Question 1 is already done for you357 ÷ 5
Hundreds 3 ÷ 5 = 0, nothing fits. Look at 35
Tens 35 ÷ 5 = 7, write 7. 5 × 7 = 35, 35 − 35 = 0, bring down the 7
Ones 7 ÷ 5 = 1 remainder 2, write 1
Answer 71 remainder 2
Two-digit divisors start with an estimateIt is the same four moves as one-digit division. Only "guess" is harder.
1 Treat the divisor as a round ten 2 Find a nearby times-table fact 3 Try it
83 ÷ 21 21 → 20. 80 ÷ 20 = 4 … the estimate is 4
21 × 4 = 84 is bigger than 83! → change to 3. 21 × 3 = 63, 83 − 63 = 20
Answer 3 remainder 20 (20 is smaller than 21, so it is fine)
2Write the estimate of each quotient as a sum, like 80 ÷ 20 = 4.
(1) 58 ÷ 19 (2) 47 ÷ 16
Round both numbers to something neat: 16 → 20, 47 → 40.
3Work out 97 ÷ 31 with long division. Write the estimate too.
4Work out 86 ÷ 29 with long division.
29 → 30. Multiply the guess back: does it go over 86?
When the estimate missesIf the product is bigger than the number being divided → the quotient is too big. Take 1 off.
If the remainder is the same as the divisor or bigger → the quotient is too small. Add 1.
A remainder is always smaller than the divisor.
64 ÷ 16 16 → 20, 60 ÷ 20 = 3 … estimate 3
16 × 3 = 48, 64 − 48 = 16 … same as the divisor! → change to 4. 16 × 4 = 64, remainder 0
5A child guessed a digit for each division. Is it right? If not, fix it and write the correct quotient and remainder.
(1) 85 ÷ 17, guessed 4 (2) 55 ÷ 18, guessed 4
Multiply and subtract, then look at the remainder.
6Work out 69 ÷ 17 with long division.
17 → 20, 60 ÷ 20 = 3. After multiplying and subtracting, is the remainder smaller than 17?
7Work out 458 ÷ 52 with long division.
52 → 50. Try 450 ÷ 50 = 9 first.
When you get stuck156 ÷ 26
1 ÷ 26 is too small, and so is 15 ÷ 26. "It does not go in" and you stop
→ Look at all three digits, 156, as one lump. The quotient starts in the ones.
26 → 30, 150 ÷ 30 = 5 … estimate 5. 26 × 5 = 130, 156 − 130 = 26 … same as the divisor!
→ change to 6. 26 × 6 = 156, remainder 0. (No 0 is written in the tens.)
8Work out 138 ÷ 23 with long division.
1 and 13 are both smaller than 23. Take 138 as one lump.
9Work out 756 ÷ 21 with long division. (The quotient has two digits.)
First 75 ÷ 21. 21 → 20, 80 ÷ 20 = 4 goes over 75 when multiplied back.
10A child answered "247 ÷ 32 = 6 remainder 55". The check (32 × 6 + 55) works out. The answer is still wrong. Why? Write the correct answer too.
What a remainder means depends on the storyTake 134 ÷ 24 = 5 remainder 14 and three stories:
- 134 people ride 24-seat buses → the other 14 ride too. 5 + 1 = 6 buses (round up)
- 134 pencils go in bags of 24 → 5 bags, 14 pencils left (round down)
- 134 stickers to 24 people, the same number each → 5 each, 14 left over
The sum and the quotient are the same. Only "what to do with the remainder" differs.
11134 people will ride in buses that hold 24 each. How many buses are needed?
What happens to the people left over?
12There are 100 cookies, packed 14 to a box.
(1) How many full boxes of 14 are there, and how many cookies are left?
(2) If the leftover cookies go in a box too, how many boxes are needed in all?
13A ribbon is 230 cm long. Pieces of 35 cm are cut from it.
(1) How many pieces, and how many cm are left?
(2) How many more cm would give one more piece?
(2) How far is the leftover from 35?