Negative Numbers 2
Addition and Subtraction

In this section we consider how to add and subtract when working with negative numbers. This is done using a number line.

To add a positive number, move to the right on a number line.

To add a negative number, move to the left on a number line.

Worked Examples

1

Calculate:

(a)

−3 + 8

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Start at −3 and move 8 to the right:

So, −3 + 8 = 5.
(b)

4 + (−2)

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Start at 4 and move 2 to the left:

So, 4 + (−2) = 2.
(c)

−8 + 5

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Start at −8 and move 5 to the right:

So, −8 + 5 = −3.
(d)

−1 + (−3)

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Start at −1 and move 3 to the left:

So, −1 + (−3) = − 4.

Subtraction is the inverse (or opposite) of addition, so

To subtract a positive number, move to the left on a number line.

To subtract a negative number, move to the right on a number line.

2

Calculate:

(a)

5 − 7

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Start at 5 and move 7 to the left:

So, 5 − 7 = −2.
(b)

−2 − 3

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Start at −2 and move 3 to the left:

So, −2 − 3 = −5.
(c)

4 − (−2)

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Start at 4 and move 2 to the right:

So, 4 − (−2) = 6.
(d)

−5 − (−3)

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Start at – 5 and move 3 to the right:

So, −5 − (−3) = −2.

Exercises

Use a number line to work out the following calculations:

(a)
−4 + 6
(b)
−5 + 8
(c)
−1 + 3
(d)
−4 + 7
(e)
2 + (−3)
(f)
−1 + (−4)
(g)
−2 + (−3)
(h)
−6 + 6
(i)
−7 + 4
(j)
−6 + 2
(k)
−7 + 2
(l)
5 + (−5)

Use a number line to calculate:

(a)
4 − 6
(b)
5 − 7
(c)
2 − 4
(d)
−1 − 1
(e)
−3 − 2
(f)
−4 − (−1)
(g)
3 − (−4)
(h)
5 − (−6)
(i)
8 − 12
(j)
−5 − (−1)
(k)
4 − 9
(l)
−4 − (−4)

Write down a possible sum that could be shown by each number line below:

(a)

=

(b)

=

(c)

=

(d)

=

(e)

=

(f)

=

(g)

=

Complete this addition table:

+−4−2024
−3
−1
1
3

Fill in the missing numbers on a copy of this addition table:

+13
−5−5−1
−3
0
−20

Fill in the missing numbers:

(a)
4 + = 1
(b)
3 − = −6
(c)
−6 + = −7
(d)
+ 7 = 2
(e)
− 7 = −8
(f)
4 − = 7

Write down the next 5 terms in each sequence:

(a)

10, 8, 6, 4,  ,  ,   ,  , 

(b)

−10, −7, −4, −1,  ,  , ,   , 

(c)

19, 14, 9, 4,   , ,  ,  ,  

(d)

−1, −3, −5, −7,  ,  ,   ,  , 

(e)

−20, −16, −12, −8,  ,  ,  ,   , 

(f)

−5, −10, −15, −20,  ,   ,  ,  , 

(g)

18, 15, 12, 9,  ,  ,   , ,  

(h)

−16, −12, −8, −4,   ,  , ,  ,  

Overnight, the temperature dropped from 5 °C to –14 °C. By how many degrees did the temperature fall?

  °C

One day the level of the water in a river was 30 cm above its average level. One week later it was 12 cm below its average level. How far did the water level drop in the week?

  cm

A chest of treasure was hidden in the year 64 BC and found in 284 AD. For how long was the chest hidden?

  years