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Step-by-step practice: Maths · Level 3Chapter 5 · Subtracting within 1000
Level 3 · Chapter 5

Subtracting within 1000

By the end of this chapter you will be able to

  • Subtract with exchange from the ones
  • Subtract 2-digit and 3-digit numbers with exchange
  • Check a subtraction by adding back
  • Find a missing number
  • Solve subtraction word problems

You should already know

  • Adding within 1000 with carrying (chapter 4)
  • Subtracting within 100 without exchange (Level 2, chapter 7)

Where this leads

  • Multiplication as repeated addition (chapter 6)

Step-by-step practice: maths (Level 3). Small steps, repeated until fluent. Content: Subtract a 1-digit number, a 2-digit number and a 3-digit number, exchanging a ten or a hundred, Set subtractions out in columns with the hundreds, tens and ones lined up, Check a subtraction by adding the answer back to the number taken away, Find a missing number in a subtraction, such as 432 - ___ = 245, Solve one-step subtraction word problems.

Exercise P  Do you remember?

Non-calculator
1
FWork out 58 - 34.
5834-
2
FWork out 96 - 41.
9641-
3
FWork out 47 - 12.
4712-
4
FWork out 75 - 28.
7528-
5
FWork out 89 - 3.
893-
5.1

Subtracting a 1-digit number with exchange

Level 3
Subtract a 1-digit number, exchanging a ten when the ones on top are too small
Video lesson: Subtracting a 1-digit number with exchangeComing soon

Sometimes the ones on top are too small to take away. Then we exchange one ten for ten ones.

Now the ones are big enough. Subtract the ones, then the tens.

3428-
Column subtraction: 2 ones are too few for 8 ones, so exchange one ten for ten ones.

Key ideas

  • Subtract the ones first.
  • If the ones on top are too small, exchange a ten for ten ones.
  • Then subtract the tens.
Worked example 5.1.1
Work out 342 - 8.

Method. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.

  1. Write the numbers in columns. Keep the ones under the ones and the tens under the tens.
    342 over 8
  2. Exchange 1 ten for 10 ones. The ones on top (2) are fewer than the ones below (8), so we need more ones.
    4 tens become 3 tens, and the ones go from 2 to 12
  3. Subtract the ones. 12 - 8 = 4.
    12 - 8 = 4
  4. Subtract the tens. 3 - 0 = 3.
    3 - 0 = 3
  5. Subtract the hundreds. 3 - 0 = 3.
    3 - 0 = 3
  6. Write the answer. Read the columns from left to right.
    334

Check. Check: 334 + 8 = 342.

Watch out. Exchange a ten for ten ones when the ones on top are too small. Then take away.

Worked example 5.1.2
Work out 725 - 7.

Method. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.

  1. Write the numbers in columns. Keep the ones under the ones and the tens under the tens.
    725 over 7
  2. Exchange 1 ten for 10 ones. The ones on top (5) are fewer than the ones below (7), so we need more ones.
    2 tens become 1 tens, and the ones go from 5 to 15
  3. Subtract the ones. 15 - 7 = 8.
    15 - 7 = 8
  4. Subtract the tens. 1 - 0 = 1.
    1 - 0 = 1
  5. Subtract the hundreds. 7 - 0 = 7.
    7 - 0 = 7
  6. Write the answer. Read the columns from left to right.
    718

Check. Check: 718 + 7 = 725.

Watch out. Exchange a ten for ten ones when the ones on top are too small. Then take away.

Worked example 5.1.3
Work out 81 - 6.

Method. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.

  1. Write the numbers in columns. Keep the ones under the ones and the tens under the tens.
    81 over 6
  2. Exchange 1 ten for 10 ones. The ones on top (1) are fewer than the ones below (6), so we need more ones.
    8 tens become 7 tens, and the ones go from 1 to 11
  3. Subtract the ones. 11 - 6 = 5.
    11 - 6 = 5
  4. Subtract the tens. 7 - 0 = 7.
    7 - 0 = 7
  5. Write the answer. Read the columns from left to right.
    75

Check. Check: 75 + 6 = 81.

