THE Z SET OF INTEGERS 6

If we take the N set of natural numbers and, for each number other than zero, +a, we add another with the negative sign, –a, the result is what is known in mathematics as the set of integers. It is represented by the letter Z.

Absolute and opposite value of an integer

• The absolute value of an integer is the natural number that we get from taking away the sign. It is written between bars.

Remember

The absolute value of a number is equal to its distance from zero on the number line.

anayaeducacion.es

Order from smallest to highest.

Examples

(–7) < 0 < (+1)

(–12) < (–9) < (–2)

Let's practise!

8 absolute value of a

Example |+7| = 7 |–7| = 7

• The opposite of an integer is another integer of identical absolute value, but with the opposite sign.

Example

The opposite of (+7) 8 (–7) The opposite of (–7) 8 (+7)

Order of the Z set

To represent integers, we write them in order on a number line.

This way, we can see that a number is bigger than any number to its left, and smaller than any number to its right.

• Any positive number is greater than zero, and zero is greater than any negative number.

• Negative numbers are ordered backwards compared to positive numbers. In a group of negative numbers, the biggest number is the one with the smallest absolute value.

1 Write the absolute value and the opposite of each number.

a) –3 b) +8 c) –11 d) +23 e) –37 f ) +60

2 Order these numbers from smallest to biggest: –7, –13, +8, –1, +1, +5, 0, +10, –24 a) Any integer is also a natural number. b) Any natural number is an integer. c) Only negative numbers have opposites. d) Two opposite integers have the same absolute value. anayaeducacion.es Activities for practising addition and subtraction.

3 True or false?