Year 6: Long division with two-digit divisors
Part of the Year 6 long multiplication, long division and bodmas chapter. Chapter overview · whole chapter on one page
Long division with two-digit divisors
In long division we share a number into equal groups, one digit of the answer at a time. First find how many times the divisor fits into the first digits. Write that digit on top. Multiply it by the divisor and subtract. Then bring down the next digit and repeat.
Sometimes a number does not share out exactly. The part left over is the remainder. A remainder must always be smaller than the divisor. What you do with the remainder depends on the problem: you might write it as a whole number, as a fraction, or round the answer up or down.
Key ideas
- Long division is repeated subtraction, written neatly. Each digit of the answer is worked out with multiplication.
- Estimate the first digit by thinking about the divisor. Round it to a friendly number, such as 23 is about 20.
- The remainder is always smaller than the divisor. If it is not, the answer is one more group.
- Check with multiplication: divisor × quotient + remainder = the number you started with.
- Decide what the remainder means: round up (for example, buses needed), round down (full boxes), or write it as a fraction (sharing).
Key words. In long division, the dividend is the number being divided, the divisor is the number we divide by, the quotient is the answer and the remainder is what is left over.
Method. Set out the division. Find how many times the divisor fits into the first part of the number, write that digit on top, subtract, and bring down the next digit.
- Find quotient digit 1. Start with the first digits that are big enough to hold the divisor.Use 204. How many 23s fit into 204? 8, because 23 × 8 = 184. Subtract: 204 − 184 = 20.
- Find quotient digit 2. Bring down the next digit and see how many times the divisor fits.Bring down the 8 to make 208. How many 23s fit into 208? 9, because 23 × 9 = 207. Subtract: 208 − 207 = 1.
- Write the answer. The quotient goes on top. The number left at the end is the remainder.
89 23 ) 2048 184 --- 20 207 --- 1
Answer 89 r 1
Check. 23 × 89 = 2,047, and 2,047 + 1 = 2,048. ✓
Watch out. Keep going until the number left is smaller than the divisor. A remainder must always be smaller than the divisor.
Key words. In long division, the dividend is the number being divided, the divisor is the number we divide by, the quotient is the answer and the remainder is what is left over.
Method. Set out the division. Find how many times the divisor fits into the first part of the number, write that digit on top, subtract, and bring down the next digit.
- Find quotient digit 1. Start with the first digits that are big enough to hold the divisor.Use 15. How many 14s fit into 15? 1, because 14 × 1 = 14. Subtract: 15 − 14 = 1.
- Find quotient digit 2. Bring down the next digit and see how many times the divisor fits.Bring down the 9 to make 19. How many 14s fit into 19? 1, because 14 × 1 = 14. Subtract: 19 − 14 = 5.
- Find quotient digit 3. Bring down the next digit and see how many times the divisor fits.Bring down the 7 to make 57. How many 14s fit into 57? 4, because 14 × 4 = 56. Subtract: 57 − 56 = 1.
- Write the answer. The quotient goes on top. The number left at the end is the remainder.
114 14 ) 1597 14 -- 1 14 -- 5 56 -- 1
Answer 114 r 1
Check. 14 × 114 = 1,596, and 1,596 + 1 = 1,597. ✓
Watch out. Keep going until the number left is smaller than the divisor. A remainder must always be smaller than the divisor.
Key words. In long division, the dividend is the number being divided, the divisor is the number we divide by, the quotient is the answer and the remainder is what is left over.
Method. Set out the division. Find how many times the divisor fits into the first part of the number, write that digit on top, subtract, and bring down the next digit.
- Find quotient digit 1. Start with the first digits that are big enough to hold the divisor.Use 50. How many 36s fit into 50? 1, because 36 × 1 = 36. Subtract: 50 − 36 = 14.
- Find quotient digit 2. Bring down the next digit and see how many times the divisor fits.Bring down the 0 to make 140. How many 36s fit into 140? 3, because 36 × 3 = 108. Subtract: 140 − 108 = 32.
- Find quotient digit 3. Bring down the next digit and see how many times the divisor fits.Bring down the 0 to make 320. How many 36s fit into 320? 8, because 36 × 8 = 288. Subtract: 320 − 288 = 32.
- Write the answer. The quotient goes on top. The number left at the end is the remainder.
138 36 ) 5000 36 -- 14 108 --- 32 288 --- 32
Answer 138 r 32
Check. 36 × 138 = 4,968, and 4,968 + 32 = 5,000. ✓
Watch out. Keep going until the number left is smaller than the divisor. A remainder must always be smaller than the divisor.
