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Negative numbers
In this chapter you will learn to use negative numbers.
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2.1 Below zero
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Numbers below zero are used in many situations.
One of the most common is temperature.
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20
26
30
25
20
24
These numbers are called negative numbers.
10
23
0
0
22
10
10
21
10
20
19
18
17
16
Exercise 2.1
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14
1 Write the temperatures shown on these thermometers.
(a)
(b)
(c)
13
(d)
20
20
20
20
10
10
10
10
0
0
0
0
10
10
10
10
12
11
10
9
8
7
6
5
2 Write which temperature is lower in each pair.
(a)
(b)
(c)
4
(d)
20
20
20
20
20
20
20
20
10
10
10
10
10
10
10
10
0
0
0
0
0
0
0
0
10
10
10
10
10
10
10
10
3
2
1
0
1
2
3
3 Write the temperature which is:
(a) 3 degrees lower than 1°C
(c) 6 degrees higher than 9°C
(e) 12 degrees higher than 12°C
(g) 9 degrees higher than 3°C
4
(b) 4 degrees lower than 2°C
(d) 5 degrees higher than 6°C
(f) 15 degrees lower than 8°C
(h) 7 degrees lower than 2°C
4 The temperature in Braemar at 8 pm was 3°C. At midnight the temperature
had fallen by 5°C. What was the temperature at midnight?
5
6
7
8
9
10
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Chapter 2
5 Find the difference in temperature between each pair of thermometers:
(a)
(b)
(c)
(d)
20
20
20
20
20
20
20
20
10
10
10
10
10
10
10
10
0
0
0
0
0
0
0
0
10
10
10
10
10
10
10
10
6 Find the difference in temperature between:
(a) Montreal 7°C and Seattle 3°C
(b) Thurso 2°C and Dubai 15°C
(c) Berlin 3°C and Edinburgh 4°C
(d) Warsaw 6°C and Glasgow 1°C
2.2 Adding and Subtracting positive numbers
Subtract
3
2
1
0
Add
1
2
Example 1
Find (a) (5) 2
3
4
5
6
7
8
(b) (6) 10
6 5 4 3 2 1 0
1
2
3
4
(5) 2 3
7 6 5 4 3 2 1 0
1
2
3
4
(6) 10 4
Example 2
Find (a) 5 7
(b) (3) 5
4 3 2 1 0
1
2
3
4
5 7 2
5
6
10 9 8 7 6 5 4 3 2 1 0
(3) 5 8
Exercise 2.2
1 Find:
(a) (5) 4
(b) (3) 1
5 4 3 2 1 0
4 3 2 1 0
1
(c) (3) 5
4 3 2 1 0
1
2
(d) (6) 2
1
2
3
4
5
(f) (5) 0
6 5 4 3 2 1 0
7 6 5 4 3 2 1 0
(e) (8) 12
1
2
(h) (10) 5
10 9 8 7 6 5 4 3 2 1 0
8 7 6 5 4 3 2 1 0
1
(g) (6) 6
6 5 4 3 2 1 0
1
2
3
2
3
4
5
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Chapter 2
2 Copy and complete these sums.
(b) (6) 4
(a) 1 5
(d) (3) 10
3 Find:
(a) 3 6
(e) (4) 6
(i) (32) 15
(e) (8) 1
(b) (9) 2
(f) (6) 15
(j) (23) 10
(c) (2) 3
(f) (7) 5
(c) (8) 9
(g) (20) 30
(k) (15) 20
(d) (1) 5
(h) (10) 7
(l) (12) 8
4 Find:
(b) 5 6
(a) 6 3
0
1
2
3
4
5
6
7
3 2 1 0
8
2
3
4
5
4 3 2 1 0
1
2
3
4
(d) 7 10
(c) (2) 3
6 5 4 3 2 1 0
1
2
3
5
6
(f) (3) 3
(e) (5) 4
12 1110 9 8 7 6 5 4 3 2 1 0
109 8 7 6 5 4 3 2 1 0
1
5 Copy and complete these sums.
(b) 5 3
(a) 8 2
(d) (8) 10
1
(e) 6 6
(c) (3) 5
(f) (7) 12
6 Calculate:
(a) 4 2
(e) (9) 2
(i) 2 13
(m) (18) 6
(b) (3) 5
(f) (1) 6
(j) ( 20) 2
(n) (15) 35
(c)
(g)
(k)
(o)
7 Calculate:
(a) 1 3 10
(d) 2 5 9
(b) 7 10 6
(e) 7 1 12
(c) 4 5 3
(f) 3 8 1
4 10
10 15
(13) 2
14 20
(d) (2) 7
(h) (6) 5
(l) (11) 15
(p) (6) 5
8 (a) The temperature on the 16th February in several cities is shown below.
Put these cities in order of temperature starting with the lowest:
Denver
1°C
Vienna
3°C
Edinburgh
Vladivostock 12°C
Montreal 8°C
Hong Kong
(b) Which two cities have the biggest temperature difference?
(c) What is the biggest temperature difference?
2°C
14°C
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Chapter 2
9 Put the following lists of numbers in order starting with the smallest.
(a) 8, 14, 0, 5, 1, 3, 2, 4
(b) 12, 15, 7, 10, 1, 1
(c) 1, 6, 5, 3, 7, 4
(d) 16, 2, 20, 5, 14, 8
(e) 10, 15, 4, 12, 22, 17
2.3 Adding negative numbers
Numbers can be added in any order. 8 5 5 8
5 (7)
(7) 5
2
57
2
also
6 (2)
(2) 6
4
62
4
also
Adding a negative number is the same as subtracting the positive number.
