We reach the number \(7\).
Thus, \(15-8=7\)
A
B
C
D
To show subtraction of \(4\) from \(8\) on the number line, start from \(8\) and then move \(4\) points backward (as we have to subtract \(4\)), by taking one point at a time.
We reach the number \(4\).
Thus, \(8-4=4\)
Hence, option (D) is correct.
Option D is Correct
Case 1: Closure property is obeyed in subtraction of whole numbers
Whole number – whole number = whole number
\(a-b=c\)
\((a\geq b) \) 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
\(a-b \neq c \)
\(b>a, \,a\) 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 \(4+6 = 6+4\)
\((a-b)\neq(b-a)\)
\(\begin{array} {c c c} (7-5) & \neq & (5-7)\\ 2&\neq &-2 \end{array}\)
In both the expressions, answer is different.
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.
\(a-(b-c)\neq(a-b)-c\)
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.
