What Have We Discussed ?
1.The numbers 1, 2, 3,... which we use for counting are known as
2. If you add 1 to a natural number, we get its
3. Every natural number has a
4. If we add the number zero to the collection of natural numbers, we get the collection of
Thus, the numbers 0, 1, 2, 3,... form the collection of
5. Every whole number has a
6. All natural numbers are
7. We take a line, mark a point on it and label it 0. We then mark out points to the right of 0, at equal intervals. Label them as 1, 2, 3,.... Thus, we have a number line with the whole numbers represented on it. We can easily perform the number operations of addition, subtraction and multiplication on the number line.
8. Addition corresponds to moving to the right on the number line, whereas subtraction corresponds to moving to the left. Multiplication corresponds to making jumps of equal distance starting from zero.
Properties of Whole numbers
| Property | Operations | |||
|---|---|---|---|---|
| Name | Addition | Subtraction | Multiplication | Division |
| Closure | a+εb w | a-b∈/w | axbεw | a÷b∈/w |
| Commutative | a+b =b+a | a-b≠ b-a | axb=bxa | a÷b≠b÷a |
| Assosiative | a+(b+c)=(a+b)+c | (a-b)-c≠a-(b-c) | (axb)xc=axbxc | (a÷b)÷c≠a÷(b÷c) |
| Distributive | ax(b+c)=ab+ac | ax(b-c)=ab-ac | Not applicable | Not applicable |
| Identity | a+0=a | a-0=a | ax1=a | a÷1=a |