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Step-by-step practice: Maths · Level 2Chapter 7 · Adding and subtracting within 100
Level 2 · Chapter 7

Adding and subtracting within 100

By the end of this chapter you will be able to

  • Add a 1-digit number and a multiple of 10
  • Add two 2-digit numbers by tens and ones
  • Subtract two 2-digit numbers by tens and ones
  • Set out sums in columns

You should already know

  • Tens and ones (Chapter 2)
  • Adding within 20 (Chapter 5)
  • Taking away within 20 (Chapter 6)

Where this leads

  • Money (Chapter 8)
  • Adding and subtracting with carrying (Level 3)

Step-by-step practice: maths (Level 2). Small steps, repeated until fluent. Content: Add a 1-digit number to a 2-digit number, Add a multiple of 10 to a 2-digit number, Add two 2-digit numbers by adding tens and ones, when no carrying is needed, Subtract two 2-digit numbers by subtracting tens and ones, when no exchange is needed, Set out sums and differences in columns with the tens above the ones.

Exercise P  Do you remember?

Non-calculator
1
FWork out 22 + 6.
2
FWork out 15 + 30.
3
FWork out 21 + 12.
4
FWork out 58 - 34.
5
FWork out the answer. Set it out in columns: 41 + 27
4127+
7.1

Adding a 1-digit number to a 2-digit number

Level 2
Add a 1-digit number to a 2-digit number, within 100
Video lesson: Adding a 1-digit number to a 2-digit numberComing soon

Split the 2-digit number into tens and ones. Add the 1-digit number to the ones.

If the ones still add up to 9 or less, the tens do not change. Put the tens back.

TensOnes101010
34 is 3 tens and 4 ones. Adding 5 to the ones gives 39.

Key ideas

  • Split the number into tens and ones.
  • Add to the ones.
  • Put the tens back on the total.
Worked example 7.1.1
Work out 34 + 5.

Method. Split the 2-digit number into tens and ones. Add the ones, then put the tens back.

  1. Split 34 into 30 and 4. The tens and the ones are kept apart.
    34 = 30 + 4
  2. Add the ones: 4 + 5. 4 + 5 = 9 is less than 10, so no tens change.
    4 + 5 = 9
  3. Put the tens back: 30 + 9. Add the tens and the ones together.
    30 + 9 = 39
  4. Write the answer.
    39

Check. Count on 5 from 34: you reach 39.

Watch out. Only the ones change when you add a 1-digit number and the ones do not go past 9.

Worked example 7.1.2
Work out 61 + 3.

Method. Split the 2-digit number into tens and ones. Add the ones, then put the tens back.

  1. Split 61 into 60 and 1. The tens and the ones are kept apart.
    61 = 60 + 1
  2. Add the ones: 1 + 3. 1 + 3 = 4 is less than 10, so no tens change.
    1 + 3 = 4
  3. Put the tens back: 60 + 4. Add the tens and the ones together.
    60 + 4 = 64
  4. Write the answer.
    64

Check. Count on 3 from 61: you reach 64.

Watch out. Only the ones change when you add a 1-digit number and the ones do not go past 9.

Worked example 7.1.3
Work out 27 + 2.

Method. Split the 2-digit number into tens and ones. Add the ones, then put the tens back.

  1. Split 27 into 20 and 7. The tens and the ones are kept apart.
    27 = 20 + 7
  2. Add the ones: 7 + 2. 7 + 2 = 9 is less than 10, so no tens change.
    7 + 2 = 9
  3. Put the tens back: 20 + 9. Add the tens and the ones together.
    20 + 9 = 29
  4. Write the answer.
    29

Check. Count on 2 from 27: you reach 29.

Watch out. Only the ones change when you add a 1-digit number and the ones do not go past 9.

Watch out

Watch out. Keep the tens. 34 + 5 is 39, not 310 and not 49.

