\(-4<-3<-2<-1<0<1<2<3<4\)
A Point \(A\)
B Point \(B\)
C Point \(C\)
D Point \(D\)
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.
A \(12 \div2 = 6\)
B \(2 \div 12 = \dfrac{1}{6}\)
C \(4 \div 12 = \dfrac{1}{3}\)
D \(9 \div 18 = 0.5\)
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.
So, \(15 \div 3 = 5\) (moves)
\((a \div b)\neq(b\div a)\)
\((8 \div 4)\neq(4 \div 8)\\ \;\;\;\;2\;\;\;\;\;\;\;\;\;\;\;\;\dfrac{1}{2}\)
In both the expressions, answer is not same.
A It shows closure property is not obeyed in division.
B It shows commutative property is not obeyed in division.
C It shows commutative property is obeyed in division.
D It shows closure property is obeyed in division.
\(a\div (b\div c)\neq(a\div b)\div c\)
\(1\div (4\div2)\neq(1\div4)\div2\)
\(1\div2\neq\dfrac{1}{4}\div2\)
\(\dfrac{1}{2}\neq\dfrac{1}{8}\)
Answer of both the expressions are not same.
So, we can say that division is not associative for whole numbers.
A It shows closure property is obeyed in division.
B It shows associative property is obeyed in division.
C It shows commutative property is not obeyed in division.
D It shows associative property is not obeyed in division.