Q57. - Algebra 1

Question

Does the Commutative Property sometimes, always, or never hold for subtraction? Explain your reasoning.

Step-by-Step Solution

Answer

The commutative property for subtraction holds sometimes not always.

Step 1. Commutative property.

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

$a*b=b*a$

Where ‘a’ and ‘b’ are any numbers.

Step 2. DESCRIPTION OF STEP.

The commutative property for subtraction is defined as:

$a-b=b-a$

Now note that the above doesn’t always hold, as in case ‘a’ and ‘b’ are the same number, i.e.

a=b, then

$\begin{array}{l}a-b=b-a\\ a-a=a-a\\ 0=0\end{array}$

But in case a is not equal to be, for example, a=2, and b=4, then

$\begin{array}{l}a-b=2-4\\ a-b=-2\\ \text{ But;}\\ b-a=4-2\\ b-a=2\\ \Rightarrow a-b\ne b-a\end{array}$

Thus, commutative property for subtraction holds sometimes not always.