5 x 2 and 2 x 3 here then it will be 10 and it will be 6 which 2 x 3= 6 now I apply the fundamental property of proportions which is just cross multiplying, right so here I will multiply 60 times 6, 60 x 6 are 360 and what I do now I divide for what was left, just like when I did it in the rule of three when it was directly proportional, I multiplied it crosswise and divided it by what was left by the third value, so now I divide by 10, 360 divided by 10 will give 36, already doing the short process here, right?
I mean the question was how many towels will be produced would you put as an answer, then 36 towels will be produced ok? Let's do one more example, shall we? Guys, look at the second situation that I brought for us to solve using the rule of three, compound by compound or by simple, how will I identify it?
Do you remember, we have to see the number of quantities involved, so I'll read it until the first point in a house that is not Gis's house, my house is very small, 6 painters paint an area of 300 square meters in 2 hours look there I arrived at the first point I can now identify what the magnitudes are you already know which ones So tell me what they are, let's go then I have the quantity and then it's the quantity of painters, it's a quantity very well, you said that to me, the second quantity involved is the area and the other quantity involved is the time, time is magnitude, time is magnitude, time is a unit of measurement, right, and the other is time, very well, and now let's put the values just to represent so that we can identify in what magnitude the unknown term is found here, so I have 6 painters, they paint an area of 300 square meters in 2 hours, right, how many painters, look here, where is ours, our term of It is then known how many painters working at the same pace as others will be needed to paint 400 square meters in one hour. And now, now we need to compare the quantities, always two by two, remember what I said, so first I'm going to identify the one that has our unknown, it's the number of painters, I'm going to compare the number of painters with the area, then I'm going to identify If it's GDP or if it's GIP, then I'll compare the number of painters over time, okay, so let's compare if I increase the number of painters there to paint my house, right, it's not my house, right, my house is small, the house from the neighbor, what will happen to the area ? needing more painters to meet that deadline isn't it, so the two arrows are in the same direction here, so the magnitude and the number of painters with the area are directly proportional, okay, so, this magnitude with this one I'll do here, they are gdp ok now so keep the arrow here in the same direction if I increase the number of painters there to do the painting what will happen over time the time will decrease ?
that's not it, so this magnitude here goes down, this goes down, so it means that the number of painters over time are inversely proportional magnitudes, but now what does this have to do with it ? reasons referring to each one, so remember that before the equal sign here is the reason referring to the magnitude that has the unknown term which is the number of painters so it will be 6 for the unknown term, ok you want x here in place of a question mark, feel free, no problem, I like to use a question mark because it's a custom, okay, just as others put x, it's also the custom, so even if I put it here guys, I put a multiplication between the remaining quantities, but Now that's the secret, I always have to do two by two when I compared the area with the number of painters, right, the number of painters here, in this case our protagonist, because that's where the unknown value is, what happened to these two quantities? look at the arrow, the arrows are in the same direction, so the magnitude 300, the ratio 300 to 400 will remain the same as it is so it will be 300 is to 400 so here is the ratio referring to what, the area magnitude and now we magnitude time compared to magnitude quantity of painters is inversely proportional so when I make the ratio here I do the ratio inverted, 1 will be on top and 2 will be below because this magnitude is inversely proportional to this magnitude by This is what I inverted if the area was also an inversely proportional quantity, I would also invert the 300 with 400 in the right place, so I created a little calculation scheme here that I should now do the ratio 6 to?
is equal to 6 is for, 6 for ? So, what do I do here? Now I multiply, right?
I have a multiplication of fractions, so to go faster I can cut 00 here with 00 here, that's it, so 3 to 4 x 1/2, multiply the two, multiply the two, you should have multiplied. right, but let's do it, I like to do it in detail so that everyone understands, so it will give 3 x 1 are 3, 4 x 2 are 8 and finally I apply the fundamental property of proportions there, which is to multiply crossed, so 6 of 18 always multiplies crossed and I divided by the remaining term 6 x 8 is 48 then I divide by the remaining term divide by 3, 48 / 3 will give one times 3, 3 left over 1 below 8 which will give 6, 6 times 3 are 18 so the question was how many painters at the same pace as those others would be necessary to paint an area of 400 notice that I increased the area but I decreased the time and then what happened to the number of painters the number of painters increased because the more painters the time decreases as I decrease the time I I would need more painters to do the job in the area, which has also increased, so my answer here would be, and then in your notebook you can write the complete answer here, ok guys? Well, I hope you have understood this content of the compound rule of three, okay, it involves all the subjects that we have already studied, from ratio proportion to magnitudes to the simple rule of three itself, right, so you can identify which one it is, so I hope you have I understand, you liked my explanation, oh and don't forget to subscribe to Gis' channel if you're not subscribed and leave me a thumbs up.
Until next time. . .