Watch out. Exchange a ten for ten ones when the ones on top are too small. Then take away.

Watch out

Watch out. When you exchange a ten, the tens go down by one. 40 - 6 is 34, not 46.

Exam tip

Grown-up tip. Use ten sticks and ones cubes. Break one stick into ten ones, then take away.

Exercise 5A  Practice: a 1-digit number with exchange

Non-calculator
1
FWork out 158 - 9.
1589-
2
FWork out 987 - 9.
9879-
3
FWork out 402 - 5.
4025-
4
FWork out 916 - 9.
9169-
5
FWork out 940 - 7.
9407-
6
FWork out 847 - 9.
8479-
7
FWork out 686 - 7.
6867-
8
FWork out 383 - 9.
3839-
9
FWork out 727 - 9.
7279-
10
FWork out 748 - 9.
7489-
11
FWork out 867 - 8.
8678-
12
FWork out 601 - 4.
6014-
13
FWork out 41 - 8.
418-
14
FWork out 542 - 7.
5427-
15
FWork out 573 - 8.
5738-
16
FWork out 521 - 2.
5212-
5.2

Subtracting 2-digit numbers with exchange

Level 3
Subtract a 2-digit number from a 2-digit number, exchanging a ten
Video lesson: Subtracting 2-digit numbers with exchangeComing soon

Some 2-digit subtractions need exchange. Check the ones first. If the top ones are fewer, exchange a ten for ten ones.

Write the new tens and ones in the columns, then take away.

Key ideas

  • Check the ones first.
  • Exchange a ten for ten ones when you need to.
  • Take the ones away, then the tens.
Worked example 5.2.1
Work out 73 - 38.

Method. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.

  1. Write the numbers in columns. Keep the ones under the ones and the tens under the tens.
    73 over 38
  2. Exchange 1 ten for 10 ones. The ones on top (3) are fewer than the ones below (8), so we need more ones.
    7 tens become 6 tens, and the ones go from 3 to 13
  3. Subtract the ones. 13 - 8 = 5.
    13 - 8 = 5
  4. Subtract the tens. 6 - 3 = 3.
    6 - 3 = 3
  5. Write the answer. Read the columns from left to right.
    35

Check. Check: 35 + 38 = 73.

Watch out. Exchange a ten for ten ones when the ones on top are too small. Then take away.

Worked example 5.2.2
Work out 64 - 27.

Method. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.

  1. Write the numbers in columns. Keep the ones under the ones and the tens under the tens.
    64 over 27
  2. Exchange 1 ten for 10 ones. The ones on top (4) are fewer than the ones below (7), so we need more ones.
    6 tens become 5 tens, and the ones go from 4 to 14
  3. Subtract the ones. 14 - 7 = 7.
    14 - 7 = 7
  4. Subtract the tens. 5 - 2 = 3.
    5 - 2 = 3
  5. Write the answer. Read the columns from left to right.
    37

Check. Check: 37 + 27 = 64.

Watch out. Exchange a ten for ten ones when the ones on top are too small. Then take away.

Worked example 5.2.3
Work out 92 - 47.

Method. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.

  1. Write the numbers in columns. Keep the ones under the ones and the tens under the tens.
    92 over 47
  2. Exchange 1 ten for 10 ones. The ones on top (2) are fewer than the ones below (7), so we need more ones.
    9 tens become 8 tens, and the ones go from 2 to 12
  3. Subtract the ones. 12 - 7 = 5.
    12 - 7 = 5
  4. Subtract the tens. 8 - 4 = 4.
    8 - 4 = 4
  5. Write the answer. Read the columns from left to right.
    45

Check. Check: 45 + 47 = 92.

Watch out. Exchange a ten for ten ones when the ones on top are too small. Then take away.

Watch out

Watch out. After you exchange, the top tens are one less. 73 - 38 is 35, not 45.

