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  4d) >  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.

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

Next Steps Read Examples 1-7 Work Problems in text on p , odds; 71-76, all Do Online homework corresponding to this section