TenMarks teaches you how to apply commutative property.
Read the full transcript »
In this track, we will learn about Commutative Properties of Numbers. We’re given two particular problems. The first one says, for us to fill in the blanks and we’re given two different sub-problems. Let’s do that first. The first problem says 2+3 should be equal to 3+ and we have to determine what’s the blank and determine the value. For this, we’re going to use the Commutative Law of Addition. Commutative Laws says that A+B=B+A, very simple. So, this is true that on the left hand side which is right here A+B means A equals 2 and B equals 3 so, this is true. Right hand side should be true as well which is B+A, B equals 3 and A equals 2, so 3+2. B+A means 3+2 is what should be on the right hand side and since 2 was a blank I can substitute it so, the answer is 2. Now, let’s add these numbers. Let’s double check 2+3=5, 3+2 also equals 5 so the final value addition is 5, so the right answer is 2 and 5. Let’s do the second part which says (3*4) equal four times a blank and what is the final value? I'm going to create a little bit of extra space and look at how do we do this. Well again, Commutative Law of Multiplication says that A*B=B*A, so this is true, A=3 and B=4. If that is indeed true then on the right inside B*A means 4*3 should be equal to 3*4. So 4*3=3*4, the missing value here is the value 3. Now, let’s compare the answers. 3*4 is 12, 4*3 is also 12, so we know this particular law works. So, the missing value is 3 in the first blank and in the second blank is 12. First blank is 3, second blank is 12. Similarly here, first blank is 2 and the second blank is 5. Now, the second question says, “Well, we like this Commutative Law, does it work for subtraction and division as well?” Well, let’s try it. Let’s create a little bit of extra space and let’s try and see if Commutative Law works for subtraction and for division. If we were to check for subtraction, what would it look like? Well, it should be A-B should be equal to B-A because A*B equals B*A, subtraction should say A-B equals B-A. Let’s put some random numbers in there, let’s say 3 and 2. So, 3-2 is 1. Let’s see on the right hand side B is 2, A is 3, 2-3 is -1. Left side and right side are not equal right. So, subtraction Commutative Law does not hold good, this is no. Let’s try on the division side. Let’s say division, for division to be true, A/B must be equal to B/A. Let’s substitute the values again. So, let’s say A=6 and B=2. So, 6/2=3 that is the left hand side. The right hand side says B=2/6. Well, 2/6 is 1/3. It’s actually 0 with a remainder of 3. So if that is the case, this two are not equal which means that the Commutative Law does not hold good for division either. Pretty easy, right? All I did was try and actually substitute the values and see what the answer was for the left hand side and for the right hand side. So, it seems like Commutative Law only works for addition and for multiplication. So, what we learned is commutative law for addition works, A+B=B+A and A*B is the same as B*A. Commutative Law works for addition and multiplication. When it comes to subtraction and division, it does not work.