Exam tip

Grown-up tip. Ask: “Are the ones on top big enough? If not, which ten can we break?”

Exercise 5B  Practice: 2-digit numbers with exchange

Non-calculator
1
FWork out 30 - 18.
3018-
2
FWork out 72 - 68.
7268-
3
FWork out 94 - 29.
9429-
4
FWork out 44 - 36.
4436-
5
FWork out 53 - 45.
5345-
6
FWork out 82 - 36.
8236-
7
FWork out 63 - 37.
6337-
8
FWork out 50 - 23.
5023-
9
FWork out 90 - 42.
9042-
10
FWork out 51 - 36.
5136-
11
FWork out 62 - 16.
6216-
12
FWork out 97 - 19.
9719-
13
FWork out 83 - 54.
8354-
14
FWork out 43 - 37.
4337-
15
FWork out 30 - 26.
3026-
16
FWork out 52 - 14.
5214-
5.3

Subtracting 3-digit numbers with exchange

Level 3
Subtract 3-digit numbers, exchanging a ten or a hundred where the top digit is too small, Set subtractions out in columns with the hundreds, tens and ones lined up
Video lesson: Subtracting 3-digit numbers with exchangeComing soon

When the tens on top are too small, exchange a hundred for ten tens. When the hundreds are used up, the number in the hundreds goes down by one.

Line up the columns. Work from the ones, then the tens, then the hundreds.

432187-
432 - 187 set out in columns, with the digits lined up.

Key ideas

  • Line up the columns.
  • Exchange a ten for ten ones if the ones are too small.
  • Exchange a hundred for ten tens if the tens are too small.
Worked example 5.3.1
Work out 432 - 187.

Method. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.

  1. Write the numbers in columns. Keep the ones under the ones and the tens under the tens.
    432 over 187
  2. Exchange 1 ten for 10 ones. The ones on top (2) are fewer than the ones below (7), so we need more ones.
    3 tens become 2 tens, and the ones go from 2 to 12
  3. Exchange 1 hundred for 10 tens. The tens on top are fewer than the tens below (8 tens), so we need more tens.
    4 hundreds become 3 hundreds, and 2 tens become 12 tens
  4. Subtract the ones. 12 - 7 = 5.
    12 - 7 = 5
  5. Subtract the tens. 12 - 8 = 4.
    12 - 8 = 4
  6. Subtract the hundreds. 3 - 1 = 2.
    3 - 1 = 2
  7. Write the answer. Read the columns from left to right.
    245

Check. Check: 245 + 187 = 432.

Watch out. When a column is too small, exchange one from the column to its left. Ten ones make one ten, ten tens make one hundred.

Worked example 5.3.2
Work out 500 - 286.

Method. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.

  1. Write the numbers in columns. Keep the ones under the ones and the tens under the tens.
    500 over 286
  2. Exchange 1 hundred for 10 tens. There are no tens to take from, so we first change a hundred into tens.
    5 hundreds and 0 tens become 4 hundreds and 10 tens
  3. Exchange 1 ten for 10 ones. The ones on top (0) are fewer than the ones below (6), so we need more ones.
    10 tens become 9 tens, and the ones go from 0 to 10
  4. Subtract the ones. 10 - 6 = 4.
    10 - 6 = 4
  5. Subtract the tens. 9 - 8 = 1.
    9 - 8 = 1
  6. Subtract the hundreds. 4 - 2 = 2.
    4 - 2 = 2
  7. Write the answer. Read the columns from left to right.
    214

Check. Check: 214 + 286 = 500.

Watch out. When a column is too small, exchange one from the column to its left. Ten ones make one ten, ten tens make one hundred.

Worked example 5.3.3
Work out 604 - 258.

Method. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.

