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Step-by-step practice: Maths · Level 4Chapter 3 · Column addition and subtraction
Level 4 · Chapter 3

Column addition and subtraction

By the end of this chapter you will be able to

  • Add and subtract a multiple of 10, 100 or 1000 in your head
  • Add two four-digit numbers in columns with carrying
  • Subtract two four-digit numbers in columns with exchange
  • Subtract across a zero in the middle
  • Estimate, check by the inverse, and find missing numbers

You should already know

  • Column addition and subtraction to 1000 (Level 3, chapters 4 and 5)
  • Place value to 10000 (chapter 1)
  • Rounding to 1000 (chapter 2)

Where this leads

  • Times tables 3 and 4 (chapter 4)

Step-by-step practice: maths (Level 4). Small steps, repeated until fluent. Content: Add and subtract mentally a four-digit number and ones, tens or hundreds (AS1), Add and subtract up to four digits in columns, exchanging across two or more places (AS2), Estimate the answer and check it with the inverse operation (AS3), Solve missing number problems with four-digit numbers (AS4).

Exercise P  Do you remember?

Non-calculator
1
FWhat is 4 + 6 + 3?
2
FWork out 48 + 35.
3
FWork out 200 - 45.
4
FWhat is 10 less than 500?
5
FWork out 7 x 3.
3.1

Adding and subtracting in your head

Level 4
Add and subtract mentally a four-digit number and a ones, tens or hundreds number
Video lesson: Adding and subtracting in your headComing soon

When you add or take away a ten, a hundred or a thousand, only one column changes.

Look at the column that matches the number you are adding or taking away. Change that digit only.

Key ideas

  • Adding 10, 100 or 1000 changes one column.
  • Take away in the same column.
  • Check the other digits are the same.
Worked example 3.1.1
Work out 3275 + 400.

Method. Change only the column that matches the number you add or take away.

  1. Find the hundred digit in 3275. Only the hundred column changes, because 400 is 4 hundreds.
    3275 has 2 hundreds
  2. Add 4 hundreds. Change that digit only. The other digits stay the same.
    2 + 4 = 6
  3. Write the answer. Check that the other digits are the same.
    3675

Check. Check: 3675 - 400 = 3275.

Watch out. Adding or taking away a friendly number changes only one column, when no carry or exchange is needed.

Worked example 3.1.2
Work out 6450 - 300.

Method. Change only the column that matches the number you add or take away.

  1. Find the hundred digit in 6450. Only the hundred column changes, because 300 is 3 hundreds.
    6450 has 4 hundreds
  2. Take away 3 hundreds. Change that digit only. The other digits stay the same.
    4 - 3 = 1
  3. Write the answer. Check that the other digits are the same.
    6150

Check. Check: 6150 + 300 = 6450.

Watch out. Adding or taking away a friendly number changes only one column, when no carry or exchange is needed.

Worked example 3.1.3
Work out 6024 - 20.

Method. Change only the column that matches the number you add or take away.

  1. Find the ten digit in 6024. Only the ten column changes, because 20 is 2 tens.
    6024 has 2 tens
  2. Take away 2 tens. Change that digit only. The other digits stay the same.
    2 - 2 = 0
  3. Write the answer. Check that the other digits are the same.
    6004

Check. Check: 6004 + 20 = 6024.

Watch out. Adding or taking away a friendly number changes only one column, when no carry or exchange is needed.

Watch out

Watch out. 6024 - 20 is 6004, because only the tens change. Do not change the ones.

Exam tip

Grown-up tip. Ask: “Which column changes?” before the child works out the answer.

Exercise 3A  Practice: adding and subtracting in your head

Non-calculator
1
FWork out 5490 - 3000.
2
FWork out 6811 + 2000.
3
FWork out 8853 - 3000.
4
FWork out 2338 + 2000.
5
FWork out 5704 + 100.
6
FWork out 2861 + 20.
7
FWork out 7591 - 30.
8
FWork out 7918 + 50.
9
FWork out 7469 + 100.
10
FWork out 6650 - 400.
11
FWork out 9091 - 30.
12
FWork out 6856 + 765 in your head. Write the answer.
13
FWork out 9890 - 3000.
14
FWork out 8517 - 2000.
15
FWork out 8619 - 3000.
16
FWork out 2627 + 732 in your head. Write the answer.
3.2

Column addition with carrying

Level 4
Add two four-digit numbers in columns, carrying across the hundreds and the thousands
Video lesson: Column addition with carryingComing soon

Write the numbers in columns, with the thousands, hundreds, tens and ones lined up.