Watch out
Do not stop when you run out of digits. Keep going until the number left is smaller than the divisor. A remainder bigger than the divisor is always a mistake. Also, do not give the remainder before you have checked the answer with multiplication.Exercise 2B Long division and remainders
Non-calculatorKey words. In long division, the dividend is the number being divided, the divisor is the number we divide by, the quotient is the answer and the remainder is what is left over.
Method. Set out the division. Find how many times the divisor fits into the first part of the number, write that digit on top, subtract, and bring down the next digit.
- Find quotient digit 1. Start with the first digits that are big enough to hold the divisor.Use 136. How many 15s fit into 136? 9, because 15 × 9 = 135. Subtract: 136 − 135 = 1.
- Find quotient digit 2. Bring down the next digit and see how many times the divisor fits.Bring down the 5 to make 15. How many 15s fit into 15? 1, because 15 × 1 = 15. Subtract: 15 − 15 = 0.
- Write the answer. The quotient goes on top. The number left at the end is the remainder.
91 15 ) 1365 135 --- 1 15 -- 0
Answer 91
Check. 15 × 91 = 1,365, with no remainder. ✓
Watch out. Keep going until the number left is smaller than the divisor. A remainder must always be smaller than the divisor.
Key words. In long division, the dividend is the number being divided, the divisor is the number we divide by, the quotient is the answer and the remainder is what is left over.
Method. Set out the division. Find how many times the divisor fits into the first part of the number, write that digit on top, subtract, and bring down the next digit.
- Find quotient digit 1. Start with the first digits that are big enough to hold the divisor.Use 172. How many 24s fit into 172? 7, because 24 × 7 = 168. Subtract: 172 − 168 = 4.
- Find quotient digit 2. Bring down the next digit and see how many times the divisor fits.Bring down the 8 to make 48. How many 24s fit into 48? 2, because 24 × 2 = 48. Subtract: 48 − 48 = 0.
- Write the answer. The quotient goes on top. The number left at the end is the remainder.
72 24 ) 1728 168 --- 4 48 -- 0
Answer 72
Check. 24 × 72 = 1,728, with no remainder. ✓
Watch out. Keep going until the number left is smaller than the divisor. A remainder must always be smaller than the divisor.
Key words. In long division, the dividend is the number being divided, the divisor is the number we divide by, the quotient is the answer and the remainder is what is left over.
Method. Set out the division. Find how many times the divisor fits into the first part of the number, write that digit on top, subtract, and bring down the next digit.
- Find quotient digit 1. Start with the first digits that are big enough to hold the divisor.Use 264. How many 32s fit into 264? 8, because 32 × 8 = 256. Subtract: 264 − 256 = 8.
- Find quotient digit 2. Bring down the next digit and see how many times the divisor fits.Bring down the 0 to make 80. How many 32s fit into 80? 2, because 32 × 2 = 64. Subtract: 80 − 64 = 16.
- Write the answer. The quotient goes on top. The number left at the end is the remainder.
82 32 ) 2640 256 --- 8 64 -- 16
Answer 82 r 16
Check. 32 × 82 = 2,624, and 2,624 + 16 = 2,640. ✓
Watch out. Keep going until the number left is smaller than the divisor. A remainder must always be smaller than the divisor.
Key words. In long division, the dividend is the number being divided, the divisor is the number we divide by, the quotient is the answer and the remainder is what is left over.
Method. Set out the division. Find how many times the divisor fits into the first part of the number, write that digit on top, subtract, and bring down the next digit.
- Find quotient digit 1. Start with the first digits that are big enough to hold the divisor.Use 34. How many 17s fit into 34? 2, because 17 × 2 = 34. Subtract: 34 − 34 = 0.
- Find quotient digit 2. Bring down the next digit and see how many times the divisor fits.Bring down the 1 to make 1. How many 17s fit into 1? 0, because 17 × 0 = 0. Subtract: 1 − 0 = 1.
- Find quotient digit 3. Bring down the next digit and see how many times the divisor fits.Bring down the 2 to make 12. How many 17s fit into 12? 0, because 17 × 0 = 0. Subtract: 12 − 0 = 12.
- Write the answer. The quotient goes on top. The number left at the end is the remainder.
