Step-by-step Maths Level 5: Short division with no remainder
Part of the Step-by-step Maths Level 5 short division with remainders chapter. Chapter overview · whole chapter on one page
Short division with no remainder
Short division shares a number into equal groups, one column at a time. Start with the tens. Share the tens into groups, then bring down the ones and share them too.
In 68 ÷ 4, 6 tens shared into groups of 4 make 1 ten each with 2 tens left, and so on.
Key ideas
- Share the tens first, then the ones.
- Write each answer above its column.
- A remainder is what is left at the end.
Method. Use the short method. Share the tens first, then the ones with what is left.
- Share the tens. Share the 6 tens into groups of 4.6 ÷ 4 = 1 r 2
- Bring down the ones. The tens left over become ten ones each.2 tens and 8 ones = 28
- Share 28 into groups of 4. How many groups of 4 are in 28?28 ÷ 4 = 7 r 0
- Write the answer. The remainder is what is left over; write it after the answer.17
Check. Check: 17 × 4 + 0 = 68.
Watch out. The remainder must be smaller than the number you divide by.
Method. Use the short method. Share the tens first, then the ones with what is left.
- Share the tens. Share the 8 tens into groups of 6.8 ÷ 6 = 1 r 2
- Bring down the ones. The tens left over become ten ones each.2 tens and 4 ones = 24
- Share 24 into groups of 6. How many groups of 6 are in 24?24 ÷ 6 = 4 r 0
- Write the answer. The remainder is what is left over; write it after the answer.14
Check. Check: 14 × 6 + 0 = 84.
Watch out. The remainder must be smaller than the number you divide by.
Method. Divide, then check: answer × divisor + remainder = the number we started with.
- Find how many groups of 5 are in 47. Use the times table of the divisor.9 groups of 5 = 45
- Find what is left over. The remainder is the number left after the groups.47 - 45 = 2
- Check with multiplication and addition. Multiply the answer by the divisor, then add the remainder.9 × 5 + 2 = 45 + 2 = 47
- Write the answer. This is the answer with its remainder.9 remainder 2
Check. Check: 9 × 5 + 2 = 47.
Watch out. If the check does not give the number you started with, divide again.
Watch out
Watch out. Do not divide the ones before the tens. Start from the left, with the tens.
Exam tip
Grown-up tip. Ask the child to use the times table first: “How many 4s make 68?” before they use the layout.
Exercise 5A Practice: short division, no remainder
Non-calculatorMethod. Use the short method. Share the tens first, then the ones with what is left.
- Share the tens. Share the 4 tens into groups of 3.4 ÷ 3 = 1 r 1
- Bring down the ones. The tens left over become ten ones each.1 tens and 8 ones = 18
- Share 18 into groups of 3. How many groups of 3 are in 18?18 ÷ 3 = 6 r 0
- Write the answer. The remainder is what is left over; write it after the answer.16
Check. Check: 16 × 3 + 0 = 48.
Watch out. The remainder must be smaller than the number you divide by.
Method. Use the short method. Share the tens first, then the ones with what is left.
- The tens are fewer than the number of groups. 4 tens cannot make a group of 5 on their own, so use all of 40.40 is the number to share
- Share 40 into groups of 5. How many groups of 5 are in 40?40 ÷ 5 = 8 r 0
- Write the answer. The remainder is what is left over; write it after the answer.8
Check. Check: 8 × 5 + 0 = 40.
Watch out. The remainder must be smaller than the number you divide by.
Method. Use the short method. Share the tens first, then the ones with what is left.
- Share the tens. Share the 7 tens into groups of 2.7 ÷ 2 = 3 r 1
- Bring down the ones. The tens left over become ten ones each.1 tens and 2 ones = 12
- Share 12 into groups of 2. How many groups of 2 are in 12?12 ÷ 2 = 6 r 0
- Write the answer. The remainder is what is left over; write it after the answer.36
Check. Check: 36 × 2 + 0 = 72.
Watch out. The remainder must be smaller than the number you divide by.
Method. Use the short method. Share the tens first, then the ones with what is left.
- Share the tens. Share the 7 tens into groups of 6.7 ÷ 6 = 1 r 1
- Bring down the ones. The tens left over become ten ones each.1 tens and 8 ones = 18
- Share 18 into groups of 6. How many groups of 6 are in 18?18 ÷ 6 = 3 r 0
- Write the answer. The remainder is what is left over; write it after the answer.13
Check. Check: 13 × 6 + 0 = 78.
Watch out. The remainder must be smaller than the number you divide by.
Method. Use the short method. Share the tens first, then the ones with what is left.
- The tens are fewer than the number of groups. 2 tens cannot make a group of 6 on their own, so use all of 24.24 is the number to share
- Share 24 into groups of 6. How many groups of 6 are in 24?24 ÷ 6 = 4 r 0
- Write the answer. The remainder is what is left over; write it after the answer.4
Check. Check: 4 × 6 + 0 = 24.
Watch out. The remainder must be smaller than the number you divide by.
Method. Use the short method. Share the tens first, then the ones with what is left.
- The tens are fewer than the number of groups. 6 tens cannot make a group of 9 on their own, so use all of 63.63 is the number to share
- Share 63 into groups of 9. How many groups of 9 are in 63?63 ÷ 9 = 7 r 0
- Write the answer. The remainder is what is left over; write it after the answer.7
Check. Check: 7 × 9 + 0 = 63.
