Step-by-step Maths Level 5: Writing a remainder
Part of the Step-by-step Maths Level 5 short division with remainders chapter. Chapter overview · whole chapter on one page
Writing a remainder
Sometimes the number does not share exactly. The part left over is the remainder. Write it after the answer: 47 ÷ 5 = 9 remainder 2.
The remainder is always smaller than the number you divide by.
Key ideas
- Write the answer as: whole number remainder the amount left.
- The remainder must be smaller than the divisor.
- If there is no remainder, write the whole number only.
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 47.47 is the number to share
- Share 47 into groups of 5. How many groups of 5 are in 47?47 ÷ 5 = 9 r 2
- Write the answer. The remainder is what is left over; write it after the answer.9 remainder 2
Check. Check: 9 × 5 + 2 = 47.
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. 7 tens cannot make a group of 8 on their own, so use all of 73.73 is the number to share
- Share 73 into groups of 8. How many groups of 8 are in 73?73 ÷ 8 = 9 r 1
- Write the answer. The remainder is what is left over; write it after the answer.9 remainder 1
Check. Check: 9 × 8 + 1 = 73.
Watch out. The remainder must be smaller than the number you divide by.
Method. Check with multiplication and addition: groups × divisor + remainder must equal the number, and the remainder must be smaller than the divisor.
- Multiply the whole number of groups by the divisor, then add the remainder. Check with multiplication and addition.9 × 5 + 2 = 47
- Compare with 47. The result must be 47, and the remainder must be smaller than 5.47 is the same as 47; 2 is smaller than 5
- Write Yes or No. Yes if the check works; No if it does not.Yes
Check. The correct answer is 9 remainder 2.
Watch out. A remainder that is as big as the divisor means the answer is wrong. Find the mistake if the check does not work.
Watch out
Watch out. A remainder of 5 or more when dividing by 5 means the answer is wrong. Share one more group.
Exam tip
Grown-up tip. Ask: “Is the remainder smaller than the number you divided by?”
Exercise 5B Practice: writing a remainder
Non-calculatorMethod. 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 8 on their own, so use all of 20.20 is the number to share
- Share 20 into groups of 8. How many groups of 8 are in 20?20 ÷ 8 = 2 r 4
- Write the answer. The remainder is what is left over; write it after the answer.2 remainder 4
Check. Check: 2 × 8 + 4 = 20.
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 6 tens into groups of 3.6 ÷ 3 = 2 r 0
- Bring down the ones. The tens left over become ten ones each.0 tens and 4 ones = 4
- Share 4 into groups of 3. How many groups of 3 are in 4?4 ÷ 3 = 1 r 1
- Write the answer. The remainder is what is left over; write it after the answer.21 remainder 1
Check. Check: 21 × 3 + 1 = 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 7 tens into groups of 4.7 ÷ 4 = 1 r 3
- Bring down the ones. The tens left over become ten ones each.3 tens and 1 ones = 31
- Share 31 into groups of 4. How many groups of 4 are in 31?31 ÷ 4 = 7 r 3
- Write the answer. The remainder is what is left over; write it after the answer.17 remainder 3
Check. Check: 17 × 4 + 3 = 71.
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 6 tens into groups of 6.6 ÷ 6 = 1 r 0
- Bring down the ones. The tens left over become ten ones each.0 tens and 3 ones = 3
- Share 3 into groups of 6. How many groups of 6 are in 3?3 ÷ 6 = 0 r 3
- Write the answer. The remainder is what is left over; write it after the answer.10 remainder 3
Check. Check: 10 × 6 + 3 = 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.
- The tens are fewer than the number of groups. 1 tens cannot make a group of 4 on their own, so use all of 11.11 is the number to share
- Share 11 into groups of 4. How many groups of 4 are in 11?11 ÷ 4 = 2 r 3
- Write the answer. The remainder is what is left over; write it after the answer.2 remainder 3
Check. Check: 2 × 4 + 3 = 11.
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 6 tens into groups of 6.6 ÷ 6 = 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 6. How many groups of 6 are in 8?8 ÷ 6 = 1 r 2
- Write the answer. The remainder is what is left over; write it after the answer.11 remainder 2
Check. Check: 11 × 6 + 2 = 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.
- The tens are fewer than the number of groups. 5 tens cannot make a group of 7 on their own, so use all of 54.54 is the number to share
- Share 54 into groups of 7. How many groups of 7 are in 54?54 ÷ 7 = 7 r 5
- Write the answer. The remainder is what is left over; write it after the answer.7 remainder 5
Check. Check: 7 × 7 + 5 = 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.
- 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 7 ones = 17
- Share 17 into groups of 6. How many groups of 6 are in 17?17 ÷ 6 = 2 r 5
- Write the answer. The remainder is what is left over; write it after the answer.12 remainder 5
Check. Check: 12 × 6 + 5 = 77.
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 7 ones = 7
- Share 7 into groups of 8. How many groups of 8 are in 7?7 ÷ 8 = 0 r 7
- Write the answer. The remainder is what is left over; write it after the answer.10 remainder 7
Check. Check: 10 × 8 + 7 = 87.
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 7.7 ÷ 7 = 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 7. How many groups of 7 are in 8?8 ÷ 7 = 1 r 1
- Write the answer. The remainder is what is left over; write it after the answer.11 remainder 1
Check. Check: 11 × 7 + 1 = 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.
- 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 0 ones = 10
- Share 10 into groups of 3. How many groups of 3 are in 10?10 ÷ 3 = 3 r 1
- Write the answer. The remainder is what is left over; write it after the answer.13 remainder 1
Check. Check: 13 × 3 + 1 = 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 7.7 ÷ 7 = 1 r 0
- Bring down the ones. The tens left over become ten ones each.0 tens and 3 ones = 3
- Share 3 into groups of 7. How many groups of 7 are in 3?3 ÷ 7 = 0 r 3
- Write the answer. The remainder is what is left over; write it after the answer.10 remainder 3
Check. Check: 10 × 7 + 3 = 73.
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 4.7 ÷ 4 = 1 r 3
- Bring down the ones. The tens left over become ten ones each.3 tens and 5 ones = 35
- Share 35 into groups of 4. How many groups of 4 are in 35?35 ÷ 4 = 8 r 3
- Write the answer. The remainder is what is left over; write it after the answer.18 remainder 3
Check. Check: 18 × 4 + 3 = 75.
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 6 tens into groups of 5.6 ÷ 5 = 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 5. How many groups of 5 are in 16?16 ÷ 5 = 3 r 1
- Write the answer. The remainder is what is left over; write it after the answer.13 remainder 1
Check. Check: 13 × 5 + 1 = 66.
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 9 ones = 19
- Share 19 into groups of 2. How many groups of 2 are in 19?19 ÷ 2 = 9 r 1
- Write the answer. The remainder is what is left over; write it after the answer.39 remainder 1
Check. Check: 39 × 2 + 1 = 79.
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 4.8 ÷ 4 = 2 r 0
- Bring down the ones. The tens left over become ten ones each.0 tens and 3 ones = 3
- Share 3 into groups of 4. How many groups of 4 are in 3?3 ÷ 4 = 0 r 3
- Write the answer. The remainder is what is left over; write it after the answer.20 remainder 3
Check. Check: 20 × 4 + 3 = 83.
Watch out. The remainder must be smaller than the number you divide by.