Integer division, including remainders.

The idea

Integer division divides one whole number by another and discards any fractional part, keeping only the whole-number quotient. The remainder is what is left over after that whole-number quotient is taken. In many languages the operator DIV (or //) gives the quotient while MOD (%) gives the remainder, so 11 DIV 2 is 5 and 11 MOD 2 is 1, because 2 × 5 = 10 and 11 − 10 = 1. Learners must keep the two results distinct: the quotient answers 'how many whole times does the divisor fit', and the remainder answers 'what is left'. A reliable check is quotient × divisor + remainder = original number, so 5 × 2 + 1 = 11. Contrast this with real division, where 11/2 gives 5.5.

What earns the marks

• Integer division returns the whole-number quotient and discards the fractional part, so 11 DIV 2 = 5.
• The remainder is the amount left after the whole-number quotient is taken, so 11 MOD 2 = 1.
• Quotient and remainder are different values and must not be confused; DIV gives 5 while MOD gives 1 for 11 and 2.
• The relationship quotient × divisor + remainder = original number can be used to verify both results.
• Integer division differs from real division, which would give 5.5 for 11/2.

Common mistakes and how to put them right

• Giving 5.5 as the result of integer division.

  Put it right: Integer division discards the fraction and gives 5.

• Reporting the remainder as 5 or as 0.5.

  Put it right: The remainder is 1 because 11 − (2 × 5) = 1.

• Swapping the DIV and MOD results.

  Put it right: DIV gives the quotient (5) and MOD gives the remainder (1).

Exam tips

• Work out the whole-number quotient first, then subtract quotient × divisor from the original number to find the remainder.
• Use the check quotient × divisor + remainder = original number to confirm both answers before selecting an option.
• Read the operator carefully: DIV (or //) asks for the quotient, MOD (%) asks for the remainder, and a plain division sign asks for the real value.