  1. Write the numbers in columns. Keep the ones under the ones and the tens under the tens.
    604 over 258
  2. Exchange 1 hundred for 10 tens. There are no tens to take from, so we first change a hundred into tens.
    6 hundreds and 0 tens become 5 hundreds and 10 tens
  3. Exchange 1 ten for 10 ones. The ones on top (4) are fewer than the ones below (8), so we need more ones.
    10 tens become 9 tens, and the ones go from 4 to 14
  4. Subtract the ones. 14 - 8 = 6.
    14 - 8 = 6
  5. Subtract the tens. 9 - 5 = 4.
    9 - 5 = 4
  6. Subtract the hundreds. 5 - 2 = 3.
    5 - 2 = 3
  7. Write the answer. Read the columns from left to right.
    346

Check. Check: 346 + 258 = 604.

Watch out. When a column is too small, exchange one from the column to its left. Ten ones make one ten, ten tens make one hundred.

Watch out

Watch out. 500 - 286 needs two exchanges: a hundred becomes ten tens, then a ten becomes ten ones. The answer is 214.

Exam tip

Grown-up tip. Draw the columns on squared paper. Ask the child to say each exchange out loud before writing it.

Exercise 5C  Practice: 3-digit numbers with exchange

Non-calculator
1
FWork out 315 - 199.
315199-
2
FWork out 541 - 512.
541512-
3
FWork out 382 - 46.
38246-
4
FWork out 150 - 137.
150137-
5
FWork out 536 - 271.
536271-
6
FWork out 382 - 173.
382173-
7
FWork out 320 - 171.
320171-
8
FWork out 238 - 147.
238147-
9
FWork out 391 - 109.
391109-
10
FWork out 427 - 378.
427378-
11
FWork out 373 - 93.
37393-
12
FWork out 518 - 490.
518490-
13
FWork out 368 - 298.
368298-
14
FWork out 352 - 176.
352176-
15
FWork out 827 - 131.
827131-
16
FWork out 864 - 375.
864375-
5.4

Checking, missing numbers and word problems

Level 3
Check a subtraction by adding the answer back, Find a missing number in a subtraction, Solve one-step subtraction word problems
Video lesson: Checking, missing numbers and word problemsComing soon

Addition undoes subtraction. To check a subtraction, add the answer back to the number taken away. You should get the number you started with.

To find a missing number, think about the addition that matches it.

Key ideas

  • Check: answer + the number taken away = the start.
  • Missing number: think of the matching addition.
  • Words like left, eaten and gives mean take away.
Worked example 5.4.1
Fill in the missing number: 432 - ___ = 245

Method. Use addition to work out the missing number, then check it with subtraction.

  1. Think of the take away as a missing number. The number taken away is the missing part.
    432 - ? = 245
  2. Use addition to find it. Taking away the missing number leaves 245, so 245 + ? = 432.
    245 + ? = 432
  3. Work out the missing number. Subtract the answer from the start.
    432 - 245 = 187
  4. Write the missing number. Check: the number taken away is this.
    187

Check. Check: 432 - 187 = 245.

Watch out. Check the missing number by putting it back in the question.

Worked example 5.4.2
Fill in the missing number: ___ - 215 = 425

Method. Use addition to work out the missing number, then check it with subtraction.

  1. Think about what we started with. The starting number is the one we took from.
    ? - 215 = 425
  2. Add back the number taken away. Adding 215 back to 425 gives the starting number.
    425 + 215 = 640
  3. Write the missing number. This is the number we started with.
    640

Check. Check: 640 - 215 = 425.

Watch out. Check the missing number by putting it back in the question.

Worked example 5.4.3
A bag has 340 sweets. 178 sweets are eaten. How many sweets are left?

Method. Find the operation, then work out what is left.

  1. Find the operation. Words like left, gives and empty mean take away.
    340 - 178
  2. Work out the answer. Use column subtraction, and exchange if needed.
    340 - 178 = 162
  3. Write the answer. This is the number left.
    162

Check. Check: 162 + 178 = 340.

Watch out. Words like left, gone and gives away mean take away.

Watch out

Watch out. When a number is missing from the start, add the answer and the number taken away. Do not subtract them.

Exam tip

Grown-up tip. Ask the child to put the answer back into the question to see if it fits.

