If \(a\) and \(b\) are two integers, then which of the following may not be an integer?
\(a+b\)
\(a-b\)
\(a\times b\)
\(a\div b\)
Step 1: Know what integers are. Integers are whole numbers … like −3, −2, −1, 0, 1, 2, 3, …
Step 2: Check each option one by one.
(a) a + b → Adding two integers always gives an integer.
(2 + 3 = 5)
(-4 + 1 = -3)
(b) a − b → Subtracting two integers always gives an integer.
(5 - 2 = 3)
(-3 - 4 = -7)
(c) a imes b → Multiplying two integers always gives an integer.
(3 imes (-2) = -6)
(d) a div b → Division is not always an integer.
Example where it is not an integer:
(a = 1,; b = 2)
(a div b = 1 div 2 = frac{1}{2})
( frac{1}{2}) is not an integer.
Example where it is an integer (only when (b) divides (a)):
(a = 6,; b = 3)
(a div b = 6 div 3 = 2)
Important: Division by zero is not defined.
(a div 0) → not defined
Conclusion: (a), (b), and (c) are always integers, but (d) may or may not be an integer. So the correct answer is (d).