• A number line is a pictorial representation of real numbers.
• We can plot whole numbers on a number line. Number line can be drawn as long as we want but we can never find infinity on it.
• Zero lies at the middle of the number line.

• The positive numbers always lie on the right side of zero and negative numbers always lie on the left side of zero.

• A number which is farther to the right on the number line is greater than its previous numbers.

\(-4<-3<-2<-1<0<1<2<3<4\)

• The section of the number line between two numbers is called an interval.

• If the numbers are placed in their correct order, then the interval of numbers is always equal.

• Closure property is obeyed for division only if the division of two whole numbers is a whole number.

Case 1: Closure property is obeyed in division for whole numbers

Division of any two whole numbers can be a whole number.

Whole number \(\div\) whole number = whole number

This case is only obeyed when divisor is a factor of dividend.

For example: 

\(8 \div 4 = 2\)

\(4\) is a factor of \(8\) and both are whole numbers. So, the result is also a whole number i.e. 2.

Case 2: Closure property is not obeyed in division for whole numbers

Division of any two whole numbers is not always a whole number.

Whole number \(\div\) whole number \(\neq\) whole number

In this case, divisor is not a factor of dividend. so the quotient is not a whole number.

For example: \(2 \div 4 = \dfrac{1}{2}\)

\(2\) and \(4\), both are whole numbers but \(\dfrac{1}{2}\) is not a whole number. 

• The zero property of division have two cases.

Case (i): If we divide zero by a whole number, the answer will be zero.

\(0 \;\div 12 = 0\)

Case (ii): If a whole number is divided by zero, then the problem cannot be solved. 

\(12 \div 0\)

The answer is undefined. 

• Number line is quite easy way of understanding operation of whole numbers.
• To show division of 15 by 3 on the number line, we start from 15 and move 3 points backward at a time. 

• Now, keep on making such moves till we reach zero.

• We made 5 moves of 3 points each.
• Thus, the number of moves of 3 steps represent the result.

So, \(15 \div 3 = 5\) (moves) 

• Division is not commutative for whole numbers. This means that if we change the order of numbers in the division expression the result also changes.

\((a \div b)\neq(b\div a)\)

• For example: Consider division of two whole numbers \(8 \) and \(4\).

\((8 \div 4)\neq(4 \div 8)\\ \;\;\;\;2\;\;\;\;\;\;\;\;\;\;\;\;\dfrac{1}{2}\)

In both the expressions, answer is not same.

• So, we can say that division is not commutative for whole numbers.

• Associative property does not work with division. This means that when we change the grouping of numbers, the result also changes.

\(a\div (b\div c)\neq(a\div b)\div c\)

• For example:

\(1\div (4\div2)\neq(1\div4)\div2\)

\(1\div2\neq\dfrac{1}{4}\div2\)

\(\dfrac{1}{2}\neq\dfrac{1}{8}\)

Answer of both the expressions are not same.

So, we can say that division is not associative for whole numbers.