Example
(a)
10 (3)
10 3
7
(b)
5 (8)
58
3
(c)
(4) (3)
(4) 3
7
Exercise 2.3
1 Copy and complete:
(a) 6 (4)
6
(e)
3 (7)
(b)
(f)
2 Calculate:
(a) 5 (2)
(e) 3 (7)
(i) 9 (9)
(m) (3) (10)
10 (5)
10 7 (8)
(b) 6 (10)
(f) 12 (5)
(j) 3 (12)
(n) (4) (2)
3 In an ice dance competition, scores were given
for technique and artistic expression. Calculate
the total scores of the following couples.
Couple
Tom and Penelope
Helen and Fraser
Jenny and Chris
Fred and Wilma
Technique
Artistic expression
4
3
5
8
7
6
9
2
(c)
(g)
(c)
(g)
(k)
(o)
15 (8)
8
(5) (2)
4 (8)
10 (9)
(1) (3)
(4) (4)
(d)
(h)
14 (12)
14 (8) (3)
(d) 10 (2)
(h) 11 (5)
(l) (2) (5)
(p) (11) (8)
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Chapter 2
4 Copy and complete:
(a) 3 6 (2)
36
(b)
7 (2) 5
75
5 Calculate:
(a) 5 7 (8)
(c)
10 (4) 2
10 2
(b) 3 6 (3)
(b) 10 4 (1)
(d) 20 (5) 2
(c) 16 (3) (10)
(f) 18 (10) (9)
6 The temperatures at midnight in Portree for one week are shown below.
Day
Mon
Tues
Wed
Thurs
Fri
Sat
Sun
3
1
2
5
1
2
1
Temperature
Calculate the average temperature.
7 Find the missing numbers.
(a) 5 2
(b) 10 6
(c) 3 2
(d) (3) 5
(e) (5) 1
(f) 7 3
8 Write the next two numbers in each sequence.
(a) 18, 15, 12, 9, ___ , ___
(b) 14, 11, 8, 5, ___ , ___
(c) 6, 2, 2, 6, ___ , ___
(d) 25, 20, 15, 10, ___ , ___
9 In a school maths competition two points are awarded for a correct
answer and one point is deducted for a wrong answer.
Each pupil must answer 15 questions.
(a) Find the total score for the following pupils.
Name
Correct
Incorrect
Avril
Ateka
Barry
Martin
11
13
5
3
4
2
10
12
(b) In the same quiz Rahman scored 6 points and Nikki scored 15.
How many correct answers did they each give?
Fig A37 to come
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Chapter 2
2.4 Greater than or less than
means ‘is less than’
2 5 means ‘2 is less than 5’
means ‘is greater than’
8 6 means ‘8 is greater than 6’
These symbols show
inequalities.
Exercise 2.4
1 State whether each of the following inequalities is true or false.
(a) 3 5
(b) 10 7
(c) 5 0
(d) 2 1
(f) 2 0
(g) 1 2
(h) 4 6
(i) 7 5
(e) 3 3
(j) 0 4
2 Copy each pair of numbers and write or between them to make a true inequality.
(a) 3 7
(b) 15 11
(c) 6 10
(d) 32 31
(e) 4 0
(f) 10 20
(g) 50 10
(h) 130 200
3 Copy each pair of numbers and write or between them to make a true inequality.
(a) 5 2
(b) 3 6
(c) 4 0
(d) 3 3
(e) 6 2
(f) 11 5 (g) 2 5
(h) 10 12
Review exercise 2
1 Write the temperature which is:
(a) 6 degrees lower than 4°C
(c) 7 degrees higher than 10°C
(e) 2 degrees lower than 8°C
(b) 3 degrees lower than 3°C
(d) 5 degrees higher than 3°C
(f) 9 degrees lower than 4°C
2 Find the difference in temperature between:
(a) Bonn 7°C and Venice 2°C
(b) Lerwick 3°C and Caracas 24°C
(c) Reykjavik 3°C and Ayr 2°C
(d) Oslo 8°C and Glasgow 1°C
3 Find:
(a) 9 12
(e) (10) 2
(i) 3 10
(b) (7) 2
(f) (1) 13
(j) (2) 8
(c) 4 10
(g) 9 15
(k) (7) 6
(d) (3) 4
(h) (6) 11
(l) (12) 7
4 Calculate:
(a) 10 (4)
(e) 7 (7)
(i) (3) (10)
(b) 2 (7)
(f) (6) (4)
(j) 5 (12)
(c) (6) (6)
(g) 10 (6)
(k) (1) 3
(d) 7 (2)
(h) 14 (10)
(l) (2) (5)
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Chapter 2
5 Put the following lists of numbers in order starting with the smallest.
(a) 7, 2, 5, 3, 1, 1
(b) 7, 1, 0, 8, 18, 10, 5
6 Calculate:
(a) 6 8 (3)
(b) (5) (1) 10
(c) 7 (9) (4)
7 Copy each pair of numbers and write or between them to make a true inequality.
(a) 2 5
(b) 5 3
(c) 14 11
(d) 6 3
(e) 10 6
(f) 7 0
(g) 3 0
(h) 7 8
Summary
Numbers less than zero are called negative numbers.
You may use a number line to help with calculations.
10 9 8 7 6 5 4 3 2 1
0
1
2
3
4
5
6
7
8
9
10
8
9
10
9
10
When adding a positive number move right along the number line.
10 9 8 7 6 5 4 3 2 1
0
1
2
3
4
5
6
7
When subtracting a positive number move left along the number line.
10 9 8 7 6 5 4 3 2 1
0
1
2
3
4
5
6
7
8
When adding a negative number move left along the number line.
Adding a negative number is the same as subtracting the positive number.
means ‘is less than’
2 5 means ‘2 is less than 5’
means ‘is greater than’
8 6 means ‘8 is greater than 6’
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