42
The remainder
Textbook: Part 2, lesson 42, pp. 10–12
GoalThe idea of a remainder: when the dividend does not divide exactly, a remainder is left, and it is smaller than the divisor.
New words
remainder · qoldiqincomplete quotient · to‘liqsiz bo‘linmadivisor · bo‘luvchiexact division · butun bo‘linish
Explanation
Share 11 apples between 3 plates: each gets 3 and 2 apples are left over: 11 : 3 = 3 (remainder 2). The remainder is always smaller than the divisor: dividing by 3 the remainder can only be 0, 1 or 2. If the remainder is 0 the division is exact and no remainder is written: 12 : 3 = 4.
Worked examples
26 : 6 = 4 (remainder 2), because 6 × 4 = 24 and 26 − 24 = 2.
20 : 5 = 4 with no remainder; 21 : 5 = 4 (remainder 1).
Class activity
“In groups”: children group 11 pencils into twos, threes and fours. Each time they say how many groups they made and how many pencils are left.
Practice
1
17 : 5 = ? (with a remainder)
3 remainder 2
2
A cook has 23 plates. She stacks them in twos. How many plates are left over?
1
3
What remainders are possible when a number is divided by 5?
0, 1, 2, 3 or 4 (numbers smaller than 5)
4
30 : 7 = ? (with a remainder)
4 remainder 2