Exam tip

Grown-up tip. Make the number with tens sticks and ones cubes. Add the cubes to the ones pile and count.

Exercise 7A  Practice: adding a 1-digit number

Non-calculator
1
FWork out 50 + 8.
2
FWork out 60 + 8.
3
FWork out 78 + 1.
4
FWork out 85 + 3.
5
FWork out 30 + 8.
6
FWork out 13 + 6.
7
FWork out 10 + 1.
8
FWork out 46 + 3.
9
FWork out 34 + 1.
10
FWork out 50 + 2.
11
FWork out 72 + 4.
12
FWork out 73 + 3.
13
FWork out 80 + 7.
14
FWork out 53 + 5.
15
FWork out 72 + 5.
16
FWork out 75 + 4.
7.2

Adding a multiple of 10

Level 2
Add a multiple of 10 to a 2-digit number
Video lesson: Adding a multiple of 10Coming soon

Adding 10, 20, 30 and so on changes only the tens. The ones stay the same.

Add the tens first, then keep the ones.

Key ideas

  • Adding 10 adds one ten.
  • Adding 20 adds two tens.
  • The ones digit does not change.
Worked example 7.2.1
Work out 34 + 20.

Method. Add the tens together. The ones stay the same.

  1. Find the tens of 20. 20 is 2 tens.
    20 = 2 tens
  2. Add the tens. 3 tens + 2 tens = 5 tens.
    3 + 2 = 5
  3. Keep the ones. The ones are still 4.
    5 tens and 4 ones
  4. Write the answer.
    54

Check. 34 + 20 goes up by 2 tens. The answer is 54.

Watch out. Adding a multiple of 10 changes only the tens digit.

Worked example 7.2.2
Work out 42 + 30.

Method. Add the tens together. The ones stay the same.

  1. Find the tens of 30. 30 is 3 tens.
    30 = 3 tens
  2. Add the tens. 4 tens + 3 tens = 7 tens.
    4 + 3 = 7
  3. Keep the ones. The ones are still 2.
    7 tens and 2 ones
  4. Write the answer.
    72

Check. 42 + 30 goes up by 3 tens. The answer is 72.

Watch out. Adding a multiple of 10 changes only the tens digit.

Worked example 7.2.3
Work out 15 + 40.

Method. Add the tens together. The ones stay the same.

  1. Find the tens of 40. 40 is 4 tens.
    40 = 4 tens
  2. Add the tens. 1 tens + 4 tens = 5 tens.
    1 + 4 = 5
  3. Keep the ones. The ones are still 5.
    5 tens and 5 ones
  4. Write the answer.
    55

Check. 15 + 40 goes up by 4 tens. The answer is 55.

Watch out. Adding a multiple of 10 changes only the tens digit.

Watch out

Watch out. 34 + 20 is 54, not 74. Only the tens go up by 2.

Exam tip

Grown-up tip. Count in tens from the number. Ask: “How many tens have we added?”

Exercise 7B  Practice: adding multiples of 10

Non-calculator
1
FWork out 19 + 50.
2
FWork out 84 + 10.
3
FWork out 41 + 20.
4
FWork out 48 + 20.
5
FWork out 26 + 20.
6
FWork out 55 + 10.
7
FWork out 25 + 60.
8
FWork out 32 + 60.
9
FWork out 44 + 40.
10
FWork out 37 + 50.
11
FWork out 83 + 10.
12
FWork out 74 + 20.
13
FWork out 81 + 10.
14
FWork out 53 + 20.
15
FWork out 46 + 10.
16
FWork out 85 + 10.
7.3

Adding two 2-digit numbers

Level 2
Add two 2-digit numbers by adding tens and ones, with no carrying
Video lesson: Adding two 2-digit numbersComing soon

To add two 2-digit numbers, add the tens together and add the ones together. Then put the two answers together.

In this step, the ones never go past 9, so you never need to carry.

