10 Construction Mathematics

Any positive integer having no factors other than itself and unity iscalled a prime number. Also, prime numbers are greater than 1. Some ofthe prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 etc.

The factors of 7 are 7 and 1, as 7 � 1 � 7

Similarly the factors of 11 are 11 and 1, as 11 � 1 � 11

Prime numbers can be divided only by their factors, for example:

A composite number can have other factors in addition to itself and 1.For example, number 12, which is not a prime number, has the follow-ing factors:

2 � 6 � 12

2 � 2 � 3 � 12

3 � 4 � 12

1 � 12 � 12

A number that can be obtained by squaring another number is called asquare number. 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 are some of the squarenumbers as they can be obtained by squaring 1, 2, 3, 4, 5, 6, 7, 8, 9 and10 respectively.

Addition involves combining two or more numbers to give the sumtotal. The plus sign (�) is used to denote addition.

Subtraction involves taking a number away from another number.The minus or negative sign (�) is used to denote subtraction. The fol-lowing rules apply to addition/subtraction:

(a) x � y � x � y for example: 11 � 5 � 16(b) x � y � x � y 11 � 5 � 6(c) x � (�y) � x � y 11 � (�5) � 11 � 5 � 6(d) x � (�y) � x � y 11 � (�5) � 11 � 5 � 16(e) �x �y � � (x � y) �11 �5 � �(11 � 5) � �16

EXAMPLE 2.1

A bricklayer bought the following items at a local DIY store:

concrete bricks – £80.00; cement – £7.50; sand – £8.80

If the cost of delivering the materials was £6.00, find:

(a) The total amount of the bill(b) The change he received if he gave £110 to the cashier

71

7 and7

1� �7

2.5 Squarenumbers

2.6 Addition andsubtraction

2.4 Prime andcomposite numbers