Add the ones first. If the total is 10 or more, write the ones digit and carry the ten to the tens column. Keep going to the thousands.

Key ideas

  • Line up the place value columns.
  • Add the ones first, then the tens, hundreds and thousands.
  • Carry 1 when a column is 10 or more.
Worked example 3.2.1
Work out 4826 + 2375.

Method. Add column by column, starting with the ones. Carry any ten to the next column on the left.

  1. Add the ones column. Add the digits, and the carried 1 if there is one.
    6 + 5 = 11: Write 1 and carry 1 to the next column.
  2. Add the tens column. Add the digits, and the carried 1 if there is one.
    2 + 7 + 1 = 10: Write 0 and carry 1 to the next column.
  3. Add the hundreds column. Add the digits, and the carried 1 if there is one.
    8 + 3 + 1 = 12: Write 2 and carry 1 to the next column.
  4. Add the thousands column. Add the digits, and the carried 1 if there is one.
    4 + 2 + 1 = 7: Write 7. There is nothing to carry.
  5. Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.
    7201

Check. Check: 7201 - 2375 = 4826.

Watch out. Do not forget the carried 1 in the next column. Write the carried 1 small above the column.

Worked example 3.2.2
Work out 3047 + 2596.

Method. Add column by column, starting with the ones. Carry any ten to the next column on the left.

  1. Add the ones column. Add the digits, and the carried 1 if there is one.
    7 + 6 = 13: Write 3 and carry 1 to the next column.
  2. Add the tens column. Add the digits, and the carried 1 if there is one.
    4 + 9 + 1 = 14: Write 4 and carry 1 to the next column.
  3. Add the hundreds column. Add the digits, and the carried 1 if there is one.
    0 + 5 + 1 = 6: Write 6. There is nothing to carry.
  4. Add the thousands column. Add the digits, and the carried 1 if there is one.
    3 + 2 = 5: Write 5. There is nothing to carry.
  5. Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.
    5643

Check. Check: 5643 - 2596 = 3047.

Watch out. Do not forget the carried 1 in the next column. Write the carried 1 small above the column.

Worked example 3.2.3
Work out 1859 + 6378.

Method. Add column by column, starting with the ones. Carry any ten to the next column on the left.

  1. Add the ones column. Add the digits, and the carried 1 if there is one.
    9 + 8 = 17: Write 7 and carry 1 to the next column.
  2. Add the tens column. Add the digits, and the carried 1 if there is one.
    5 + 7 + 1 = 13: Write 3 and carry 1 to the next column.
  3. Add the hundreds column. Add the digits, and the carried 1 if there is one.
    8 + 3 + 1 = 12: Write 2 and carry 1 to the next column.
  4. Add the thousands column. Add the digits, and the carried 1 if there is one.
    1 + 6 + 1 = 8: Write 8. There is nothing to carry.
  5. Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.
    8237

Check. Check: 8237 - 6378 = 1859.

Watch out. Do not forget the carried 1 in the next column. Write the carried 1 small above the column.

Watch out

Watch out. Do not forget the carried 1. In 2375 + 4826, the ones make 11, so carry 1 to the tens.

Exam tip

Grown-up tip. Ask the child to say the carry out loud: “Six and five is eleven, write one, carry one.”