Watch out. The remainder must be smaller than the number you divide by.
Method. Use the short method. Share the tens first, then the ones with what is left.
- Share the tens. Share the 9 tens into groups of 3.9 ÷ 3 = 3 r 0
- Bring down the ones. The tens left over become ten ones each.0 tens and 0 ones = 0
- Share 0 into groups of 3. How many groups of 3 are in 0?0 ÷ 3 = 0 r 0
- Write the answer. The remainder is what is left over; write it after the answer.30
Check. Check: 30 × 3 + 0 = 90.
Watch out. The remainder must be smaller than the number you divide by.
Method. Use the short method. Share the tens first, then the ones with what is left.
- Share the tens. Share the 9 tens into groups of 8.9 ÷ 8 = 1 r 1
- Bring down the ones. The tens left over become ten ones each.1 tens and 6 ones = 16
- Share 16 into groups of 8. How many groups of 8 are in 16?16 ÷ 8 = 2 r 0
- Write the answer. The remainder is what is left over; write it after the answer.12
Check. Check: 12 × 8 + 0 = 96.
Watch out. The remainder must be smaller than the number you divide by.
Method. Use the short method. Share the tens first, then the ones with what is left.
- The tens are fewer than the number of groups. 5 tens cannot make a group of 9 on their own, so use all of 54.54 is the number to share
- Share 54 into groups of 9. How many groups of 9 are in 54?54 ÷ 9 = 6 r 0
- Write the answer. The remainder is what is left over; write it after the answer.6
Check. Check: 6 × 9 + 0 = 54.
Watch out. The remainder must be smaller than the number you divide by.
Method. Use the short method. Share the tens first, then the ones with what is left.
- The tens are fewer than the number of groups. 1 tens cannot make a group of 9 on their own, so use all of 18.18 is the number to share
- Share 18 into groups of 9. How many groups of 9 are in 18?18 ÷ 9 = 2 r 0
- Write the answer. The remainder is what is left over; write it after the answer.2
Check. Check: 2 × 9 + 0 = 18.
Watch out. The remainder must be smaller than the number you divide by.
Method. Use the short method. Share the tens first, then the ones with what is left.
- Share the tens. Share the 4 tens into groups of 3.4 ÷ 3 = 1 r 1
- Bring down the ones. The tens left over become ten ones each.1 tens and 2 ones = 12
- Share 12 into groups of 3. How many groups of 3 are in 12?12 ÷ 3 = 4 r 0
- Write the answer. The remainder is what is left over; write it after the answer.14
Check. Check: 14 × 3 + 0 = 42.
Watch out. The remainder must be smaller than the number you divide by.
Method. Use the short method. Share the tens first, then the ones with what is left.
- Share the tens. Share the 5 tens into groups of 5.5 ÷ 5 = 1 r 0
- Bring down the ones. The tens left over become ten ones each.0 tens and 0 ones = 0
- Share 0 into groups of 5. How many groups of 5 are in 0?0 ÷ 5 = 0 r 0
- Write the answer. The remainder is what is left over; write it after the answer.10
Check. Check: 10 × 5 + 0 = 50.
Watch out. The remainder must be smaller than the number you divide by.
Method. Use the short method. Share the tens first, then the ones with what is left.
- The tens are fewer than the number of groups. 6 tens cannot make a group of 8 on their own, so use all of 64.64 is the number to share
- Share 64 into groups of 8. How many groups of 8 are in 64?64 ÷ 8 = 8 r 0
- Write the answer. The remainder is what is left over; write it after the answer.8
Check. Check: 8 × 8 + 0 = 64.
Watch out. The remainder must be smaller than the number you divide by.
Method. Use the short method. Share the tens first, then the ones with what is left.
- Share the tens. Share the 8 tens into groups of 8.8 ÷ 8 = 1 r 0
- Bring down the ones. The tens left over become ten ones each.0 tens and 0 ones = 0
- Share 0 into groups of 8. How many groups of 8 are in 0?0 ÷ 8 = 0 r 0
- Write the answer. The remainder is what is left over; write it after the answer.10
Check. Check: 10 × 8 + 0 = 80.
Watch out. The remainder must be smaller than the number you divide by.
Method. Use the short method. Share the tens first, then the ones with what is left.
- Share the tens. Share the 8 tens into groups of 8.8 ÷ 8 = 1 r 0
- Bring down the ones. The tens left over become ten ones each.0 tens and 8 ones = 8
- Share 8 into groups of 8. How many groups of 8 are in 8?8 ÷ 8 = 1 r 0
- Write the answer. The remainder is what is left over; write it after the answer.11
Check. Check: 11 × 8 + 0 = 88.
Watch out. The remainder must be smaller than the number you divide by.
Method. Use the short method. Share the tens first, then the ones with what is left.
- Share the tens. Share the 7 tens into groups of 5.7 ÷ 5 = 1 r 2
- Bring down the ones. The tens left over become ten ones each.2 tens and 0 ones = 20
- Share 20 into groups of 5. How many groups of 5 are in 20?20 ÷ 5 = 4 r 0
- Write the answer. The remainder is what is left over; write it after the answer.14
Check. Check: 14 × 5 + 0 = 70.
Watch out. The remainder must be smaller than the number you divide by.