In this video the concept of ratio and unit rates is explained in a novel, practical and easy way. The students will learn to solve problems based on the topic in various methods.
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00:00Today, I am going to discuss the topic unit rates.
00:06This video is presented by RBA Educational Academy for grade 7.
00:13The idea of this topic is a novel in this presentation.
00:21You might have seen many topics like this on YouTube, but this idea is a novel, so I
00:30request you to watch the video till end.
00:33With me from the beginning till end.
00:36So here I have taken one example to understand the concept of ratio.
00:41So I am at two types of fruits.
00:46They are oranges, four oranges and six apples.
00:51So what I am going to do, I am going to find the ratio of number of oranges to number of
00:57apples.
00:59So boys, number of oranges is 2.
01:09This represent here, the colon represent here is 2, it represent the ratio, number of apples.
01:25The symbol colon is read as is 2, it represent ratio.
01:30So four oranges, six apples.
01:33So for every four oranges, there are six apples.
01:37Here we are comparing.
01:38What is ratio?
01:39Ratio is nothing but comparison, comparison of two quantities.
01:44Here what are the quantities?
01:45Here we are taking oranges and apple.
01:47What number four and six, for every four oranges, there will be six apples.
01:51So this is the ratio, but we want in simplified form.
01:55So I divide this four by two, I divide six by two, when I divide four by two, I get two
02:02is two.
02:03When I divide six by two, I get three.
02:06So the ratio in simplified form is two is to three.
02:12Here this two is hcf or you can also say gcd, highest common factor or greatest common divisor,
02:20you can say both.
02:22Now factor is nothing but divisor only.
02:24So if I take the factors of four, one is the factor of four, one divide four, two is the
02:30factor of four, two divide four, four is the factor of four.
02:33Every number is divisible by itself.
02:35So four is also a factor of four.
02:37If I take six, one is a factor of six, one divide six, two is the factor of six, two
02:43divide six, three is the factor of six, three divide six and six also divide six.
02:50So I want the greatest number or highest number which divide both, that is two.
02:54So hcf of this two number is two.
02:58Therefore I divide the first term of the ratio by two, second term of the ratio by two, when
03:03I divide four by two, I get two, when I divide six by two, I get three.
03:08So the ratio I got is two is to three.
03:12Now this ratio I can represent, before going that, I will tell you, I will explain you.
03:21See here, if in this basket, suppose there are only two apples, two apples, I have two
03:28apples, two oranges, sorry, for two oranges and here I take apples, what is the meaning
03:36of two is to three?
03:38For every two oranges, I will write it clear.
03:51So for every two oranges, there are three apples.
03:59Suppose I want to add two more oranges here.
04:02So I have to add three more apples here.
04:04So two plus two will be four and three plus three will be six.
04:08That means when there will be four oranges, there will be six apples, when there will
04:13be two oranges, there will be three apples.
04:15So for every two oranges, there will be three apples, the ratio is two is to three.
04:19So here we are comparing, I'm comparing two quantities by the way of division.
04:24Okay.
04:25A ratio is comparison of two quantities by division.
04:29The word ratio is used to describe a fraction.
04:32You can say, you can describe a fraction, how we can represent it, I will show you.
04:38So I can represent this two is to three in many ways, boys.
04:48I can write it as two over three, or I can write it as two slash, I will write two for
04:58every two, there is a two is to three, or ratio can also be represented in decimal form.
05:05When I divide two by three, I get 0.6666, so on.
05:11So 0.67, I can write, okay.
05:17So if I want to change into percentage, multiply by 100, decimal to percent, I get 67%.
05:25You can represent as percentage also.
05:28So here what I am going, what I am doing here actually, I'm comparing.
05:33Now I will take another example.
05:36So boys, suppose I take three numbers like 15 is to 20 is to 25, I want to find the ratio
05:51of these numbers, okay.
05:56I divide suppose this first number by 5, second number also I will divide by 5, third number
06:01also I will divide by 5, 3 times 15, 5, 4 times 20, 5, 5 times 25.
06:08The ratio is 3 is to 4 is to 5.
06:11So here I'm taking more than two numbers, I'm taking three numbers here.
06:15So in ratio, we can take more than two numbers also.
06:19And one more thing, one important thing I want to say, in ratio, ratio is the comparison
06:26of two quantities by the way of division or you can say a ratio is a way of comparison
06:32of two or more similar quantities.
