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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
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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’
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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
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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
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Ordered Paths
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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
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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.
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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
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–3 – 4
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Ordered addition square
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Mixed addition square
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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.
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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
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is the same as
3+6
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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
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is the same as
–4 + 7
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Using a number line
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Ordered subtraction square
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Mixed subtraction square
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Complete this table
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Integer cards - addition and subtraction
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Chequered sums
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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.
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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
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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
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-£34.52
Games with negative
scores.
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Sea level
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Temperatures
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Ordering temperatures
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Comparing temperatures
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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
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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
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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
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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
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Ordered multiplication square
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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
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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 =
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12
9
= –4
3 × –8 ÷ –16 = 1.5
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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.
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Mixed multiplication square
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Mixed division square
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Integer cards – multiplication and division
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Number spiral
-10
-8
-4
2
-11
3
-15
0
-16
-3
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-2
6
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