200 17 ) 3412 34 -- 0 0 - 1 0 - 12
Answer 200 r 12
Check. 17 × 200 = 3,400, and 3,400 + 12 = 3,412. ✓
Watch out. Keep going until the number left is smaller than the divisor. A remainder must always be smaller than the divisor.
Key words. In long division, the dividend is the number being divided, the divisor is the number we divide by, the quotient is the answer and the remainder is what is left over.
Method. Set out the division. Find how many times the divisor fits into the first part of the number, write that digit on top, subtract, and bring down the next digit.
- Find quotient digit 1. Start with the first digits that are big enough to hold the divisor.Use 45. How many 45s fit into 45? 1, because 45 × 1 = 45. Subtract: 45 − 45 = 0.
- Find quotient digit 2. Bring down the next digit and see how many times the divisor fits.Bring down the 0 to make 0. How many 45s fit into 0? 0, because 45 × 0 = 0. Subtract: 0 − 0 = 0.
- Find quotient digit 3. Bring down the next digit and see how many times the divisor fits.Bring down the 0 to make 0. How many 45s fit into 0? 0, because 45 × 0 = 0. Subtract: 0 − 0 = 0.
- Write the answer. The quotient goes on top. The number left at the end is the remainder.
100 45 ) 4500 45 -- 0 0 - 0 0 - 0
Answer 100
Check. 45 × 100 = 4,500, with no remainder. ✓
Watch out. Keep going until the number left is smaller than the divisor. A remainder must always be smaller than the divisor.
Key words. In long division, the dividend is the number being divided, the divisor is the number we divide by, the quotient is the answer and the remainder is what is left over.
Method. Set out the division. Find how many times the divisor fits into the first part of the number, write that digit on top, subtract, and bring down the next digit.
- Find quotient digit 1. Start with the first digits that are big enough to hold the divisor.Use 209. How many 26s fit into 209? 8, because 26 × 8 = 208. Subtract: 209 − 208 = 1.
- Find quotient digit 2. Bring down the next digit and see how many times the divisor fits.Bring down the 7 to make 17. How many 26s fit into 17? 0, because 26 × 0 = 0. Subtract: 17 − 0 = 17.
- Write the answer. The quotient goes on top. The number left at the end is the remainder.
80 26 ) 2097 208 --- 1 0 - 17
Answer 80 r 17
Check. 26 × 80 = 2,080, and 2,080 + 17 = 2,097. ✓
Watch out. Keep going until the number left is smaller than the divisor. A remainder must always be smaller than the divisor.
Key words. In long division, the dividend is the number being divided, the divisor is the number we divide by, the quotient is the answer and the remainder is what is left over.
Method. Set out the division. Find how many times the divisor fits into the first part of the number, write that digit on top, subtract, and bring down the next digit.
- Find quotient digit 1. Start with the first digits that are big enough to hold the divisor.Use 68. How many 43s fit into 68? 1, because 43 × 1 = 43. Subtract: 68 − 43 = 25.
- Find quotient digit 2. Bring down the next digit and see how many times the divisor fits.Bring down the 3 to make 253. How many 43s fit into 253? 5, because 43 × 5 = 215. Subtract: 253 − 215 = 38.
- Find quotient digit 3. Bring down the next digit and see how many times the divisor fits.Bring down the 9 to make 389. How many 43s fit into 389? 9, because 43 × 9 = 387. Subtract: 389 − 387 = 2.
- Write the answer. The quotient goes on top. The number left at the end is the remainder.
159 43 ) 6839 43 -- 25 215 --- 38 387 --- 2
Answer 159 r 2
Check. 43 × 159 = 6,837, and 6,837 + 2 = 6,839. ✓
Watch out. Keep going until the number left is smaller than the divisor. A remainder must always be smaller than the divisor.
Method. Divide the total by the group size. Then decide what the remainder means in this problem.
- Divide the total by the size of each group. 100 ÷ 14 gives 7 with 2 left over.100 ÷ 14 = 7 remainder 2
- Decide what to do with the remainder. The 2 left over still need a minibus, so we round up.7 + 1 = 8
- Write the answer with a unit. 8 minibuses
Check. 14 × 7 = 98, and 98 + 2 = 100. ✓
Watch out. The answer depends on the story. Ask: does the remainder still need a group, or is it thrown away?
Method. Divide the total by the group size. Then decide what the remainder means in this problem.
