- Number line is quite an easy way of understanding operations on whole numbers.
- Suppose we want to perform subtraction of \(8\) and \(15.\)
- To show subtraction of \(8\) from \(15\) on the number line, first draw a number line from \(0\) to \(15\).

- Start from \(15\) and then move \(8\) points backward (as we have to subtract \(8\)), by taking \(1\) point at a time.

We reach the number \(7\).

Thus, \(15-8=7\)

- Closure property of subtraction states that the difference of two whole numbers is not always a whole number.

**Case 1:** **Closure property is obeyed in subtraction of whole numbers**

Whole number – whole number = whole number

- This case is only obeyed when the first term is greater than or equal to the second one.

\(a-b=c\)

\((a\geq b) \) and \(a,b,c\) are whole numbers.

**Example:**

Consider \(a = 9 \) and \(b = 7\)

then \(a-b = 9 - 7 = 2\)

where \(9 ,7\) and \(2\) are all whole numbers and \(9\) is greater than \(7\).

**Case 2: Closure property is not obeyed in subtraction of whole numbers**

- This case is only obeyed when the first number is smaller than the second one. In this, the resultant is not a whole number.

\(a-b \neq c \)

\(b>a, \,a\) and \(b\) are whole numbers and \(c\) is not a whole number.

**Example:**

Consider \(a = 7 \) and \(b = 9\)

\(a-b = 7 - 9 = -2\)

\(7, 9\) are whole numbers and \(- 2\) is not a whole number.

A \(4-6 = -2\)

B \(6-4 = 2\)

C \(4+6 =10\)

D \(4+6 = 6+4\)

- Subtraction is not commutative for whole numbers, this means that when we change the order of numbers in subtraction expression, the result changes.

\((a-b)\neq(b-a)\)

- For example: Consider the subtraction of two whole numbers \(5\) and \(7\).

\(\begin{array} {c c c} (7-5) & \neq & (5-7)\\ 2&\neq &-2 \end{array}\)

In both the expressions, answer is different.

- So, we can say that subtraction is not commutative for whole numbers.

A It shows that closure property is not obeyed in subtraction.

B It shows that closure property is obeyed in subtraction.

C It shows that commutative property is not obeyed in subtraction.

D It shows that commutative property is obeyed in subtraction.

- Associative property does not work with subtraction, this means that when we change the order of numbers in subtraction, the result also changes.

\(a-(b-c)\neq(a-b)-c\)

**For example:**

\(1-(9-8)\neq(1-9)-8\)

\(1-1\neq(-8)-8\)

\(0\neq -16\)

Answers of both the expressions are not same.

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