5.2

The Integers

Whole Numbers

The set of whole numbers contains the set of natural numbers and the number 0.

Whole numbers = {0,1,2,3,4,…}

Integers

The set of integers consists of 0, the natural numbers, and the negative natural numbers.

Integers = {…-4,-3,-2,-1,0,1,2,3,4,…} On a number line, the positive numbers

extend to the right from zero; the negative numbers extend to the left from zero.

Writing an Inequality

Insert either > or < in the box between the paired numbers to make the statement correct.

a) 3 1 b) 9 7 3 < 1 9 < 7

c) 0 4 d) 6 8

0 > 4 6 < 8

Subtraction of Integers

a – b = a + (b)

Evaluate:

a) –7 – 3 = –7 + (–3) = –10

b) –7 – (–3) = –7 + 3 = –4

Properties Multiplication Property of Zero

Division

For any a, b, and c where b 0, means that c • b = a.

0 0 0a a

a

cb

Rules for Multiplication

The product of two numbers with like signs (positive positive or negative negative) is a positive number.

The product of two numbers with unlike signs (positive negative or negative positive) is a negative number.

Examples

Evaluate: a) (3)(4) b) (7)(5) c) 8 • 7 d) (5)(8) Solution: a) (3)(4) = 12 b) (7)(5) = 35 c) 8 • 7 = 56 d) (5)(8) = 40

Rules for Division

The quotient of two numbers with like signs (positive positive or negative negative) is a positive number.

The quotient of two numbers with unlike signs (positive negative or negative positive) is a negative number.

Example

Evaluate:

a) b)

c) d)

72

98

72

98

72

89

72

89

Next Steps

Read Examples 1-7 Work Problems in text on p. 224

47-65, odds; 71-76, all Do Online homework corresponding to this

section