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Integers are the collection of both negative and positive numbers. For example: -12, 10, -45, 67.
A number without any sign (plus or minus) is considered as positive. In the above example, we have put no sign before 10 but it is a positive number. In short you don't have to explicitly put any sign to represent positive numbers.
Creating a number line is very easy. Look at the below diagram.
(click the image to view full)
In integer the closure property is closed under the addition of two integers. In simple terms if we add two integers the answer would also be an integer number.
For example: -2 + 3 = -1
Here -2 is an integer, 3 is an integer and the answer -1 is also an integer.
The closure property is closed under the subtraction of two integers. In simple terms if we subtract two integers the answer would be also be an integer.
For example: -2 - 3 = -5
Here the -2 is an integer, 3 is an integer and the answer -5 is also an integer.
| Symbols | Rule | Sign |
| - - | Add both the numbers | - (Minus) |
| - + | Subtract both the numbers | put the sign of big number |
| + - | Subtract both the numbers | put the sign of big number |
| + + | Add both the numbers | put the sign of plus |
The closure property is closed under the multiplication of two integers. It simply means that if we multiply two integers the answer would also be an integer.
For example: -2 x 5 = -10
Here, -2 is an integer, 5 is an integer and -10 is also an integer.
The closure property is not closed under the division of two integers. It simply means that it's not necessary that division of two integer will give integer answer.
For example: 10/5 = 2
Here 10 is an integer, 5 is an integer and 2 is also an integer.
Now, let's look at the following case:
Example: 5/10 =0.5
Here 5 and 10 both are interger but 0.5 is not an integer, it's a decimal number. Hence we can say that closure property is not closed under division of two integers.
Commutative property simply means that if we add two integers, we get a answer. And if we add those intergers by changing their places, the answer will remain same.
For example: -2 +5 = 3
And 5 + (-2)
= 5 - 2
= 3
In both the above cases, the answer we get is same.
Point to remember: Commutative property is only used for two numbers.
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