Year 6 Arithmetic (SATs) · Multiplication and division · Lesson 2.3
Year 6 Arithmetic (SATs): Short division and remainders
Part of the Year 6 Arithmetic (SATs) multiplication and division chapter. Chapter overview · whole chapter on one page
2.3
Short division and remainders
Story. Ali has 83 stickers to share equally between 7 friends. He wants to know how many each friend gets, and how many stickers are left over.
Rule
In short division you divide one digit at a time, from the left. Any remainder is carried to the next column as ten times more.
The remainder must be smaller than the number you divide by.
In a problem, decide what the remainder means: sometimes you leave it, sometimes you write it as a fraction, and sometimes you round up so that everybody has a place.
Key ideas
- Divide one digit at a time, starting from the left.
- The remainder is always smaller than the number you divide by.
- Check with multiplication: quotient × divisor + remainder = the starting number.
- The context tells you which form of the remainder to give.
Worked example 2.3.1
Work out 7,268 ÷ 4.
Method. Divide each digit from the left, carrying the remainder.
- Divide the thousands part: 7 ÷ 4. Write how many times the divisor goes in, and carry the remainder to the next column.7 ÷ 4 = 1 remainder 3
- Divide the hundreds part: 32 ÷ 4. Write how many times the divisor goes in, and carry the remainder to the next column.32 ÷ 4 = 8 remainder 0
- Divide the tens part: 6 ÷ 4. Write how many times the divisor goes in, and carry the remainder to the next column.6 ÷ 4 = 1 remainder 2
- Divide the ones part: 28 ÷ 4. Write how many times the divisor goes in, and carry the remainder to the next column.28 ÷ 4 = 7 remainder 0
- Write the answer. 1,817 remainder 0
Check. 1,817 × 4 + 0 = 7,268. ✓
Watch out. Write the zero in the answer if a column does not divide.
Worked example 2.3.2
Work out 5,931 ÷ 6, and give the remainder.
Method. Divide one digit at a time from the left.
- Divide the thousands part: 5 ÷ 6. Write how many times the divisor goes in, and carry the remainder to the next column.5 ÷ 6 = 0 remainder 5
- Divide the hundreds part: 59 ÷ 6. Write how many times the divisor goes in, and carry the remainder to the next column.59 ÷ 6 = 9 remainder 5
- Divide the tens part: 53 ÷ 6. Write how many times the divisor goes in, and carry the remainder to the next column.53 ÷ 6 = 8 remainder 5
- Divide the ones part: 51 ÷ 6. Write how many times the divisor goes in, and carry the remainder to the next column.51 ÷ 6 = 8 remainder 3
- Write the answer. 988 remainder 3
Check. 988 × 6 + 3 = 5,931. ✓
Worked example 2.3.3
Ali shares 83 stickers equally between 7 friends. How many does each friend get, and how many are left?
Method. Divide the stickers by the friends, and the remainder is the number left.
- Divide the tens part: 8 ÷ 7. Write how many times the divisor goes in, and carry the remainder to the next column.8 ÷ 7 = 1 remainder 1
- Divide the ones part: 13 ÷ 7. Write how many times the divisor goes in, and carry the remainder to the next column.13 ÷ 7 = 1 remainder 6
- Write the answer. 11 each, and 6 left over
Check. 11 × 7 + 6 = 83, so 7 friends get 11 each. ✓
Watch out. The remainder 6 is less than 7, so it cannot go to each friend.
Exercise 2C Practice: short division and remainders
Non-calculator1
FWork out 4,862 ÷ 3. Give the remainder.
1,620 remainder 2
Method. Divide one digit at a time, carrying the remainder.
- Divide the thousands part: 4 ÷ 3. Write how many times the divisor goes in, and carry the remainder to the next column.4 ÷ 3 = 1 remainder 1
- Divide the hundreds part: 18 ÷ 3. Write how many times the divisor goes in, and carry the remainder to the next column.18 ÷ 3 = 6 remainder 0
- Divide the tens part: 6 ÷ 3. Write how many times the divisor goes in, and carry the remainder to the next column.6 ÷ 3 = 2 remainder 0
- Divide the ones part: 2 ÷ 3. Write how many times the divisor goes in, and carry the remainder to the next column.2 ÷ 3 = 0 remainder 2
- Write the answer. 1,620 remainder 2
Check. 1,620 × 3 + 2 = 4,862. ✓
2
FWork out 7,015 ÷ 5. Give the remainder.
1,403 remainder 0
Method. Divide one digit at a time, carrying the remainder.
