Remainder: the remainder when 11 is divided by 2 (11 MOD 2) = 1

The idea

MOD returns the remainder left after integer division. To find 11 MOD 2, first see how many whole times 2 fits into 11: it fits five times (2 × 5 = 10). Subtract that from 11 to get the remainder, 11 − 10 = 1, so 11 MOD 2 = 1. The remainder is always less than the divisor, which is a useful check. MOD is closely linked to DIV: for the same numbers, dividend = (quotient × divisor) + remainder, here 11 = (5 × 2) + 1. MOD is used to test whether a number is even or odd (a remainder of 0 after dividing by 2 means even) and to wrap values around a fixed range.

What earns the marks

• MOD returns the remainder after integer division.
• 2 fits into 11 five whole times, giving 2 × 5 = 10.
• The remainder is 11 − 10 = 1, so 11 MOD 2 = 1.
• The remainder is always less than the divisor, and dividend = (quotient × divisor) + remainder.

Common mistakes and how to put them right

• Giving 5: the learner confuses MOD with DIV.

  Put it right: Is that MOD gives the remainder (1), not the quotient.

• Giving 0.5: the learner treats the fractional part of ordinary division as the remainder.

  Put it right: Is that the remainder is a whole number found by subtraction.

• Giving 2 or more.

  Put it right: Is that a valid remainder must be less than 2 here.

Exam tips

• Multiply the whole-number quotient by the divisor, then subtract from the dividend to get the remainder.
• Check that your remainder is smaller than the divisor before selecting an answer.
• Use the relationship dividend = (quotient × divisor) + remainder to verify DIV and MOD together.