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What are natural numbers?
Counting numbers are called natural numbers. The counting starts from 1 and goes infinitely.
What are whole numbers?
The counting that start from 0 and goes infinitely is called whole numbers: (0, 1, 2, 3 ....)
What is successor and how to find the successor of the given number?
Successor is the number that comes after the given number. To find the successor we simply need to add 1 to the given number.
Example: Find the successor of 3,732.
Ans: 3,732 + 1
= 3,733
What is predecessor and how to find the predecessor of the given number?
Predecessor is the number that comes before the given number. To find the predecessor we simply need to subtract 1 from the given number.
Example: Find the predecessor of 746.
Ans: 746 - 1
= 745
The closure property in whole number say that the addition and mulitplication of two whole numbers are closed. In simple terms, it means that when you add two whole number the result is a whole number and when you multiply two whole numbers the result is a whole numbers.
For example: 2 + 3 = 5
Here 2 is a whole number, 3 is a whole number and the result or answer 5 is also a whole number.
Example (multiplication): 2 x 3 = 6
Here 2 is a whole number, 3 is a whole number and the product or answer 6 is also a whole number.
(Closure is property is not closed under subtraction and division)
Example: 2 - 3 = -1
Here 2 is whole number, 3 is a whole number but the answer -1 is an integer.
Example (division): 2 / 10 = 0.2
Here 2 is a whole number, 10 is a whole number but the answer 0.2 is a decimal number.
The commutative property of whole number says that when you add two number you get some answer.
For example: 2 + 4 = 6
And when you add the same numbers after changing their position you get the same answer.
For example: 4 + 2 = 6
In both the cases the answer is same. Hence, we conclude that two whole numbers can be added in any order.
(Point to remember: Commutative property is used for two numbers only)
Similarly, we can multiply any two whole numbers in any order.
For example: 2 x 5 = 10 and 5 x 2 = 10
The associative property is same as commutative except it is used for three numbers. This property says that we can add and multiply and three numbers in any order and the answer will be same.
Consider the following examples:
| Solution 1 | Solution 2 |
|
2 + (3 + 4) 2 + 7 9 |
(2 + 3) + 4 5 + 4 9 |
|
(2 x 10) x 3 20 x 3 60 |
2 x (10 x 3) 2 x 30 60 |
In the above table we have added and multiplied number in different order, but we got the same answer in each case.
In distributive property we solve question by distributing the numbers.
For example: 10 x 12
= 10 x (10 + 2) [Here we have distributed 12 into 10 plus 2]
=10 x 10 + 10 x 2
= 100 + 20
= 120
Zero 0 is called the additive identity because when a number is added to zero the answer is the number itself.
For example: 0 + 5 = 5 and 23 + 0 = 23
One 1 is called the multiplicative identity because when we multiply any number with 1 the answer is number itself.
For example: 1 x 10 = 10 and 32 x 1 = 32