Exercise 3B  Practice: column addition

Non-calculator
1
FWork out 5582 + 2005.
2
FWork out 6952 + 1270.
3
FWork out 8695 + 1126.
4
FWork out 5604 + 1240.
5
FWork out 3016 + 6627.
6
FWork out 3492 + 3430.
7
FWork out 1186 + 4407.
8
FWork out 3279 + 2863.
9
FWork out 4592 + 2513.
10
FWork out 6341 + 3438.
11
FWork out 4898 + 3908.
12
FWork out 6237 + 2242.
13
FWork out 2676 + 3078.
14
FWork out 6998 + 2266.
15
FWork out 7226 + 1968.
16
FWork out 8255 + 1044.
3.3

Column subtraction with exchange

Level 4
Subtract two four-digit numbers in columns, exchanging across two or more places
Video lesson: Column subtraction with exchangeComing soon

Subtract the ones first. If the top digit is too small, exchange 1 ten from the tens column for 10 ones.

If a column is too small, exchange again from the column on its left. Work from the ones to the thousands.

Key ideas

  • Work from the ones, column by column.
  • Exchange 1 from the column on the left when the top digit is too small.
  • Subtract the bottom digit from the top digit in each column.
Worked example 3.3.1
Work out 5271 - 2385.

Method. Subtract column by column from the ones. When the top digit is too small, exchange from the column on the left.

  1. Exchange in the tens column. The ones digit is too small, so exchange 1 ten for 10 ones.
    tens: 7 to 6; ones: 1 to 11
  2. Subtract the ones column. Take the bottom digit from the top digit.
    11 - 5 = 6
  3. Exchange in the hundreds column. The tens digit is too small, so exchange 1 hundred for 10 tens.
    hundreds: 2 to 1; tens: 6 to 16
  4. Subtract the tens column. Take the bottom digit from the top digit.
    16 - 8 = 8
  5. Exchange in the thousands column. The hundreds digit is too small, so exchange 1 thousand for 10 hundreds.
    thousands: 5 to 4; hundreds: 1 to 11
  6. Subtract the hundreds column. Take the bottom digit from the top digit.
    11 - 3 = 8
  7. Subtract the thousands column. Take the bottom digit from the top digit.
    4 - 2 = 2
  8. Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.
    2886

Check. Check: 2886 + 2385 = 5271.

Watch out. A zero cannot give a ten. Go left to the first column that is not zero, and exchange from there.

Worked example 3.3.2
Work out 3462 - 1875.

Method. Subtract column by column from the ones. When the top digit is too small, exchange from the column on the left.

  1. Exchange in the tens column. The ones digit is too small, so exchange 1 ten for 10 ones.
    tens: 6 to 5; ones: 2 to 12
  2. Subtract the ones column. Take the bottom digit from the top digit.
    12 - 5 = 7
  3. Exchange in the hundreds column. The tens digit is too small, so exchange 1 hundred for 10 tens.
    hundreds: 4 to 3; tens: 5 to 15
  4. Subtract the tens column. Take the bottom digit from the top digit.
    15 - 7 = 8
  5. Exchange in the thousands column. The hundreds digit is too small, so exchange 1 thousand for 10 hundreds.
    thousands: 3 to 2; hundreds: 3 to 13
  6. Subtract the hundreds column. Take the bottom digit from the top digit.
    13 - 8 = 5
  7. Subtract the thousands column. Take the bottom digit from the top digit.
    2 - 1 = 1
  8. Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.
    1587

Check. Check: 1587 + 1875 = 3462.

Watch out. A zero cannot give a ten. Go left to the first column that is not zero, and exchange from there.

Worked example 3.3.3
Work out 6135 - 2748.

Method. Subtract column by column from the ones. When the top digit is too small, exchange from the column on the left.

  1. Exchange in the tens column. The ones digit is too small, so exchange 1 ten for 10 ones.
    tens: 3 to 2; ones: 5 to 15
  2. Subtract the ones column. Take the bottom digit from the top digit.
    15 - 8 = 7
  3. Exchange in the hundreds column. The tens digit is too small, so exchange 1 hundred for 10 tens.
    hundreds: 1 to 0; tens: 2 to 12
  4. Subtract the tens column. Take the bottom digit from the top digit.
    12 - 4 = 8
  5. Exchange in the thousands column. The hundreds digit is too small, so exchange 1 thousand for 10 hundreds.
    thousands: 6 to 5; hundreds: 0 to 10
  6. Subtract the hundreds column. Take the bottom digit from the top digit.
    10 - 7 = 3
  7. Subtract the thousands column. Take the bottom digit from the top digit.
    5 - 2 = 3
  8. Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.
    3387

Check. Check: 3387 + 2748 = 6135.