Key ideas

  • Add the tens together.
  • Add the ones together.
  • Put the two answers together.
Worked example 7.3.1
Work out 23 + 45.

Method. Add the tens, then add the ones. Put the two answers together.

  1. Add the tens: 2 tens + 4 tens. Each ten is worth ten.
    2 + 4 = 6 tens, which is 60
  2. Add the ones: 3 + 5. The ones are added separately.
    3 + 5 = 8
  3. Put them together: 60 + 8. The tens and ones make the total.
    60 + 8 = 68
  4. Write the answer.
    68

Check. Count on from 23: you reach 68.

Watch out. Add the tens to the tens and the ones to the ones. Do not add the ones digit to the tens.

Worked example 7.3.2
Work out 52 + 36.

Method. Add the tens, then add the ones. Put the two answers together.

  1. Add the tens: 5 tens + 3 tens. Each ten is worth ten.
    5 + 3 = 8 tens, which is 80
  2. Add the ones: 2 + 6. The ones are added separately.
    2 + 6 = 8
  3. Put them together: 80 + 8. The tens and ones make the total.
    80 + 8 = 88
  4. Write the answer.
    88

Check. Count on from 52: you reach 88.

Watch out. Add the tens to the tens and the ones to the ones. Do not add the ones digit to the tens.

Worked example 7.3.3
Work out 31 + 27.

Method. Add the tens, then add the ones. Put the two answers together.

  1. Add the tens: 3 tens + 2 tens. Each ten is worth ten.
    3 + 2 = 5 tens, which is 50
  2. Add the ones: 1 + 7. The ones are added separately.
    1 + 7 = 8
  3. Put them together: 50 + 8. The tens and ones make the total.
    50 + 8 = 58
  4. Write the answer.
    58

Check. Count on from 31: you reach 58.

Watch out. Add the tens to the tens and the ones to the ones. Do not add the ones digit to the tens.

Watch out

Watch out. Add the tens to the tens and the ones to the ones. 23 + 45 is 68, not 612.

Exam tip

Grown-up tip. Ask: “How many tens altogether? How many ones altogether?” before writing the total.

Exercise 7C  Practice: adding two 2-digit numbers

Non-calculator
1
FWork out 63 + 22.
2
FWork out 52 + 37.
3
FWork out 34 + 24.
4
FWork out 60 + 21.
5
FWork out 17 + 21.
6
FWork out 27 + 32.
7
FWork out 51 + 13.
8
FWork out 12 + 16.
9
FWork out 38 + 41.
10
FWork out 48 + 41.
11
FWork out 31 + 61.
12
FWork out 75 + 24.
13
FWork out 60 + 11.
14
FWork out 85 + 11.
15
FWork out 38 + 51.
16
FWork out 58 + 11.
7.4

Subtracting two 2-digit numbers

Level 2
Subtract two 2-digit numbers by subtracting tens and ones, with no exchange
Video lesson: Subtracting two 2-digit numbersComing soon

To subtract, take the tens away from the tens and the ones away from the ones.

In this step, you never need to change a ten for ones, so each part can be taken away directly.

Key ideas

  • Take the tens away from the tens.
  • Take the ones away from the ones.
  • Put the two answers together.
Worked example 7.4.1
Work out 68 - 23.

Method. Take away the tens, then take away the ones. Put the two answers together.

  1. Take away the tens: 6 tens - 2 tens. We take the tens from the tens.
    6 - 2 = 4 tens, which is 40
  2. Take away the ones: 8 - 3. We take the ones from the ones.
    8 - 3 = 5
  3. Put them together: 40 + 5. The tens and the ones make the answer.
    40 + 5 = 45
  4. Write the answer.
    45

Check. Add back: 45 + 23 = 68. It is right.

Watch out. Take the ones from the ones and the tens from the tens. Do not take the ones from the tens.

Worked example 7.4.2
Work out 97 - 45.

Method. Take away the tens, then take away the ones. Put the two answers together.