- Divide the total by the size of each group. 500 ÷ 12 gives 41 with 8 left over.500 ÷ 12 = 41 remainder 8
- Decide what to do with the remainder. The 8 left over are not enough for one more full group, so we round down.41 full boxes
- Write the answer with a unit. 41 full boxes
Check. 12 × 41 = 492, and 492 + 8 = 500. ✓
Watch out. The answer depends on the story. Ask: does the remainder still need a group, or is it thrown away?
Method. Divide the total by the group size. Then decide what the remainder means in this problem.
- Divide the total by the size of each group. 500 ÷ 12 gives 41 with 8 left over.500 ÷ 12 = 41 remainder 8
- Write the remainder as a fraction. The remainder is shared as well, so write 8 out of 12 and simplify it.8/12 = 2/3, so the answer is 41 2/3
- Write the answer with a unit. 41 2/3 stickers each
Check. 12 × 41 = 492, and 492 + 8 = 500. ✓
Watch out. The answer depends on the story. Ask: does the remainder still need a group, or is it thrown away?
Method. Work in pence, then round to the nearest penny.
- Change £1,000 into pence. There are 100 pence in every pound.£1,000 = 100,000p
- Divide by 36 and find the remainder. Share the pence equally.100,000 ÷ 36 = 2,777 remainder 28
- Find the answer to the nearest penny. 28 out of 36 is 0.78 of a penny, which is more than half, so round up.2,777.78p rounds to 2,778p
- Write the answer in pounds. Divide by 100 to change pence into pounds.2,778p = £27.78
Check. 36 × £27.78 is about £1,000. ✓
Watch out. Give money to the nearest penny, with two figures after the point, for example £27.78.
Method. Check Ruby's working by multiplying the divisor by her quotient, then adding her remainder.
- Check the multiplication. Multiply 12 by 40.12 × 40 = 480
- Find the remainder. Subtract 480 from 500.500 − 480 = 20
- Check the remainder. The remainder must be smaller than 12. Here it is 20, which is too big, so we can take another 12 away.20 is bigger than 12, so 20 − 12 = 8
- Count the groups. We took one more group of 12, so the quotient goes up by 1.40 + 1 = 41, and the remainder is 8
Check. 12 × 41 = 492, and 492 + 8 = 500. ✓
Watch out. A remainder must be smaller than the divisor. If it is not, you can take another group away.
Method. Check Sam's answer by multiplying the divisor by the quotient, then adding the remainder.
- Multiply the divisor by the quotient. Work out 12 × 41.12 × 41 = 492
- Add the remainder. Add the remainder to the answer from the first step.492 + 8 = 500
- Check the remainder is small enough. The remainder must be smaller than the divisor.8 is smaller than 12. ✓
Check. Sam is right because the check gives 500 and the remainder is smaller than 12.
Watch out. Both checks must pass: the total must be right, and the remainder must be small enough.
Key words. In long division, the dividend is the number being divided, the divisor is the number we divide by, the quotient is the answer and the remainder is what is left over.
Method. Set out the division. Find how many times the divisor fits into the first part of the number, write that digit on top, subtract, and bring down the next digit.
- Find quotient digit 1. Start with the first digits that are big enough to hold the divisor.Use 98. How many 12s fit into 98? 8, because 12 × 8 = 96. Subtract: 98 − 96 = 2.
- Find quotient digit 2. Bring down the next digit and see how many times the divisor fits.Bring down the 7 to make 27. How many 12s fit into 27? 2, because 12 × 2 = 24. Subtract: 27 − 24 = 3.
- Find quotient digit 3. Bring down the next digit and see how many times the divisor fits.Bring down the 6 to make 36. How many 12s fit into 36? 3, because 12 × 3 = 36. Subtract: 36 − 36 = 0.
- Write the answer. The quotient goes on top. The number left at the end is the remainder.
823 12 ) 9876 96 -- 2 24 -- 3 36 -- 0
Answer 823
Check. 12 × 823 = 9,876, with no remainder. ✓
Watch out. Keep going until the number left is smaller than the divisor. A remainder must always be smaller than the divisor.
Method. Use the quotient and remainder to find the number. Multiply the quotient by the divisor, then add the remainder.
- Multiply the quotient by the divisor. The quotient is 38 and the divisor is 25.38 × 25 = 950
- Add the remainder. The remainder is what is left over after the groups are taken away.950 + 17 = 967
- Check by dividing. Divide the number by 25. You should get 38 remainder 17.
38 25 ) 967 75 -- 21 200 --- 17
Check. 967 ÷ 25 = 38 remainder 17. ✓
Watch out. Do not just add the quotient and the remainder. Multiply the quotient by the divisor first.