Watch out. A zero cannot give a ten. Go left to the first column that is not zero, and exchange from there.

Watch out

Watch out. Exchange before you subtract. In 5271 - 2385, the ones 1 is too small for 5, so exchange a ten first.

Exam tip

Grown-up tip. Ask: “Is the top digit big enough? If not, what can you exchange?” Let the child check by adding back.

Exercise 3C  Practice: column subtraction with exchange

Non-calculator
1
FWork out 9209 - 7674.
2
FWork out 5630 - 5496.
3
FWork out 7716 - 5674.
4
FWork out 5229 - 2847.
5
FWork out 8570 - 2352.
6
FWork out 8484 - 6009.
7
FWork out 8649 - 7760.
8
FWork out 7096 - 2770.
9
FWork out 7000 - 1891.
10
FWork out 2145 - 1170.
11
FWork out 5590 - 2914.
12
FWork out 5994 - 3338.
13
FWork out 9419 - 5819.
14
FWork out 9304 - 8176.
15
FWork out 9305 - 8757.
16
FWork out 7865 - 7656.
3.4

Subtraction with a zero in the middle

Level 4
Subtract across a zero in the middle of the top number, exchanging from the nearest non-zero column
Video lesson: Subtraction with a zero in the middleComing soon

A zero cannot give a ten. In 5004 - 2378 there are no tens and no hundreds to exchange from.

Go left to the first column that is not zero. Exchange 1 from there, then make each zero 9 as you go along.

Key ideas

  • A zero cannot be exchanged from.
  • Exchange from the first column on the left that is not zero.
  • Each zero that you pass becomes 9.
Worked example 3.4.1
Work out 5004 - 2378.

Method. Subtract column by column from the ones. When the top digit is too small, exchange from the column on the left.

  1. Exchange in the thousands column. The hundreds are 0, so exchange from further left: exchange 1 thousand for 10 hundreds.
    thousands: 5 to 4; hundreds: 0 to 10
  2. Exchange in the hundreds column. The tens are 0, so exchange from further left: exchange 1 hundred for 10 tens.
    hundreds: 10 to 9; tens: 0 to 10
  3. Exchange in the tens column. The ones digit is too small, so exchange 1 ten for 10 ones.
    tens: 10 to 9; ones: 4 to 14
  4. Subtract the ones column. Take the bottom digit from the top digit.
    14 - 8 = 6
  5. Subtract the tens column. Take the bottom digit from the top digit.
    9 - 7 = 2
  6. Subtract the hundreds column. Take the bottom digit from the top digit.
    9 - 3 = 6
  7. Subtract the thousands column. Take the bottom digit from the top digit.
    4 - 2 = 2
  8. Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.
    2626

Check. Check: 2626 + 2378 = 5004.

Watch out. A zero cannot give a ten. Go left to the first column that is not zero, and exchange from there.

Worked example 3.4.2
Work out 3001 - 1245.

Method. Subtract column by column from the ones. When the top digit is too small, exchange from the column on the left.

  1. Exchange in the thousands column. The hundreds are 0, so exchange from further left: exchange 1 thousand for 10 hundreds.
    thousands: 3 to 2; hundreds: 0 to 10
  2. Exchange in the hundreds column. The tens are 0, so exchange from further left: exchange 1 hundred for 10 tens.
    hundreds: 10 to 9; tens: 0 to 10
  3. Exchange in the tens column. The ones digit is too small, so exchange 1 ten for 10 ones.
    tens: 10 to 9; ones: 1 to 11
  4. Subtract the ones column. Take the bottom digit from the top digit.
    11 - 5 = 6
  5. Subtract the tens column. Take the bottom digit from the top digit.
    9 - 4 = 5
  6. Subtract the hundreds column. Take the bottom digit from the top digit.
    9 - 2 = 7
  7. Subtract the thousands column. Take the bottom digit from the top digit.
    2 - 1 = 1
  8. Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.
    1756

Check. Check: 1756 + 1245 = 3001.

Watch out. A zero cannot give a ten. Go left to the first column that is not zero, and exchange from there.