  1. Take away the tens: 9 tens - 4 tens. We take the tens from the tens.
    9 - 4 = 5 tens, which is 50
  2. Take away the ones: 7 - 5. We take the ones from the ones.
    7 - 5 = 2
  3. Put them together: 50 + 2. The tens and the ones make the answer.
    50 + 2 = 52
  4. Write the answer.
    52

Check. Add back: 52 + 45 = 97. It is right.

Watch out. Take the ones from the ones and the tens from the tens. Do not take the ones from the tens.

Worked example 7.4.3
Work out 86 - 31.

Method. Take away the tens, then take away the ones. Put the two answers together.

  1. Take away the tens: 8 tens - 3 tens. We take the tens from the tens.
    8 - 3 = 5 tens, which is 50
  2. Take away the ones: 6 - 1. We take the ones from the ones.
    6 - 1 = 5
  3. Put them together: 50 + 5. The tens and the ones make the answer.
    50 + 5 = 55
  4. Write the answer.
    55

Check. Add back: 55 + 31 = 86. It is right.

Watch out. Take the ones from the ones and the tens from the tens. Do not take the ones from the tens.

Watch out

Watch out. 68 - 23 is 45. Take 2 tens from 6 tens, and 3 ones from 8 ones.

Exam tip

Grown-up tip. Use tens sticks and ones cubes. Take away the sticks first, then the cubes.

Exercise 7D  Practice: subtracting two 2-digit numbers

Non-calculator
1
FWork out 85 - 54.
2
FWork out 98 - 88.
3
FWork out 95 - 65.
4
FWork out 77 - 62.
5
FWork out 65 - 42.
6
FWork out 99 - 81.
7
FWork out 86 - 14.
8
FWork out 94 - 40.
9
FWork out 37 - 23.
10
FWork out 98 - 73.
11
FWork out 79 - 34.
12
FWork out 73 - 22.
13
FWork out 98 - 76.
14
FWork out 99 - 88.
15
FWork out 49 - 28.
16
FWork out 89 - 78.
7.5

Setting out sums in columns

Level 2
Set out sums and differences in columns with the tens above the ones
Video lesson: Setting out sums in columnsComing soon

A column sum puts the tens under the tens and the ones under the ones. This keeps the digits in their places.

Work out the ones first. Then work out the tens.

5231+
Tens under tens, ones under ones: 52 + 31.

Key ideas

  • Tens under tens, ones under ones.
  • Work out the ones first.
  • Then work out the tens.
Worked example 7.5.1
Work out the answer. Set it out in columns: 52 + 31

Method. Write the numbers in columns with tens under tens and ones under ones. Work from the ones.

  1. Write the numbers in columns. The tens go in one column and the ones in another.
    5 2 and 3 1
  2. Add the ones. Work out the ones first.
    2 + 1 = 3
  3. Add the tens. Then work out the tens.
    5 + 3 = 8
  4. Write the answer. Read the tens, then the ones.
    83

Check. Check by taking 31 away: 83 - 31 = 52.

Watch out. Start with the ones column. Keep each digit in its column.

Worked example 7.5.2
Work out the answer. Set it out in columns: 68 - 23

Method. Write the numbers in columns with tens under tens and ones under ones. Work from the ones.

  1. Write the numbers in columns. The tens go in one column and the ones in another.
    6 8 and 2 3
  2. Take away the ones. Work out the ones first.
    8 - 3 = 5
  3. Take away the tens. Then work out the tens.
    6 - 2 = 4
  4. Write the answer. Read the tens, then the ones.
    45

Check. Check by adding back: 45 + 23 = 68.

Watch out. Start with the ones column. Keep each digit in its column.

Worked example 7.5.3
Work out the answer. Set it out in columns: 84 + 13

Method. Write the numbers in columns with tens under tens and ones under ones. Work from the ones.

