1. Integers Chapter Two

2. Introduction to Integers Section 2.1

3. Numbers greater than 0 are called positive numbers. Numbers less than 0 are called negative numbers. negative numbers zero positive numbers 6543210-2-3-4-5-6 3 Martin-Gay, Prealgebra, 5ed

4. - 3 indicates “negative three.” 3 and + 3 both indicate “positive three.” The number 0 is neither positive nor negative. negative numbers zero positive numbers 6543210-2-3-4-5-6 4 Martin-Gay, Prealgebra, 5ed

5. Some signed numbers are integers. Integers consist of the numbers labeled on the number line below. negative numbers zero positive numbers 6543210-2-3-4-5-6 The integers are { …, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, …} Martin-Gay, Prealgebra, 5ed

6. We compare integers just as we compare whole numbers. For any two numbers graphed on a number line, the number to the right is the greater number and the number to the left is the smaller number. < means “is less than” > means “is greater than” 6 Martin-Gay, Prealgebra, 5ed

7. 6543210-2-3-4-5-6 The graph of - 5 is to the left of - 3, so - 5 is less than - 3, written as -5 < - 3. We can also write - 3 > - 5. Since - 3 is to the right of - 5, - 3 is greater than - 5. 6543210-2-3-4-5-6 7 Martin-Gay, Prealgebra, 5ed

8. The absolute value of a number is the number’s distance from 0 on the number line. The symbol for absolute value is. is 2 because 2 is 2 units from 0. 6543210-2-3-4-5-6 is 2 because - 2 is 2 units from 0. 6543210-2-3-4-5-6 - 8 Martin-Gay, Prealgebra, 5ed

9. Since the absolute value of a number is that number’s distance from 0, the absolute value of a number is always 0 or positive. It is never negative. Helpful Hint zero a positive number - 9 Martin-Gay, Prealgebra, 5ed

10. Two numbers that are the same distance from 0 on the number line but are on the opposite sides of 0 are called opposites. 5 units 5 and - 5 are opposites 6543210-2-3-4-5-6 10 Martin-Gay, Prealgebra, 5ed

11. 5 is the opposite of - 5 and - 5 is the opposite of 5. The opposite of 4 is - 4 written as - (4) = - 4 The opposite of - 4 is 4 written as - (- (- 4) = 4 - (- 4) = 4 If a is a number, then - (- a) = a. 11 Martin-Gay, Prealgebra, 5ed

12. Remember that 0 is neither positive nor negative. Therefore, the opposite of 0 is 0. Helpful Hint 12 Martin-Gay, Prealgebra, 5ed