06:34Example, if I take 5, 15 I will take, 15 pence is to 3 pounds.
06:47So pound and pence, the units, see the units, okay.
06:55I want similar quantities.
06:56So what I will do, I will change pound to pence.
06:59So here 1 pound is equal to 100 pence.
07:06So first I will change pound to pence.
07:09So 15 pence here, 3 I will multiply by 100, 3 pounds to change pound to pence, I multiply
07:16by 100.
07:18So 15 is to 300.
07:21Now I will do two things here, 15 is to 300.
07:27If I find the SCF or if I don't want to find the SCF, suppose I divide by 5, 15 I divide
07:35by 5, I get 5, 3 times 15, here I will get 3, 5, 6 times 30 and this 0 I take here.
07:48So 5, 1 times 5, 5, 3 times 15, 5, 1 times 5, 5, 60 times is 300.
07:56Then I have to simplify further because I have not taken the SCF, highest common factor.
08:01Therefore I will divide this by 3, this also I divide by 3.
08:06Now when I divide 3 by 3, I get 1, 60 when I divide by 3, I get 20 here.
08:18If I want to find the SCF, the SCF of 15 and 300, what is the greatest number which can
08:29divide both, which can divide 15 and 300.
08:37So it is 15.
08:41So 15 divided by 15, it will be equal to 1 and when we divide 300 by 15, we get 20.
08:51So you see the answer is same, the ratio is 1 is to 20, here the ratio is 1 is to 20.
08:58Now Bose, we will discuss further.
09:17Here what you are seeing Bose, now here I am taking suppose a model boat.
09:44I am taking a model boat and this model boat, the length of the model boat, suppose it
09:53is 2 meter, I am taking the length of model boat as 1 meter.
10:05The length of model boat I am taking as 2 meter and the length of actual boat is 50
10:17meters.
10:19So what I am going to do, I am going to find the ratio, the model boat is 2 meter long
10:31whereas the actual boat is 50 meter long.
10:33So I am going to find the ratio of length of model boat to length of actual boat.
10:42So I divide, now ratio, what is the ratio, the ratio is the comparison of two quantities
10:50per division.
10:51So what I am going to do Bose, here the model boat which I have taken is 2 meters and the
11:08actual boat is 50 meters.
11:15So when I find the ratio, I divide this by 2 and this by 2.
11:22So I cancel here the units, meter and meter.
11:26Here I get 2 divided by 2 is 1 and 50, when I divide 50 by 2 I get 25.
11:34Here in this ratio there are no units.
11:37In ratio, a ratio is a way of comparing two or more similar quantities separated by colon.
11:44So here we are comparing two quantities separated by colon.
11:49So here we have comparison of two quantities by division is known as ratio and this is
11:55a mere number without any unit because since we are comparing similar units, similar quantities
12:02sorry we cancel the same unit meter and meter.
12:05Here in example I cancel the meter and meter.
12:08Now this is ratio and what is rate?
12:12Now see here, rate is a special type of ratio, this is also a ratio that compares two quantities
12:19with different kind of units.
12:24So rate is also a special type of ratio that compares two quantities with different kinds
12:29of unit.
12:30How?
12:31I will tell you how it is.
12:37So when we find each other pulse, we are actually finding the heart rate, okay.
12:44So heart rate we are finding boys, suppose the heart of a person beats 160 times, so
12:56160 beats in two minutes.
13:10When we find the pulse, we are nothing but we are finding the heart rate.
13:14So 160 times the heart beats in two minutes.
13:19So you see here, here beats and here minutes, these two units are different, different.
13:35So a rate is a special type, here what I have used the word a rate is a special type, special
13:44type of what?
13:45Ratio.
13:46So a rate is a special type of ratio, you can see here, that compares two quantities
13:50okay with different kind of units.
13:52So here 160 beats in time two minutes.
13:55So I want to simplify this.
13:57So what I do 160 beats, I divide by two and two minutes also I divide by two.
14:12So when I divide 160 by two, half of two that is 80 beats in one minute.
14:22So 80 beats in one minute, when the denominator in the in this ratio, okay, when the denominator
14:30is one unit in this rate, in this rate, why I am calling it as rate, it is also a ratio
14:36but a special type in the rate when the denominator is one, okay, one unit, okay, it is known
14:42as unit rate, we call it as unit rate, this rate, we call it as unit rate when the denominator
14:48is one.
