What is Mathematics about? It is about numbers, perhaps about shapes as well. It is true that people usually count 1,2,3... on various situations. This collection of counting numbers {1,2,3...} is called Natural numbers, denoted by N.

**WHOLE NUMBERS**

What is Mathematics about? It is about numbers,
perhaps about shapes as well. It is true that people usually count 1,2,3... on various
situations. This collection of counting numbers {1,2,3...} is called Natural numbers,
denoted by N. If this collection includes 0 as well, then the collection {0,1,2,3...}
is called Whole numebrs, denoted by W.

__ __

__1. Recall the facts on Natural and
Whole Numbers__

* The smallest natural
number is 1.

* The smallest whole
number is 0.

* Every number has a
successor. The number that comes just after the given number is its successor.

* Every number has a
predecessor. The number 1 has a predecessor in W namely ‘0’, but it has no predecessor
in N. The number ‘0’ has no predecessor in W.

* There is an order
to numbers. By comparing the two given numbers the larger of the two can be identified.

* Numbers are endless. By adding 1 to any chosen
large number, the next number can be found.

Logical and Mathematical operations of numbers are
used in everyday arithmetic of numbers. These operations can be made easier using
properties. Certain properties of numbers are already used without actually knowing
them. For example, while adding 8 + 2 + 7, one way of adding is, 8 and 2 are added
first to get 10 and then 7 is added to it.

**Try these**

**● Find the
value of 6 + 3 + 8 and 3 + 6 + 8**

**i) Are
they the same?**

**Answer:** Yes, they are same

**ii) Is
there any other way of rearranging these three numbers? **

8 + 3 + 6

**● Find
the value of 5 × 2 × 6 and 2 × 5 × 6**

**i) Are
they same?**

**Answer:** Yes, they are same

**ii) Is
there any other way of rearranging these three numbers?**

**Answer:** 6 × 5 × 2

**● Is 7 − 5, the same as 5 − 7? Why?**

**Answer:** No, it’s not same because subtraction ans division
not having commutative property.

**● What is the value of (15 − 8) −
6? Is it the same as 15 − ( 8 − 6)? Why? **

**Answer:** (15−8) − 6 7
− 6 = 1

15− (8 − 6) 15 − 2 =
13

Both are different values because subtraction and division are
not comes under commutative property.

**● What is 15 ÷ 5? Is it the same as
5 ÷ 15? Why?**

**Solution: **15/5 ≠ 5/15 ⇒ 1/3 ≠ 3

**● What is the value of (100 ÷ 10)
÷ 5? Is it the same as 100 ÷ (10 ÷ 5)? Why?**

**Solution:**

(100 **÷** 10) **÷ **5 = 10 **÷ **5 = 2

100 **÷** (10 **÷ **5) = 100 **÷ **2 = 50

No, it is not same

The properties of numbers are important facts to
be remembered, which helps to do arithmetic calculations more precisely and to avoid
mistakes.

Tags : Numbers | Term 1 Chapter 1 | 6th Maths , 6th Maths : Term 1 Unit 1 : Numbers

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6th Maths : Term 1 Unit 1 : Numbers : Whole Numbers | Numbers | Term 1 Chapter 1 | 6th Maths

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