1.1 Integers

REVISION NOTES

IGCSE Edexcel Mathematics A

1.1.1 Understand and use integers (positive, negative and zero)

1.1.2 Understand place value

1.1.3 Use directed numbers in practical situations

Directed Numbers

Directed numbers are numbers with both size and direction:
- Positive numbers: numbers with the ‘+’ sign
- Negative numbers: numbers with the ‘−’ sign
- 0 is neither positive nor negative. It is not a directed number
Two numbers with the same numerical value but different signs are called opposite numbers
- e.g. the opposite number of −6 is +6

Positive Numbers

Negative Numbers

‘Increase’

‘Going up’

‘Above’

‘Decrease’

‘Going down’

‘Below’

Example

1. Suppose 5 represents 5 floors above ground level. Use a directed number to represent 10 levels below ground level.

10 levels below ground level can be represented by –10

2. Suppose +3 km represents walking 3 km due east. Use a directed number to represent walking 7 km due west.

Walking 7km due west can be represented by –7

1.1.4 Order integers

Number Lines

Directed numbers can be represented on a straight line in order of magnitude, which is called the number line
A number line can be extended endlessly towards the two directions

If the number is on the right of another, it is a larger number
If the number is on the left of another, it is a smaller number
When we compare negative numbers, remember that:
- When the numerical value is bigger,
- It means it is a smaller number (more negative)

Example

–4 is on the left of –2, it means –4 is smaller than –2

1.1.5 Use the four rules of addition, subtraction, multiplication and division

1.1.6 Use brackets and the hierarchy of operations

Bracket

Order

Division

Multiplication

Addition

Subtraction