14:49So here the denominator, okay, the divisor with which we are devising is an independent
14:55variable and these heart beats depend upon the time.
15:01So the numerator is a dependent variable.
15:04So in unit rate, the denominator will always be equal to one voice, okay, I hope you understand
15:15the concept.
15:16Rate means we are comparing here also it is as a special, it is a special type of ratio
15:21here also we are comparing the two quantities but with different units.
15:28So heart rate, we are seeing the heart rate, okay.
15:32Now voice here, so what we understand by the term ratio, the main thing, it is a comparison,
15:53it is a comparison of two or more than two, it is a comparison of two or more than two
16:06similar quantities, similar quantities.
16:15So here the word comparison and the word similar, this is very important voice, similar
16:31quantity, similar, two or more than two similar quantities, okay.
16:38So keep this in mind.
16:42So rate is also a ratio.
16:48Now here Ahmed bike 30 miles in five hours, I am doing another example to explain you.
16:56Ahmed, he bike 30 miles in five hours if he bike at constant speed, if the speed is constant,
17:04he is not changing the speed, there is no variation, he is neither going slow nor going
17:09fast in every five hours he is covering 30 miles.
17:13So 30 miles I will write here so that should be clear to you.
17:20Ahmed covered 30 miles, okay, it's good, 30 miles is covered in five hours, okay.
17:32If he bike at constant speed, how many miles did he ride in one hour?
17:38So 30 miles is covered in five hours, so in one hour how many miles will be covered?
17:46So what we do, we divide 30 miles by five hours.
17:54You see the units voice again, this is very important, okay, 30 miles, okay, units are
18:04miles and hours, okay, two different units, okay, I want to simplify this.
18:10So I divide 30 by five and five also I divide by five, why I want to divide five by five?
18:18Because when we divide a number by itself, we will get one, I want unit, okay, one hour,
18:24how much, one hour how much, unit rate, we are doing the problem of unit rate.
18:29So boys, when I divide 30 by five, I get six miles, six miles, six miles are covered, five
18:39divided by five is in one hour, in one hour, Ahmed covered six miles.
18:46This you can do in another way, okay, that is known as you can say ratio table, I will
18:56just explain to you.
18:59You can do this in another way also boys, you should know the different ways in which
19:06we can do a particular problem.
19:09So I am going to show you a different way in which we can solve this problem.
19:18So I will make a table, okay, so here table, I will write here miles, miles and I will
19:37write here hours, okay, so 30 miles is covered by Ahmed in how many hours, five hours, so
19:56six miles is covered in how many hours, okay, in one hour, we say in one hour, sorry, here
20:0630 miles is covered in five hours, so in one hour, in one hour, Ahmed covered how many
20:19miles, so what I do, I divide this five by five, I divide this 30 also by five, when
20:33I divide, okay, divide 30 by five, what I will get, wait a bit.
20:46So when I divide 30 by five, I will get the number six, okay, so in one, Ahmed covered
20:57six miles in one hour and five hours, Ahmed covered 30 miles or you can do like this also,
21:07you can write miles and hours, 30 miles is covered in five hours, in one hour, Ahmed
21:21covered how many miles, what I do, one hour, I want to get one here, how I can get one
21:28when I divide five by five, I get one, so I will divide 30 by five, what I will get here,
21:34I will get six, so in one hour, Ahmed will cover six miles, so this was the problem on unit rate,
21:46I hope you understand it. So John is painting, this is the another question,
21:59John is painting one side of his shed, he paints 36 square feet in 45 minutes,
22:08so boys, 36 square feet is painted in 45 minutes, at this rate, how many square feet he paint in
22:21each hour, now boys, see here, see the difference, here this is the beauty of maths, so here he has
22:28given the time in minutes and he want you in hours, usually the student get confused in this too,
22:36so boys, I will show you one thing, to convert hour to minute, you have to multiply by 60,
22:51because one hour is equal to 60 minutes, in one hour, we have 60 minutes, so whenever you want
22:56to cover, whenever you have to convert hour to minute, multiply by 60, okay, and when you want
