Q60.

Determine whether the Commutative Property applies to division. Justify your answer.

Verified

Answer

The commutative property for division doesn’t always hold.

1Step 1. Commutative and associative property.

The commutative property for any operation ‘*’ is defined as,

$a * b = b * a$

Where ‘a’, and ‘b’ are any numbers.

2Step 2. Description of step.

Note that the commutative property suggests that if the operands are swapped in an expression it gives the same answer.

Now, in case of division for any numbers ‘a’, and ‘b’

$a \div b = b \div a$

Is not always true in case if a ≠ b for example as a=2, b=4

$\begin{array}{l} a \div b = 2 \div 4 = 0.5 \\ b \div a = 4 \div 2 = 2 \\ \Rightarrow a \div b \neq b \div a \end{array}$

But in the case of a=b,

$\begin{array}{l} a \div b = a \div a = 1 \\ b \div a = a \div b = 1 \\ \Rightarrow a \div b = b \div a \end{array}$

Thus, commutative property for division doesn’t always hold.