Exercise 5D  Practice: checks, missing numbers and problems

Non-calculator
1
FFill in the missing number: ___ - 113 = 348
2
FFill in the missing number: ___ - 209 = 234
3
FFill in the missing number: ___ - 145 = 412
4
FFill in the missing number: ___ - 65 = 99
5
FFill in the missing number: 837 - ___ = 665
6
FFill in the missing number: 631 - ___ = 554
7
FFill in the missing number: ___ - 95 = 742
8
FFill in the missing number: ___ - 157 = 57
9
PSA bag has 576 sweets. 395 sweets are eaten. How many sweets are left?
10
PSThere are 590 seats in a hall. 333 seats are empty. How many seats have people in them?
11
PSPriya has 705 stamps. Priya gives 479 stamps to Mei. How many stamps does Priya have now?
12
PSThere are 376 seats in a hall. 94 seats are empty. How many seats have people in them?
13
RUse 408 and 222. Answer both parts.
(a)Work out 408 - 222.
(b)Check by adding 222 to your answer. What number do you get?
14
RUse 106 and 50. Answer both parts.
(a)Work out 106 - 50.
(b)Check by adding 50 to your answer. What number do you get?
15
RUse 360 and 352. Answer both parts.
(a)Work out 360 - 352.
(b)Check by adding 352 to your answer. What number do you get?
16
RUse 504 and 311. Answer both parts.
(a)Work out 504 - 311.
(b)Check by adding 311 to your answer. What number do you get?

Chapter summary

SkillMethod
Exchange from the onesBreak a ten into ten ones when the ones on top are too small
Exchange from the tensBreak a hundred into ten tens when the tens on top are too small
Subtract in columnsLine up the columns; subtract ones, tens, then hundreds
CheckAdd the answer back to the number taken away
Missing numberUse the matching addition to find it

Can you…?

  • I can subtract a 1-digit number with exchange
  • I can subtract 2-digit numbers with exchange
  • I can subtract 3-digit numbers with exchange, using columns
  • I can check a subtraction by adding the answer back
  • I can find a missing number in a subtraction

Key terms

exchange
break one ten into ten ones, or one hundred into ten tens, to make a subtraction possible
take away
subtract, or remove a number from another
inverse
the operation that undoes another, such as addition undoing subtraction
missing number
the number we need to fill the gap in a calculation

Exercise 5Z  Check-up

Non-calculator
1
Work out 21 - 12.
2112-
2
Work out 81 - 16.
8116-
3
Work out 224 - 8.
2248-
4
Work out 716 - 141.
716141-
5
Work out 696 - 9.
6969-
6
Work out 905 - 767.
905767-
7
Work out 670 - 223.
670223-
8
A shop has 244 eggs. It sells 237 eggs. How many eggs are left in the shop?
9
Priya has 949 stamps. Priya gives 492 stamps to Mei. How many stamps does Priya have now?
10
There are 597 seats in a hall. 58 seats are empty. How many seats have people in them?

Total 19 marks. Allow about 19 minutes.

Exercise 5X  Practice test questions

Non-calculator
1
FWork out 438 - 299.[1 mark]
438299-
2
PSThere are 425 seats in a hall. 256 seats are empty. How many seats have people in them?[1 mark]
3
FWork out 985 - 6.[1 mark]
9856-
4
FWork out 840 - 3.[1 mark]
8403-
5
PSThere are 883 seats in a hall. 666 seats are empty. How many seats have people in them?[2 marks]
6
FWork out 602 - 583.[2 marks]
602583-
7
FWork out 615 - 7.[2 marks]
6157-
8
PSA bag has 536 sweets. 155 sweets are eaten. How many sweets are left?[3 marks]
9
PSThere are 966 seats in a hall. 92 seats are empty. How many seats have people in them?[3 marks]
10
FWork out 501 - 7.[3 marks]
5017-
← Chapter 4: Adding within 1000Chapter 6: Multiplication as repeated addition →

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