13
Division with remainder
Textbook: Part 1, lesson 13, pp. 54–57
GoalDo division with remainder; find the dividend from the partial quotient, divisor and remainder.
New words
remainder · qoldiqincomplete quotient · to‘liqsiz bo‘linmadivides exactly · qoldiqsiz bo‘linadidivisor · bo‘luvchi
Explanation
Numbers do not always divide exactly. Dividing 23 by 5 gives 4 and 3 is left over: 23 = 5 × 4 + 3, also written 23 : 5 = 4 (remainder 3). Here 23 is the dividend, 5 the divisor, 4 the incomplete quotient and 3 the remainder. The remainder is always smaller than the divisor. If the remainder is 0 we say the number divides exactly. To find the dividend, multiply the incomplete quotient by the divisor and add the remainder.
Worked examples
47 : 6 = 7 (remainder 5), because 6 × 7 = 42 and 47 − 42 = 5. In writing: 47 = 6 × 7 + 5, and 5 < 6.
A number divided by 15 gives incomplete quotient 12 and remainder 7. The number is 15 × 12 + 7 = 180 + 7 = 187.
Class activity
“Packing boxes”: 53 cubes are packed 6 to a box. Pupils pack them and find how many boxes fill up and how many cubes are left.
Practice
1
Divide 1 234 by 25 with remainder.
49 remainder 9
2
52 pencils are put 8 to a box. How many boxes fill up and how many pencils are left?
6 boxes, 4 pencils left
3
A number divided by 15 gives incomplete quotient 12 and remainder 7. Find the number.
187
4
Why must the remainder be smaller than the divisor?
If the remainder were at least as large as the divisor, we could divide one more time.