Definition
Remainder
A remainder is the amount left after whole-number division, and it must be smaller than the positive divisor.
Continue from this idea into connected AXIO math.
Boundary check: A remainder must be smaller than the divisor: 2 < 5.
What it means
Make as many complete equal groups as possible. The units that cannot make one more full group are the remainder. The remainder must be smaller than the group size, or another group could still be made.
Remember it
Make full groups first; the smaller leftover is the remainder.
Example
29 ÷ 6 gives quotient 4 and remainder 5 because 6 × 4 = 24 and 29 = 24 + 5. Since 5 is less than 6, no more full group of 6 can be made.
Watch for
A claimed remainder of 7 after dividing by 6 cannot be final, because 7 contains one more full group of 6.
Common mix-up
In a word problem, the remainder may be kept, shared as a fraction, discarded, or make you round up; the context decides.
Exact meaning
For a whole-number dividend a and positive divisor b, the remainder r is the unique whole number in a = bq + r with 0 ≤ r < b, where q is the whole-number quotient.