23:03to convert minute to hour, divide by 60, so first we will convert this minute, because we want the
23:13answer in hour, so to convert the minute, 45 minutes into hours, what we have to do, see here,
23:22minutes can be converted to hour, when we divide by 60, so 45 divided by 60, once again, in one
23:33hour, we have 60 minutes, so when you want to convert hour to minute, multiply by 60, and when
23:39you want to convert minute to hour, do the reverse of multiplication, that is divide by 60, so I am
23:45going to convert this minute to hours, I divide by 60, so 45 divided by 60, so I can simplify this,
23:54you can take the SCF, highest common factor, you can divide both by 50, or suppose, I don't take
24:01the highest common factor, I divide just by 5, because some student, they will think, oh, 45 is
24:08divided by 5, it's easy, I will divide by 5, okay, do it, 5, 9 times 45, and when you divide 60 by 5,
24:15you get 12, okay, 5, 12 times 60, so again, you have to simplify it further, so which number can
24:22divide both 9 and 12, that is 3, so when you divide 9 by 3, you get 3, when you divide 12 by 3, you get
24:313 over 4, so we get 3 over 4, now keep this in mind, 3 over 4 hour, so John is painting one side of his
24:44shed, he painted 36 square feet in 45 minutes, that means in 3 by 4 hour, John painted 36 square feet,
24:55keep this in mind my boys, so 36 square feet, 36 square feet is painted, square feet is painted in
25:203 by 4 hours, okay, so in one hour, how many square feet he can paint, so what I will do,
25:36I will divide 36 divided by 3 over 4, so boys, see how I can write this, 36 divided by 3 over 4, so
25:5136, this division I will change into multiplication, I will take reciprocal of this, okay, when we want
25:59to change division into multiplication, take the reciprocal of this fraction is 4 over 3, so 3,
26:051 times 3, 3, 12 times 36, so I multiply the numerator now, 12 multiply with 4 is 48,
26:18so 48 square feet is painted in one hour, how many square feet, okay, 48 square feet, now boys,
26:2936 square feet is painted in 3 by 4 hour, in one hour, how many square feet is painted,
26:36we divide 36 by 3 by 4, so this division symbol, I change into multiplication,
26:42I took reverse of 3 over 4, that is reciprocal 4 over 3, when I divide 36 by 3, I get 12,
26:5012 multiply with 4 is 48, so I want to do this problem in another way, now see here,
27:01I will show you how we can do this problem in a lighter, in another way,
27:10now after getting this 3 by 4, I will make it simple for you,
27:14now see here, I will use the bar diagram, okay, boys, okay, I am going to use the bar diagram
27:26method, so 3 over 4 hours, these are hours, so I want to find out in one hour, see each hour,
27:37how many square feet in each hour, so this 3 by 4, I write as 1 over 4,
27:431 over 4, if you add 1 over 4, 1 over 4, it will be 2 over 4, if you add one more 1 over 4,
27:51it will be 3 over 4, if you add one more 1 over 4, it will be 4 over 4, it's like this boys,
27:57if one part, I divide into 4 parts, 1 part, 2 part, 3 part, 4 part, so out of 4, I am doing 1,
28:051 over 4, 1 part, again one more part I am adding, 1 plus 1, 2 over 4, okay, again in this add,
28:12I will add one more, so 3 over 4, this is 3 part, out of 4 part, I have taken 3 part,
28:18then again I will take 4 part, 4 over 4, 4 over 4 is nothing but 1, so this represent one hour,
28:26this whole part from here to here, this length is nothing but 1 hour,
28:35but I have the information about 3 over 4, so 3 over 4, how I can represent, this part is 3 by 4,
28:41when I add this 1 over 4, 1 over 4, 1 over 4, I will get 3 over 4, so this is in hours and I will
28:49take here feet also, in 3 by 4 hour, Ahimad is painting how many square feet, see the question,
28:5636 square feet, so I will divide 36 into 3 part, 36 if I divide by 3, 3 times 1, 3, 3 times 2,
29:066, it's 12, so in each part, I will 12 square feet, 12, this is square feet, 12 square feet,
29:1712 square feet, 12 plus 12, 24, 24 plus 12, 36, from here to here, 36 is correct, see here,
29:25in 3 by 4 hours, 36, so from here 1, 2, 3, 4, when I add this all numbers, I will get 1 hour,
29:34in 1 hour, how many, 12 plus 12 plus 12 plus 12, that is 36 plus 12, that is 48,
29:42oh, I get same thing, 48 square feet, by second method also, I got same, that is 48 square feet,
29:51so this is the way we solve. Thanks for watching the video, please like, share and subscribe.