Decimal Calculations 1
Addition and Subtraction of Decimals

We first revise addition and subtraction of whole numbers and then look at some problems in contexts.

Worked Examples

1
(a)

3 + (6 + 2)

Show me
3 + (6 + 2) = 3 + 8 since 6 + 2 = 8
= 11
(b)

18 − (4 + 7)

Show me
18 − (4 + 7) = 18 − 11 since 4 + 7 = 11
= 7
(c)

12 − (4 − 2)

Show me
12 − (4 − 2) = 12 − 2 since 4 − 2 = 2
= 10
(d)

(12 − 4) − 2

Show me
(12 − 4) − 2 = 8 − 2 since 12 − 4 = 8
= 6
2

Calculate:

(a)

102.8 + 15.21

Show me

To find 102.8 + 15.21, line up the decimal points:

102.80
+15.21
118.01
(b)

92.69 − 10.4

Show me

To find 92.69 − 10.4, line up the decimal points:

92.69
−10.40
82.29

Exercises

Find:

(a)
3 + 5
(b)
8 + 3
(c)
9 + 7
(d)
7 + 8
(e)
7 + 6
(f)
5 + 9
(g)
14 + 22
(h)
18 + 9
(i)
16 + 15
(j)
21 + 22
(k)
18 + 7
(l)
14 + 31
(m)
47 + 9
(n)
82 + 6
(o)
72 + 17

Is each of these statements true or false?

(a)
3 + 9 = 9 + 3
(b)
3 − 1 = 1 − 3
(c)
8 + 2 + 9 = 9 + 8 + 2
(d)
14 + 7 + 6 = 7 + 20
(e)
3 + 16 − 3 = 16
(f)
17 − 10 = 10 − 17
(g)
4 + 16 + 9 = 11 + 16
(h)
14 + 8 = 8 + 14

Find:

(a)
8 − 5
(b)
9 − 7
(c)
7 − 4
(d)
8 − 6
(e)
15 − 3
(f)
18 − 5
(g)
28 − 15
(h)
48 − 26
(i)
12 − 9
(j)
16 − 7
(k)
14 − 5
(l)
32 − 24
(m)
122 − 86
(n)
92 − 47
(o)
57 − 39

Find:

(a)
3 + (6 − 2)
(b)
5 − (8 − 7)
(c)
(3 + 6) − 8
(d)
15 − (4 + 2)
(e)
(17 − 1) − 4
(f)
23 − (4 − 2)
(g)
5 + (14 − 7) − 3
(h)
4 + (71 − 1) + 1
(i)
8 − (3 − 2) + 5
(j)
16 − (8 − 7) − 5

Copy these sums and put brackets into each one, so that they are correct.

(a)
5 − 8 − 7 = 4 = 4
(b)
6 − 3 + 2 = 1 = 1
(c)
5 + 7 − 2 − 1 = 11 = 11
(d)
14 − 7 − 3 − 2 = 8 = 8

Find the sum of each set of numbers.

(a)
18 and 15
(b)
6, 10 and 24
(c)
42, 33 and 62
(d)
47, 82 and 37

Find the difference between each pair of numbers.

(a)
18 and 15
(b)
22 and 47
(c)
92 and 46
(d)
57 and 84

Miss Sharp teaches 2 classes in one morning. There are 32 children in the first class and 28 in the second.

(a)

How many children does she teach altogether?

(b)

How many more children are there in the first class than in the second?

There are 22 people on a bus.

(a)

At the next stop 5 people get off and 12 people get on. How many are now on the bus?

(b)

At the next stop nobody gets off and the bus leaves with 35 people on board. How many people got on at this stop?

This season Ali has scored 12 goals for his team. Last season he scored 18 goals for his team.

(a)

How many goals did he score in total in the two seasons?

(b)

What is the difference between the number of goals scored in each season?

Jane has 42 CDs. Sarah has 8 fewer than Jane. Nadia has 13 more than Sarah. How many CDs does Nadia have?

In one school there are 3 classes in Year 7. One class has 28 children, one has 29 children and the other has 31 children. How many children are there in Year 7?

There are 216 cars in a car park. In the next hour, 82 cars arrive and 73 cars leave. How many cars are in the car park at the end of the hour?

Alison goes on holiday on her motorbike. She keeps a record of how far she rides each day.

Day12345
Miles120385962119

What is the total distance she rides?

miles

Use a quick method for each of these sums.

(a)
18 + 7 + 12
(b)
108 + 19 + 12
(c)
99 + 17 + 11
(d)
17 + 19 + 13
(e)
46 + 23 − 16
(f)
128 − 15 − 13
(g)
72 + 11 + 38
(h)
19 + 6 − 9
(i)
52 + 23 − 12
(j)
16 + 18 − 6
(k)
37 + 42 − 2
(l)
68 + 19 + 1
(m)
33 − 7 + 17
(n)
67 + 18 + 13

Find:

(a)
0.3 + 0.6
(b)
0.8 + 0.1
(c)
0.42 + 0.11
(d)
1.2 + 3.7
(e)
1.46 + 3.42
(f)
5.7 + 2.4
(g)
6.7 + 3.6
(h)
5.12 + 8.99
(i)
17.2 + 0.42
(j)
5.6 + 3.21
(k)
0.04 + 1.521
(l)
6.3 + 4.72
(m)
18.14 + 3.2
(n)
16.5 + 3.218

Find:

(a)
0.7 − 0.2
(b)
0.9 − 0.6
(c)
1.3 − 0.1
(d)
4.2 − 3.1
(e)
6.9 − 3.5
(f)
8.9 − 7.3
(g)
7.2 − 5.3
(h)
6.6 − 4.8
(i)
19.24 − 8.3
(j)
18.62 − 1.7
(k)
15.2 − 3.46
(l)
11.4 − 3.12
(m)
0.7 − 0.04
(n)
0.88 − 0.49