© boardworks ltd 2006 1 of 42 ks3 mathematics n2 negative numbers

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KS3 Mathematics

N2 Negative numbers

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Contents

N2 Negative numbers

N2.1 Ordering integers

N2.4 Multiplying and dividing integers

N2.2 Adding and subtracting integers

N2.3 Using negative numbers in context

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Introducing integers

A positive or negative whole number, including zero, is called an integer.

A positive or negative whole number, including zero, is called an integer.

–3 is an example of 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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Positive and negative integers can be shown on a number line.

Positive integersNegative integers

We can use the number line to compare integers.

For example:

–3–8

–3 > –8

–3 ‘is greater than’ –8

Integers on a number line

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Ordering negative numbers

Write the integers –2, 8, 2, –6, –9 and 5 in order from smallest to largest.

We can also use a number line to help us write integers in order.

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

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N2.2 Adding and subtracting integers

N2.4 Multiplying and dividing integers

N2.1 Ordering integers

N2.3 Using negative numbers in context

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Mid-points

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Adding integers

We can use a number line to help us add positive and negative integers.

–2 + 5 =

-2 3

= 3

To add a positive integer we move forwards up the number line.

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We can use a number line to help us add positive and negative integers.

To add a negative integer we move backwards down the number line.

–3 + –4 == –7

-3-7

–3 + –4 is the same as –3 – 4

Adding integers

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Ordered addition square

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Mixed addition square

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5-3

Subtracting integers

We can use a number line to help us subtract positive and negative integers.

5 – 8 == –3

To subtract a positive integer we move backwards down the number line.

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3 – –6 =

3 9

= 9

We can use a number line to help us subtract positive and negative integers.

To subtract a negative integer we move forwards up the number line.

3 – –6 is the same as 3 + 6

Subtracting integers

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We can use a number line to help us subtract positive and negative integers.

–4 – –7 =

-4 3

= 3

To subtract a negative integers we move forwards up the number line.

–4 – –7 is the same as –4 + 7

Subtracting integers

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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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Magic Square

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Chequered sums

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Integer circle 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.

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.a + –b is the same as a – b.

a – –b is the same as a + b.a – –b is the same as a + b.

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N2.3 Using negative numbers in context

Contents

N2 Negative numbers

N2.4 Multiplying and dividing integers

N2.1 Ordering integers

N2.2 Adding and subtracting integers

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Negative numbers in context

There are many real life situations which use negative numbers.

Temperature

Balance -£34.52

Bank balances

Games with negative scores.

Measurements taken below sea level

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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

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N2.4 Multiplying and dividing integers

N2.1 Ordering integers

N2.2 Adding and subtracting integers

N2.3 Using negative numbers in context

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–3 + –3 + –3 + –3 + –3 =

0–3–6–9–12

–3

–15

–15

5 × –3 = –15

A positive number × a negative number = a negative numberA positive number × a negative number = a negative number

Multiplying and dividing integers

–3–3–3–3

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–7 × 3 == 3 × –7 =

0

–7

–7

–7

–14

–7

–21

–21

A negative number × a positive number = a negative numberA negative number × a positive number = a negative number

Multiplying and dividing negative numbers

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–4 × –6 =

0

– –6

6

– –6

12

– –6

18

– –6

24

24

A negative number × a negative number = a positive numberA negative number × a negative number = a positive number

Multiplying and dividing negative numbers

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Ordered multiplication square

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When multiplying negative numbers remember:

Rules for multiplying and dividing

Dividing is the inverse operation to multiplying.

When we are dividing negative numbers similar rules apply:

+ × + = +

–+ × = –

–+× =–

– +× =–

+ ÷ + = +

–+ ÷ = –

–+÷ =–

– +÷ =–

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Multiplying and dividing integers

Complete the following:

–3 × 8 = –24

42 ÷ = –6–7

× –8 = 96–12

47 × = 1413

–72 ÷ –6 = 12

–36 ÷ = –49

÷ –90 = –6540

–7 × = 175–25

–4 × –5 × –8 = –160

3 × –8 ÷ = 1.5–16

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Using a calculator

We can enter negative numbers into a calculator by using thesign 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

3

–7–4

×2–8

–2–10 ÷ –5

2

× –1

–2

+ 8

6÷ –2–3×

5

–15

+ 4–11

– 5

–16+ 16

0