Properties of Addition
An interactive math lesson about the commutative, associative, distributive and multiplicative identity properties of addition. Elementary math curricula often include a discussion of number properties, specifically the properties of addition and subtraction. In other words: is there any structural definition of "addition" or "multiplication"?. If both meet group properties, what else tells one from the other.
Commutative Property The commutative property says that the positions of the numbers in a mathematical equation do not affect the ultimate solution. Five plus three is the same as three plus five.
This applies to addition, regardless of how many numbers you add together. The commutative property allows you to add a large group of numbers together in any order.
Properties of Addition and Subtraction | Sciencing
The commutative property does not apply to subtraction. Five minus three is not the same as three minus five. Associative Property The associative property applies to more complicated equations that use parentheses or brackets to separate groups of numbers.
The associative property says that numbers you are adding together can be grouped in any order. When you are adding numbers together, you can move the parentheses around. The associative property also does not apply to subtraction since 3 - 4 - 2 does not equal 3 - 4 - 2.
Addition and subtraction as inverse operations Video transcript Let's say that we have the number 5, and we're asked, what number do we add to the number 5 to get to 0? And you might already know this, but I'll just draw it out.
So let's say we have a number line right over here. And 0 is sitting right over there. And we are already sitting here at 5. So to go from 5 to 0, we have to go five spaces to the left.
Inverse property of addition
And if we're going five spaces to the left, that means that we are adding negative 5. So if we add negative 5 right here, then that is going to get us back to 0. That is going to get us back right over here to 0. And you probably already knew this.
Inverse property of addition (video) | Khan Academy
And this is a pretty maybe common sense thing right here. But there's a fancy word for it called the additive inverse property. And all the additive-- I'll just write it down. I think it's kind of ridiculous that it's given such a fancy word for such a simple idea-- additive inverse property.
- Properties of addition
And it's just the idea that if you have a number and you add the additive inverse of the number, which is what most people call the negative of the number-- if you add the negative of the number to your number, you're going to get back to 0 because they have the same size, you could view it that way.
They both have a magnitude of 5, but this is going five to the right and then you're going five back to the left.