Download N2 Negative numbers

KS3 Mathematics
N2 Negative numbers
1 of 42
© Boardworks Ltd 2004
Contents
N2 Negative numbers
N2.1 Ordering integers
N2.2 Adding and subtracting integers
N2.3 Using negative numbers in context
N2.4 Multiplying and dividing integers
2 of 42
© Boardworks Ltd 2004
Introducing integers
A positive or negative whole number, including zero, is
called an integer.
For example, –3 is an integer.
–3 is read as ‘negative three’.
This can also be written as –3 or (–3).
It is 3 less than 0.
0 – 3 = –3
Or in words,
‘zero minus three equals negative three’
3 of 42
© Boardworks Ltd 2004
Integers on a number line
Positive and negative integers can be shown on a number line.
–8
–3
Negative integers
Positive integers
We can use the number line to compare integers.
For example,
–3 > –8
–3 ‘is greater than’ –8
4 of 42
© Boardworks Ltd 2004
Ordering negative numbers
We can also use a number line to help us write integers in order.
Write the integers –2, 8, 2, –6, –9 and 5 in
order from smallest to largest.
Look at the position of the integers on the number line:
–9
–6
–2
2
5
8
So, the integers in order are:
–9, –6, –2, 2 , 5, and 8
5 of 42
© Boardworks Ltd 2004
Ordered Paths
6 of 42
© Boardworks Ltd 2004
Contents
N2 Negative numbers
N2.1 Ordering integers
N2.2 Adding and subtracting integers
N2.3 Using negative numbers in context
N2.4 Multiplying and dividing integers
7 of 42
© Boardworks Ltd 2004
Mid-points
8 of 42
© Boardworks Ltd 2004
Adding integers
We can use a number line to help us add positive and
negative integers.
–2 + 5 = 3
-2
3
To add a positive integer we move forwards up the
number line.
9 of 42
© Boardworks Ltd 2004
Adding integers
We can use a number line to help us add positive and
negative integers.
–3 + –4 == –7
-7
-3
To add a negative integer we move backwards down the
number line.
–3 + –4 is the same as
10 of 42
–3 – 4
© Boardworks Ltd 2004
Ordered addition square
11 of 42
© Boardworks Ltd 2004
Mixed addition square
12 of 42
© Boardworks Ltd 2004
Subtracting integers
We can use a number line to help us subtract positive and
negative integers.
5 – 8 == –3
-3
5
To subtract a positive integer we move backwards down
the number line.
13 of 42
© Boardworks Ltd 2004
Subtracting integers
We can use a number line to help us subtract positive and
negative integers.
3 – –6 = 9
3
9
To subtract a negative integer we move forwards up the
number line.
3 – –6
14 of 42
is the same as
3+6
© Boardworks Ltd 2004
Subtracting integers
We can use a number line to help us subtract positive and
negative integers.
–4 – –7= =3
-4
3
To subtract a negative integers we move forwards up the
number line.
–4 – –7
15 of 42
is the same as
–4 + 7
© Boardworks Ltd 2004
Using a number line
16 of 42
© Boardworks Ltd 2004
Ordered subtraction square
17 of 42
© Boardworks Ltd 2004
Mixed subtraction square
18 of 42
© Boardworks Ltd 2004
Complete this table
19 of 42
© Boardworks Ltd 2004
Integer cards - addition and subtraction
20 of 42
© Boardworks Ltd 2004
Magic Square
21 of 42
© Boardworks Ltd 2004
Chequered sums
22 of 42
© Boardworks Ltd 2004
Integer circle sums
23 of 42
© Boardworks Ltd 2004
Adding and subtracting integers summary
To add a positive integer we move forwards up the
number line.
To add a negative integer we move backwards down the
number line.
a + –b is the same as a – b.
To subtract a positive integer we move backwards down
the number line.
To subtract a negative integer we move forwards up the
number line.
a – –b is the same as a + b.
24 of 42
© Boardworks Ltd 2004
Contents
N2 Negative numbers
N2.1 Ordering integers
N2.2 Adding and subtracting integers
N2.3 Using negative numbers in context
N2.4 Multiplying and dividing integers
25 of 42
© Boardworks Ltd 2004
Negative numbers in context
There are many real life situations which use negative
numbers.
For example,
Bank balances
Temperature
Balance
Measurements taken below
sea level
26 of 42
-£34.52
Games with negative
scores.
© Boardworks Ltd 2004
Sea level
27 of 42
© Boardworks Ltd 2004
Temperatures
28 of 42
© Boardworks Ltd 2004
Ordering temperatures
29 of 42
© Boardworks Ltd 2004
Comparing temperatures
30 of 42
© Boardworks Ltd 2004
Contents
N2 Negative numbers
N2.1 Ordering integers
N2.2 Adding and subtracting integers
N2.3 Using negative numbers in context
N2.4 Multiplying and dividing integers
31 of 42
© Boardworks Ltd 2004
Multiplying and dividing integers
–3 + –3 + –3 + –3 + –3 = –15
–3
–15
–3
–12
–3
–9
–3
–6
–3
–3
0
5 × –3 = –15
A positive number × a negative number = a negative number
32 of 42
© Boardworks Ltd 2004
Multiplying and dividing negative numbers
–7 × 3 = 3 × –7 = –21
–7
–21
–7
–7
–14
–7
0
A negative number × a positive number = a negative number
33 of 42
© Boardworks Ltd 2004
Multiplying and dividing negative numbers
–4 × –6 = 24
0
– –6
– –6
– –6
6
12
– –6
18
24
A negative number × a negative number = a positive number
34 of 42
© Boardworks Ltd 2004
Ordered multiplication square
35 of 42
© Boardworks Ltd 2004
Rules for multiplying and dividing
When multiplying negative numbers remember:
positive × positive = positive
positive × negative = negative
negative × positive = negative
negative × negative = positive
Dividing is the inverse operation to multiplying.
When we are dividing negative numbers similar rules apply:
positive ÷ positive = positive
positive ÷ negative = negative
negative ÷ positive = negative
negative ÷ negative = positive
36 of 42
© Boardworks Ltd 2004
Multiplying and dividing integers
Complete the following:
–3 × 8 = –24
–36 ÷
42 ÷
–7 = –6
540 ÷ –90 = –6
–12 × –8 = 96
–7 × –25 = 175
47 ×
–4 × –5 × –8 = –160
3
= 141
–72 ÷ –6 =
37 of 42
12
9
= –4
3 × –8 ÷ –16 = 1.5
© Boardworks Ltd 2004
Using a calculator
We can enter negative numbers into a calculator by using the
sign change key: (–)
For example:
–417 ÷ –0.6 can be entered as:
(–)
4
1
7
÷
(–)
0
.
6
=
The answer will be displayed as 695.
Always make sure that answers given by a calculator are
sensible.
38 of 42
© Boardworks Ltd 2004
Mixed multiplication square
39 of 42
© Boardworks Ltd 2004
Mixed division square
40 of 42
© Boardworks Ltd 2004
Integer cards – multiplication and division
41 of 42
© Boardworks Ltd 2004
Number spiral
-10
-8
-4
2
-11
3
-15
0
-16
-3
42 of 42
-2
6
© Boardworks Ltd 2004