- Divide the thousands part: 7 ÷ 5. Write how many times the divisor goes in, and carry the remainder to the next column.7 ÷ 5 = 1 remainder 2
- Divide the hundreds part: 20 ÷ 5. Write how many times the divisor goes in, and carry the remainder to the next column.20 ÷ 5 = 4 remainder 0
- Divide the tens part: 1 ÷ 5. Write how many times the divisor goes in, and carry the remainder to the next column.1 ÷ 5 = 0 remainder 1
- Divide the ones part: 15 ÷ 5. Write how many times the divisor goes in, and carry the remainder to the next column.15 ÷ 5 = 3 remainder 0
- Write the answer. 1,403 remainder 0
Check. 1,403 × 5 + 0 = 7,015. ✓
3
FWork out 9,276 ÷ 8. Give the remainder.
1,159 remainder 4
Method. Divide one digit at a time, carrying the remainder.
- Divide the thousands part: 9 ÷ 8. Write how many times the divisor goes in, and carry the remainder to the next column.9 ÷ 8 = 1 remainder 1
- Divide the hundreds part: 12 ÷ 8. Write how many times the divisor goes in, and carry the remainder to the next column.12 ÷ 8 = 1 remainder 4
- Divide the tens part: 47 ÷ 8. Write how many times the divisor goes in, and carry the remainder to the next column.47 ÷ 8 = 5 remainder 7
- Divide the ones part: 76 ÷ 8. Write how many times the divisor goes in, and carry the remainder to the next column.76 ÷ 8 = 9 remainder 4
- Write the answer. 1,159 remainder 4
Check. 1,159 × 8 + 4 = 9,276. ✓
4
FWork out 3,094 ÷ 6. Give the remainder.
515 remainder 4
Method. Divide one digit at a time, carrying the remainder.
- Divide the thousands part: 3 ÷ 6. Write how many times the divisor goes in, and carry the remainder to the next column.3 ÷ 6 = 0 remainder 3
- Divide the hundreds part: 30 ÷ 6. Write how many times the divisor goes in, and carry the remainder to the next column.30 ÷ 6 = 5 remainder 0
- Divide the tens part: 9 ÷ 6. Write how many times the divisor goes in, and carry the remainder to the next column.9 ÷ 6 = 1 remainder 3
- Divide the ones part: 34 ÷ 6. Write how many times the divisor goes in, and carry the remainder to the next column.34 ÷ 6 = 5 remainder 4
- Write the answer. 515 remainder 4
Check. 515 × 6 + 4 = 3,094. ✓
5
FWork out 5,728 ÷ 4. Give the remainder.
1,432 remainder 0
Method. Divide one digit at a time, carrying the remainder.
- Divide the thousands part: 5 ÷ 4. Write how many times the divisor goes in, and carry the remainder to the next column.5 ÷ 4 = 1 remainder 1
- Divide the hundreds part: 17 ÷ 4. Write how many times the divisor goes in, and carry the remainder to the next column.17 ÷ 4 = 4 remainder 1
- Divide the tens part: 12 ÷ 4. Write how many times the divisor goes in, and carry the remainder to the next column.12 ÷ 4 = 3 remainder 0
- Divide the ones part: 8 ÷ 4. Write how many times the divisor goes in, and carry the remainder to the next column.8 ÷ 4 = 2 remainder 0
- Write the answer. 1,432 remainder 0
Check. 1,432 × 4 + 0 = 5,728. ✓
6
FWork out 6,451 ÷ 7. Give the remainder.
921 remainder 4
Method. Divide one digit at a time, carrying the remainder.
- Divide the thousands part: 6 ÷ 7. Write how many times the divisor goes in, and carry the remainder to the next column.6 ÷ 7 = 0 remainder 6
- Divide the hundreds part: 64 ÷ 7. Write how many times the divisor goes in, and carry the remainder to the next column.64 ÷ 7 = 9 remainder 1
- Divide the tens part: 15 ÷ 7. Write how many times the divisor goes in, and carry the remainder to the next column.15 ÷ 7 = 2 remainder 1
- Divide the ones part: 11 ÷ 7. Write how many times the divisor goes in, and carry the remainder to the next column.11 ÷ 7 = 1 remainder 4
- Write the answer. 921 remainder 4
Check. 921 × 7 + 4 = 6,451. ✓
7
FWork out 8,009 ÷ 9. Give the remainder.
889 remainder 8
Method. Divide one digit at a time, carrying the remainder.
