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### Course: Class 6 (Old) > Unit 2

Lesson 6: Identity properties of 0 and 1# Identity property of 0

Sal shows how any number plus 0 is the original number. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- By what do you multiply 1587 to get 1?(37 votes)
- Multiply it by the inverse.

For Example:

X * 1/X=1(10 votes)

- Does negative zero exist?(7 votes)
- No, it's not positive or negative.(6 votes)

- Is the identity property of 0 similar to the identity property of addition or the identity property of multiplication?(10 votes)
- It is a different way of describing the identity property of addition.(10 votes)

- i wonder why letters are in math ?(8 votes)
- The letters are called variables .they are used if we dont know the value of that number.

example - x ,y,z etc.(2 votes)

- Specifically with the properties of 0, I found myself pondering a question about multiplying and dividing by 0.

As a 'rule', any number times 0 is equal to 0. Mathmatically, 0*x=0

Also, as a 'rule', any number divided by 0 is undefined. Mathmatically, x/0 is undefined.

My question stems from the issue of simplifying and resolving complex algebraic equations where an intermediate step may result in dividing by 0 but that portion cancels.

Is 0*(x/0) equal to 0 or undefined?(5 votes)- If you divide by 0, in any step, it is undefined. This is actually a trick that is often used to prove things like 1=0. ;-)

If you have something like [(x+1)(x-1)]/(x+1), it will be undefined at x=-1, even though the (x+1) cancels.(7 votes)

- I always thought 0 is by far one of the most interesting things in math : 0 multiply something, even if the something is huge, even if it is near an infinite number, will give 0 as a result. Definitely there's something magic behind the zero ! By the way is zero is consider as a "number"? I mean 0 represents nothing. Could we call nothing a number? If not what is the proper term?(4 votes)
- 0 has indeed been considered as a number for a few years already

a number is considered as a mathematical object used to count, label, and measure

//sources :

http://en.wikipedia.org/wiki/Number http://en.wikipedia.org/wiki/0_(number)(4 votes)

- Why is zero in math expressions when all we do is ignore the zero? I was always confused as to why we have zeros in math.(3 votes)
- Zeroes occur in many ways in math. You can't always ignore them.

I can't ignore these zeroes... they all have meaning and/or will affect the math:

205: The 0 fills a place value. Without it the number's value changes. It can't be ignored.

2 * 0 + 5: The zero impacts the math. If you ignore it, you would get 7. The correct answer is 5

These are just a couple of example of why you can't always ignore zeroes.(1 vote)

- will someone talk to me i have no friends(2 votes)
- What's the difference between the associative and commutative law of addition?(1 vote)
- Commutative property shows you that you can change the
**order of the numbers**and you will get the same result. This means, if you try to add:`2 + 3 + 5`

, you could also do`3 + 2 + 5`

, or`5 + 3 + 2`

and other variations. All of them will create the same answer. Thus, when you are adding numbers, the order doesn't matter. Add them in whatever order you want.

The Associative Property shows us that we can**move the grouping symbols**and we will still get the same answer. For example:`3 + (5 + 7)`

will create the same answer as`(3 + 5) + 7`

. This property only moves the parentheses or other grouping symbols. It will not move the numbers.

Hope this helps.(3 votes)

- can you explain it more easily?(1 vote)
- The identity property of 0, also known as the identity property of addition, tells us that any number + 0 = the original number. Adding zero will not change the "identity" or value of the number you are adding it to. For example:

5+0 = 5

Adding 0 didn't change the value of the 5.(3 votes)

## Video transcript

Evaluate 0 plus y plus -7 when y is equal to -3 and y is equal to 0 and y is equal to 7. So let's take the first situation where y is equal to -3... Then this expression right here would be... 0 plus -3 (because that's our "y" now) plus -7. Now 0 plus or minus anything won't change its value So you can really just ignore the 0 here. This is going to be the same thing, this is going to be the exact same thing, as -3 plus -7. -3 plus -7 Now we could draw a number line here, just to help us visualize it But even if we didn't have the number line, we could say "Look, we're already 3 below zero... We're going to go another 7 to the left... another 7 more negative." So we're 3 away from zero, we're going to go 7 more away from zero So we're going to be 10 to the left of zero, or -10. Or another way to think of it... Lemme draw the number line there (always better to have the visual). So we're starting (this is zero) We're starting at -3, and to that we're adding -7 So we're starting at -3, the absolute value is -3[sic] is our starting point. To that we're adding another negative 7 We're going to move another 7 to the left. So we're adding (let me draw this)... we're adding a negative 7 right over here We're adding a negative 7 right over here So what's the length of this over here? The absolute value of -7 is equal to 7... that's the length of this arrow. But we're moving it to the left. The abolsute value of this arrow right here (the absolute value of negative 3) is 3. So we're already 3 to the left, now we're moving 7 more to left So now we're going to be 10 to the left. We are going to be 10 to left. 10 to the left. This is literally, this is equal to the absolute value of -7... Let me do it in the order that we wrote it in the problem... So this is equal to the absolute value of -3 (you'd want to use the same colors) The absolute value of -3 plus the absolute value of -7. But we're to the left of zero (we've been moving to the left) so it's the <i>negative</i> of that which is -10 So if your signs are the same, you can just take the absolute value of them say "ok, that's how far we're going to move, total. and we're that far from zero to the left" So the answer here is -10 That was when y is -3. Let's think about when y is equal to 0. When y is equal to 0, this expression up here becomes 0 plus 0 (our y here is going to be zero)... (We'll do it in that same blue color.) .... plus 0 plus -7. Now, if you add 0 to anything it's not going to change the value. So this thing over here, this is pretty straight-forward, these don't matter It's just going to be equal to -7 Now let's do the last one (when y is equal to 7) It's going to be 0 plus (our y is equal to 7) so 0 plus 7 and then we have plus -7 Now there's a couple of ways to do this... You could literally just say "now adding a negative number is equivalent to subtracting the number". You could say this is equivalent to 0 plus 7 minus 7 Plus -7 is the same thing as subtracting a 7 The zero doesn't matter, so this is equal to 7 minus 7... which is equal to zero! Another way to think about it... Let's draw a number line So let's say that this is zero We're starting off at 7. We're 7 to the right of zero. And to that we're adding a -7. So we're going to move 7 to the left of where we were. 7 to the left of 7 which was 7 to the right of 0! This gets us back to 0. So the answer is... zero.