What is Remainder? — Mathematics

Definition 17.3 Primary & Middle School Mathematics · Chapter 17 — Sharing and Division

Sharing $23$ marbles among $4$ children gives $5$ marbles each — and $3$ marbles left over, not enough for another round. We write

23 = 4 \times 5 + 3 ,

and say: the quotient is $5$ , the remainder is $3$ . The remainder is always smaller than the number of children — otherwise another round of sharing would be possible.

Sharing 23 among 4: after 5 rounds, 3 marbles remain — too few for a 6th round. — Sharing $23$ among $4$ : after $5$ rounds, $3$ marbles remain — too few for a $6$ th round.

Examples

Example 17.4

Divide $58$ by $7$ . Scan the table of $7$ : $7 \times 8 = 56$ is the biggest product that fits under $58$ ( $7 \times 9 = 63$ is too much). So

58 = 7 \times 8 + 2 :

quotient $8$ , remainder $2$ . Check: $56 + 2 = 58$ , and $2 < 7$ .

Example 17.6

$58$ students go canoeing, $7$ per canoe. $58 = 7 \times 8 + 2$ : eight canoes are full, and $2$ students remain — they need a canoe too. So $9$ canoes must be booked.

Read in context →