Commutative, Associative and Distributive Properties 1-1

Commutative, Associative and Distributive Properties 1-1

This video is going to be about the
commutative, associative and distributive properties. Basically these things are common sense,
and you probably know them already. Probably the only hard part is
remembering the names for them. So let’s start with the commutative
property. The commutative property says that if you
have 2 numbers… let’s say 5 and 10… you can add them in two different ways. You
can either say ‘5 plus 10′ or you can say ’10 plus 5’ Kinda makes sense. The same thing will work for variables. So if you have x plus y that would be the same as y plus x. So why is it called commutative? Well, when two things commute, when people commute, like if they commute to work they move, they change places, and what we’re doing is we’re taking
these numbers, the 5 and the 10, for instance, or the x and y and we’re changing their places. So this is the commutative property of
addition because we’re dealing with addition. We’ve also got a commutative property of
multiplication and all that says is if we have two numbers, let’s use 5 and 10 again we can say 5 times 10 or we can say 10 times 5 and and we’ll get the same results either way. And if we have variables we can say x times y or we can say one times x y times x. All that’s happening is the numbers or
the variables are moving, they’re changing places and so they’re
communicating, and this becomes the commutative property. Okay so we have the commutative property of
addition and the commutative property of
multiplication. Let’s go on to the associative property. So Let’s say we have three numbers, let’s say we have 2 and 3 and 4, and we want to add them. Well we could either add the 2 and the 3 together first and then the 4, or we could take the same three numbers, 2, 3 and 4, we can add the 2 to the sum of the 3 and the 4. and we’re going to get the same result either
way. When things associate, when you have an association of people, you have groups of people, so this is the associative property of addition. Once again it will also work for
variables. So I could have x plus y in parentheses plus z and that would be the same as x plus and then my parentheses y plus z. You realize, it’s pretty obvious these
things are equal. Okay, and that’s the associative property of
addition, associative because these things are forming associations, they’re forming little groups. We also have an associative property of multiplication, and all that says is that if I have 2, 3 and 4 and I want to multiply them, I could multiply 2 times 3 first and then multiply that result by 4 or 4 could take 2, 3 and 4 and multiply the 2 times the product of the 3 and 4. Once again these things will be exactly
the same, and once again we can do the same thing
with variables. So I can have x times y times z, and I can multiply the x and y first and then multiply the product times z, or I could have x and y and z, and multiply the x by the product of y and z. So this is the associative property of
multiplication. Once again i think this is common sense and you probably knew it
already. So the last property is called the distributive property of
multiplication over addition, which is a great name. Here’s all it means… let’s say I’ve got 2 and I want to multiply that by 3 plus 4. Well, what the distributive property
tells me is that I can distribute this multiplication, the 2 times something, to whatever is in the parentheses. So I’m going to distribute the ‘2 times’ to the 3 and distribute it to the 4. 2 times 3, let’s just write that as ‘2 times 3’ I’ll take my plus sign and then 2 times 4. Carrying out this multiplication I’m going to get 2 times 3 is 6, plus 2 times fo4r is 8 and that’s going to be equal to 14. The other way I could have done this, the way you might have been thinking, is I could take 2 times 3 plus 4, add the 3 and the 4 together, in other words, turn this into 2 times … 3 plus for is 7 … and 2 times 7 is 14. Either way I get
the same answer. So the distributive property of
multiplication over addition says that if I’m multiplying a number or variable times the sum of numbers or variables… that’s what’s in this parentheses here… what I can do is multiply that number
times each of the parts of that sum separately, and I can have more than two parts here, so in other words I could have something
like 3 times let’s say 4 uh… let’s put a minus sign in… minus let’s use a variable, 2x plus 5y and to distribute this multiplication what I’m gonna do is take the 3 times the 4, and that’s going to get me… 3 times 4 is 12, I take the 3 times the negative 2x, so I have negative 6x, 3 times the 5y so that will give me a positive 3 times 5 is 15. Okay, and the result I get from distributing this 3 over this 4 minus 2x plus 5y is going to be this 12 minus 6x plus 15y. And that’s it for that for those
properties. Take care, I’ll see you next time.

100 thoughts on “Commutative, Associative and Distributive Properties 1-1

  1. I wanted to know the following : what if it's 3/4* 5/6 + 10 – 9/8 + 1/6
    Well these r random number I put in …but the sum is the same kind of any of u know this put that in comment

  2. Thanks! Was stressing about a test in a few days time that included this and your video really cleared thing up and helped me understand.

  3. Like and Subscribe to this channel for similar videos guys..

  4. i hated my math teacher in seventh grade (last year) so i didn't pay attention and never learned these. the way you explained them though, made perfect sense and i immediately understood. you're very good at teaching. thank you!

  5. Why can I understand this video while I can't understand in my class??


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