  1. Write the numbers in columns. The tens go in one column and the ones in another.
    8 4 and 1 3
  2. Add the ones. Work out the ones first.
    4 + 3 = 7
  3. Add the tens. Then work out the tens.
    8 + 1 = 9
  4. Write the answer. Read the tens, then the ones.
    97

Check. Check by taking 13 away: 97 - 13 = 84.

Watch out. Start with the ones column. Keep each digit in its column.

Watch out

Watch out. Line up the digits. The 3 in 31 must sit under the 2 in 52, not under the 5.

Exam tip

Grown-up tip. Draw the columns on squared paper, one digit in each square. Ask the child to read the ones first.

Exercise 7E  Practice: column sums

Non-calculator
1
FWork out the answer. Set it out in columns: 10 + 77
1077+
2
FWork out the answer. Set it out in columns: 84 - 54
8454-
3
FWork out the answer. Set it out in columns: 77 - 57
7757-
4
FWork out the answer. Set it out in columns: 35 + 12
3512+
5
FWork out the answer. Set it out in columns: 41 - 10
4110-
6
FWork out the answer. Set it out in columns: 78 - 58
7858-
7
FWork out the answer. Set it out in columns: 99 - 83
9983-
8
FWork out the answer. Set it out in columns: 67 - 47
6747-
9
FWork out the answer. Set it out in columns: 87 + 12
8712+
10
FWork out the answer. Set it out in columns: 80 + 18
8018+
11
FWork out the answer. Set it out in columns: 65 - 40
6540-
12
FWork out the answer. Set it out in columns: 38 + 61
3861+
13
FWork out the answer. Set it out in columns: 79 - 36
7936-
14
FWork out the answer. Set it out in columns: 30 + 48
3048+
15
FWork out the answer. Set it out in columns: 79 - 41
7941-
16
FWork out the answer. Set it out in columns: 96 - 35
9635-

Chapter summary

SkillMethod
Add a 1-digit numberAdd to the ones; keep the tens
Add a multiple of 10Add the tens; keep the ones
Add two 2-digit numbersAdd the tens, add the ones, put together
Subtract two 2-digit numbersTake the tens away, take the ones away, put together
ColumnsTens under tens, ones under ones; ones first

Can you…?

  • I can add a 1-digit number to a 2-digit number
  • I can add a multiple of 10 to a 2-digit number
  • I can add two 2-digit numbers by adding tens and ones
  • I can subtract two 2-digit numbers by subtracting tens and ones
  • I can set out a sum in columns

Key terms

sum
an addition, for example 23 + 45
difference
the answer to a subtraction, for example 68 - 23 = 45
column
a line of digits in the same place value, for example all the tens together
no carrying
the ones add to 9 or less, so the tens do not change

Exercise 7Z  Check-up

Non-calculator
1
Work out 89 - 37.
2
Work out the answer. Set it out in columns: 95 - 85
9585-
3
Work out 72 + 12.
4
Work out 86 + 10.
5
Work out 49 + 20.
6
Work out 61 + 2.
7
Work out 52 + 43.
8
Work out the answer. Set it out in columns: 68 + 11
6811+
9
Work out 26 + 2.
10
Work out 13 + 70.

Total 19 marks. Allow about 19 minutes.

Exercise 7X  Practice test questions

Non-calculator
1
FWork out 62 + 6.[1 mark]
2
FWork out the answer. Set it out in columns: 53 + 36[1 mark]
5336+
3
FWork out 47 + 30.[1 mark]
4
FWork out the answer. Set it out in columns: 49 - 10[1 mark]
4910-
5
FWork out 26 + 41.[2 marks]
6
FWork out 66 - 13.[2 marks]
7
FWork out 48 + 1.[2 marks]
8
FWork out the answer. Set it out in columns: 37 - 25[3 marks]
3725-
9
FWork out 28 + 61.[3 marks]
10
FWork out 78 - 40.[3 marks]
← Chapter 6: Taking away within 20Chapter 8: Money →

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