Unit 15 Section 1 : Adding and Subtracting Negative Numbers

In this section we look at adding and subtracting when negative numbers are involved.
We will use a number line like the one below to help us.

We already know what happens when we add or subtract positive numbers.

If you add a positive number you move to the right on a number line.
If you subtract a positive number you move to the left on a number line.
Always start from the position of the first number.
Adding Examples
3 + 5 = 8 (start at 3 and move 5 to the right)
-4 + 5 = 1 (start at -4 and move 5 to the right)
-9 + 5 = -4 (start at -9 and move 5 to the right)
Subtracting Examples
9 - 7 = 2 (start at 9 and move 7 to the left)
3 - 7 = -4 (start at 3 and move 7 to the left)
-1 - 7 = -8 (start at -1 and move 7 to the left)
Check the examples yourself on the number line above.

Practice Questions
Work out the answer to each of these questions then click on the button marked Click on this button below to see the correct answer to see whether you are correct.
(a) -3 + 8
(b) -8 + 5
(c) 5 - 7
(d) -2 - 3

We can also use a number line when adding or subtracting negative numbers.

Adding or subtracting a negative number goes in the opposite direction to adding or subtracting a positive number.

If you add a negative number you move to the left on a number line.
If you subtract a negative number you move to the right on a number line.
Again, start the movement from the position of the first number.
Adding Examples
7 + (-4) = 3 (start at 7 and move 4 to the left)
1 + (-4) = -3 (start at 1 and move 4 to the left)
-3 + (-4) = -7 (start at -3 and move 4 to the left)
Subtracting Examples
4 - (-3) = 7 (start at 4 and move 3 to the right)
-2 - (-3) = 1 (start at -2 and move 3 to the right)
-8 - (-3) = -5 (start at -8 and move 3 to the right)
Check the examples yourself on the number line above.

Practice Questions
Work out the answer to each of these questions then click on the button marked Click on this button below to see the correct answer to see whether you are correct.
(a) 4 + (-2)
(b) -1 + (-3)
(c) 4 - (-2)
(d) -5 - (-3)

This table may help you remember the rules:

Adding a positive - move rightSubtracting a positive - move left
Adding a negative - move leftSubtracting a negative - move right
Remember that it doesn't matter whether
you start with a positive or negative number

 

Exercises

Work out the answers to the questions below and fill in the boxes. Click on the Click this button to see if you are correct button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on Click on this button to see the correct answer to see the answer.

Question 1
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) =

Question 2
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) =

Question 3
Complete this addition table:

+
-4
-2
0
2
4
 -3 
-1
1
3

Question 4
Fill in the missing numbers on this addition table:

+
1
3
 -5 
-5
-1
-3
0
-2
0

Question 5
Fill in the missing number in each of these equations:

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

Question 6
Write down the next five terms in each of the sequences below.
You must separate the numbers in your answer with commas, like this: You must type commas between the numbers in lists

(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,

Question 7
Overnight, the temperature dropped from 5 ºC to -14 ºC.
By how many degrees did the temperature fall?
ºC

Question 8
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

Question 9
A chest of treasure was hidden in the year 64 BC and found in 284 AD.
For how long was the chest hidden?
years

You have now completed Unit 15 Section 1
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Produced by A.J.Reynolds January 2001