- Divide the thousands part: 8 ÷ 9. Write how many times the divisor goes in, and carry the remainder to the next column.8 ÷ 9 = 0 remainder 8
- Divide the hundreds part: 80 ÷ 9. Write how many times the divisor goes in, and carry the remainder to the next column.80 ÷ 9 = 8 remainder 8
- Divide the tens part: 80 ÷ 9. Write how many times the divisor goes in, and carry the remainder to the next column.80 ÷ 9 = 8 remainder 8
- Divide the ones part: 89 ÷ 9. Write how many times the divisor goes in, and carry the remainder to the next column.89 ÷ 9 = 9 remainder 8
- Write the answer. 889 remainder 8
Check. 889 × 9 + 8 = 8,009. ✓
8
FWork out 2,517 ÷ 2. Give the remainder.
1,258 remainder 1
Method. Divide one digit at a time, carrying the remainder.
- Divide the thousands part: 2 ÷ 2. Write how many times the divisor goes in, and carry the remainder to the next column.2 ÷ 2 = 1 remainder 0
- Divide the hundreds part: 5 ÷ 2. Write how many times the divisor goes in, and carry the remainder to the next column.5 ÷ 2 = 2 remainder 1
- Divide the tens part: 11 ÷ 2. Write how many times the divisor goes in, and carry the remainder to the next column.11 ÷ 2 = 5 remainder 1
- Divide the ones part: 17 ÷ 2. Write how many times the divisor goes in, and carry the remainder to the next column.17 ÷ 2 = 8 remainder 1
- Write the answer. 1,258 remainder 1
Check. 1,258 × 2 + 1 = 2,517. ✓
9
FWork out 1,903 ÷ 4. Give the remainder.
475 remainder 3
Method. Divide one digit at a time, carrying the remainder.
- Divide the thousands part: 1 ÷ 4. Write how many times the divisor goes in, and carry the remainder to the next column.1 ÷ 4 = 0 remainder 1
- Divide the hundreds part: 19 ÷ 4. Write how many times the divisor goes in, and carry the remainder to the next column.19 ÷ 4 = 4 remainder 3
- Divide the tens part: 30 ÷ 4. Write how many times the divisor goes in, and carry the remainder to the next column.30 ÷ 4 = 7 remainder 2
- Divide the ones part: 23 ÷ 4. Write how many times the divisor goes in, and carry the remainder to the next column.23 ÷ 4 = 5 remainder 3
- Write the answer. 475 remainder 3
Check. 475 × 4 + 3 = 1,903. ✓
10
PS47 eggs are packed into boxes of 6. How many full boxes are there, and how many eggs are left over?
7 full boxes, and 5 eggs left over
Method. Divide the eggs by 6. The full boxes are the quotient and the left over eggs are the remainder.
- Divide the tens part: 4 ÷ 6. Write how many times the divisor goes in, and carry the remainder to the next column.4 ÷ 6 = 0 remainder 4
- Divide the ones part: 47 ÷ 6. Write how many times the divisor goes in, and carry the remainder to the next column.47 ÷ 6 = 7 remainder 5
- Write the answer. 7 full boxes, and 5 eggs left over
Check. 7 × 6 + 5 = 47. ✓
11
PSA baker packs 500 biscuits into packs of 7. How many full packs are there, and how many biscuits are left?
71 full packs, and 3 biscuits left
Method. Divide, and keep the remainder.
- Divide the hundreds part: 5 ÷ 7. Write how many times the divisor goes in, and carry the remainder to the next column.5 ÷ 7 = 0 remainder 5
- Divide the tens part: 50 ÷ 7. Write how many times the divisor goes in, and carry the remainder to the next column.50 ÷ 7 = 7 remainder 1
- Divide the ones part: 10 ÷ 7. Write how many times the divisor goes in, and carry the remainder to the next column.10 ÷ 7 = 1 remainder 3
- Write the answer. 71 full packs, and 3 biscuits left
Check. 71 × 7 + 3 = 500. ✓
12
RSam says 60 ÷ 9 = 5 remainder 15. Explain why this is wrong, and write the correct answer.
Accept any answer that says the remainder 15 is too big because it must be less than 9, and gives 6 remainder 6. For example: The remainder must be less than 9. The answer is 6 remainder 6, because 9 × 6 = 54 and 60 - 54 = 6.
Method. Check that the remainder is smaller than the number you divide by.
- Check the remainder. The remainder 15 is bigger than 9, so it is impossible.15 > 9
- Divide again. 9 × 6 = 54, and 60 - 54 = 6.60 ÷ 9 = 6 remainder 6
- Write the answer. The remainder must be less than 9. The answer is 6 remainder 6, because 9 × 6 = 54 and 60 - 54 = 6.
Check. 6 × 9 + 6 = 60. ✓