Page 8 - Mathematics Coursebook

1 Integers

!e "rst numbers you learn about are Key words
whole numbers, the numbers used for
counting: 1, 2, 3, 4, 5, …, … Make sure you learn and

!e whole number zero was only understand these key words:
understood relatively recently in whole number

human history. !e symbol 0 that is negative number
used to represent it is also a recent positive number

invention. !e word ‘zero’ itself is of integer
Arabic origin. multiple
From the counting numbers, people developed common multiple
lowest common multiple
the idea of negative numbers, which are used, for factor
°
example, to indicate temperatures below zero on ° C F remainder
the Celsius scale. 50 120
40 100 common factor
In some countries, there may be high mountains 30 divisible
and deep valleys. !e height of a mountain is 20 80 prime number

measured as a distance above sea level. !is is the 10 60 sieve of Eratosthenes

place where the land meets the sea. Sometimes 0 40 20 product
the bottoms of valleys are so deep that they are –10 0 square number

described as ‘below sea level’. !is means that the –20 –20 square root
distances are counted downwards from sea level. –30 –40 inverse
–40

!ese can be written using negative numbers.

!e lowest temperature ever recorded on the
Earth’s surface was −89 °C, in Antarctica in 1983.
!e lowest possible temperature is absolute zero, −273 °C.

When you refer to a change in temperature, you must always describe it as a number of degrees. When
you write 0 °C, for example, you are describing the freezing point of water; 100 °C is the boiling point
of water. Written in this way, these are exact temperatures.
To distinguish them from negative numbers, the counting numbers are called positive numbers.
Together, the positive (or counting) numbers, negative numbers and zero are called integers.
!is unit is all about integers. You will learn how to add and subtract integers and you will study

some of the properties of positive integers. You will explore other properties of numbers, and
di$erent types of number.

You should know multiplication facts up to 10 × 10 and the associated division facts.
For example, 6 × 5 = 30 means that 30 ÷ 6 = 5 and 30 ÷ 5 = 6.

!is unit will remind you of these multiplication and division facts.

1 Integers 7