Worked example 3.4.3
Work out 4500 - 1268.

Method. Subtract column by column from the ones. When the top digit is too small, exchange from the column on the left.

  1. Exchange in the hundreds column. The tens are 0, so exchange from further left: exchange 1 hundred for 10 tens.
    hundreds: 5 to 4; tens: 0 to 10
  2. Exchange in the tens column. The ones digit is too small, so exchange 1 ten for 10 ones.
    tens: 10 to 9; ones: 0 to 10
  3. Subtract the ones column. Take the bottom digit from the top digit.
    10 - 8 = 2
  4. Subtract the tens column. Take the bottom digit from the top digit.
    9 - 6 = 3
  5. Subtract the hundreds column. Take the bottom digit from the top digit.
    4 - 2 = 2
  6. Subtract the thousands column. Take the bottom digit from the top digit.
    4 - 1 = 3
  7. Write the answer. Read the digits from the top: thousands, hundreds, tens and ones.
    3232

Check. Check: 3232 + 1268 = 4500.

Watch out. A zero cannot give a ten. Go left to the first column that is not zero, and exchange from there.

Watch out

Watch out. 5004 - 2378 is 2626, not 2636. Each zero becomes 9 after the exchange, and the last column gets 10 more.

Exam tip

Grown-up tip. Ask the child to point to the first non-zero digit on the left before exchanging.

Exercise 3D  Practice: subtraction across zeros

Non-calculator
1
FWork out 4078 - 3893.
2
FWork out 2070 - 1782.
3
FWork out 5048 - 4288.
4
FWork out 9072 - 2185.
5
FWork out 9072 - 1191.
6
FWork out 5050 - 4757.
7
FWork out 8078 - 1599.
8
FWork out 4002 - 1488.
9
FWork out 6005 - 1576.
10
FWork out 2002 - 1590.
11
FWork out 2012 - 1408.
12
FWork out 3041 - 2160.
13
FWork out 8038 - 6543.
14
FWork out 2066 - 1683.
15
FWork out 8022 - 3085.
16
FWork out 6041 - 3803.
3.5

Estimating, checking and missing numbers

Level 4
Estimate the answer by rounding, and check it with the inverse operation, Find a missing number in an addition or subtraction
Video lesson: Estimating, checking and missing numbersComing soon

Estimate first: round each number to the nearest thousand, then add or subtract. Your exact answer should be close to the estimate.

Check an addition by subtracting. Check a subtraction by adding. For a missing number, use the inverse operation.

Key ideas

  • Estimate by rounding to the nearest 1000.
  • Check with the inverse: subtract to check an addition.
  • For a missing number, do the opposite operation.
Worked example 3.5.1
Round 4826 and 2375 to the nearest 1000. Add the rounded numbers to estimate the total of 4826 + 2375.

Method. Round each number, then add the rounded numbers. This gives an estimate close to the answer.

  1. Round 4826 to the nearest 1000. Look at the hundreds, tens and ones: 826 is more than 500.
    4826 rounds to 5000
  2. Round 2375 to the nearest 1000. Look at 375: it is less than 500.
    2375 rounds to 2000
  3. Add the rounded numbers. This gives the estimate.
    5000 + 2000 = 7000
  4. Write the estimate. The exact total, 7201, is close to this.
    7000

Check. Check: the exact answer 4826 + 2375 = 7201 is close to 7000.

Watch out. An estimate should be about the size of the exact answer.

Worked example 3.5.2
3456 + ___ = 5000

Method. Use the inverse operation to find the missing number.

  1. Find what must be added. The gap is the difference between the total and the known number.
    5000 - 3456 = 1544
  2. Check the sum. Put the missing number back in the sum.
    3456 + 1544 = 5000
  3. Write the missing number. It fills the gap.
    1544

Check. Check: 3456 + 1544 = 5000.

Watch out. Subtract the known number from the total to find the gap.

Worked example 3.5.3
___ - 2378 = 2000

Method. Use the inverse operation to find the missing number.

