5.2

1. 5.2 The Integers

2. Whole Numbers • The set of whole numbers contains the set of natural numbers and the number 0. • Whole numbers = {0,1,2,3,4,…}

3. 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.

4. 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

5. Subtraction of Integers a – b = a + (b) Evaluate: a) –7 – 3 = –7 + (–3) = –10 b) –7 – (–3) = –7 + 3 = –4

6. Multiplication Property of Zero Division For any a, b, and c where b 0, means that c• b = a. Properties

7. Rules for Multiplication • The product of two numbers with likesigns (positive  positive or negative  negative) is a positivenumber. • The product of two numbers with unlikesigns (positive  negative or negative  positive) is a negative number.

8. 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

9. Rules for Division • The quotient of two numbers with likesigns (positive  positive or negative  negative) is a positivenumber. • The quotient of two numbers with unlikesigns (positive  negative or negative  positive) is a negative number.

10. Example • Evaluate: • a) b) • c) d)

11. 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