  1. Add the number that was taken away. Adding undoes the take away.
    2000 + 2378 = 4378
  2. Check the subtraction. Taking away the known number should give the answer.
    4378 - 2378 = 2000
  3. Write the missing number. It fills the gap.
    4378

Check. Check: 4378 - 2378 = 2000.

Watch out. Adding undoes subtracting.

Watch out

Watch out. The missing number in 3456 + ___ = 5000 is 1544, not 8456. Find the gap by subtracting.

Exam tip

Grown-up tip. Ask: “Is your answer close to the estimate? Does the check work?”

Exercise 3E  Practice: estimating, checking and missing numbers

Non-calculator
1
F___ - 1974 = 6139
2
F___ - 4874 = 4327
3
PSRound 1698 and 5815 to the nearest 1000. Add the rounded numbers to estimate the total of 1698 + 5815.
4
RCheck this sum by subtracting: 5498 + 3776 = 9274. Write the subtraction you use.
5
F4634 + ___ = 8775
6
PSRound 3728 and 4385 to the nearest 1000. Add the rounded numbers to estimate the total of 3728 + 4385.
7
PSRound 8529 and 1397 to the nearest 1000. Add the rounded numbers to estimate the total of 8529 + 1397.
8
RCheck this sum by subtracting: 4052 + 2013 = 6065. Write the subtraction you use.
9
F___ + 2161 = 8025
10
PSRound 7716 and 1250 to the nearest 1000. Add the rounded numbers to estimate the total of 7716 + 1250.
11
PSRound 7520 and 1861 to the nearest 1000. Add the rounded numbers to estimate the total of 7520 + 1861.
12
F___ - 6531 = 2214
13
PSRound 6919 and 1219 to the nearest 1000. Add the rounded numbers to estimate the total of 6919 + 1219.
14
PSRound 8848 and 1029 to the nearest 1000. Add the rounded numbers to estimate the total of 8848 + 1029.
15
PSRound 2814 and 2870 to the nearest 1000. Add the rounded numbers to estimate the total of 2814 + 2870.
16
F___ + 3915 = 9615

Chapter summary

SkillMethod
Mental addition and subtractionChange only the column that matches the number; check other digits
Column additionAdd from the ones; carry 1 when a column is 10 or more
Column subtractionSubtract from the ones; exchange 1 from the left when the top digit is too small
Subtraction across zerosGo left to the first non-zero column; each zero passed becomes 9
Estimate and checkRound to the nearest 1000 to estimate; use the inverse to check

Can you…?

  • I can add and subtract a ten, a hundred or a thousand in my head
  • I can add two four-digit numbers in columns, carrying across columns
  • I can subtract two four-digit numbers in columns, exchanging where needed
  • I can subtract across a zero in the middle of a number
  • I can estimate, check with the inverse, and find a missing number

Key terms

carry
move a ten to the next column on the left when adding
exchange
break 1 ten into 10 ones (or 1 hundred into 10 tens) when subtracting
estimate
a sensible guess of the answer, found by rounding
inverse
the operation that undoes another: addition undoes subtraction

Exercise 3Z  Check-up

Non-calculator
1
Work out 4345 + 1832.
2
6084 + ___ = 9149
3
Work out 9935 - 5860.
4
7526 + ___ = 8598
5
Work out 4015 - 1192.
6
Work out 6889 + 2653.
7
Work out 8277 + 1626.
8
Work out 7319 - 4489.
9
Work out 1073 + 3342.
10
Work out 9780 - 100.

Total 19 marks. Allow about 19 minutes.

Exercise 3X  Practice test questions

Non-calculator
1
FWork out 9750 - 1466.[1 mark]
2
FWork out 7187 + 2006.[1 mark]
3
FWork out 6788 + 2140.[1 mark]
4
FWork out 6247 + 2569.[1 mark]
5
F4835 + ___ = 9783[2 marks]
6
FWork out 8087 + 1000.[2 marks]
7
F___ - 1868 = 7934[2 marks]
8
FWork out 5724 + 3093.[3 marks]
9
FWork out 7026 - 3052.[3 marks]
10
FWork out 3096 - 1387.[3 marks]
← Chapter 2: Comparing, ordering and roundingChapter 4: Times tables 3 and 4 →

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