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Transcript
Chapter Two Integers Section 2.1 Introduction to Integers Numbers greater than 0 are called positive numbers. Numbers less than 0 are called negative numbers. zero negative numbers -6 -5 -4 -3 -2 -1 positive numbers 0 1 Martin-Gay, Prealgebra, 5ed 2 3 4 5 6 3 -3 indicates “negative three.” 3 and +3 both indicate “positive three.” The number 0 is neither positive nor negative. zero negative numbers -6 -5 -4 -3 -2 -1 positive numbers 0 1 Martin-Gay, Prealgebra, 5ed 2 3 4 5 6 4 Some signed numbers are integers. Integers consist of the numbers labeled on the number line below. The integers are { …, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, …} zero negative numbers -6 -5 -4 -3 -2 -1 positive numbers 0 1 Martin-Gay, Prealgebra, 5ed 2 3 4 5 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” Martin-Gay, Prealgebra, 5ed 6 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -6 -5 -4 -3 -2 -1 0 1 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. Martin-Gay, Prealgebra, 5ed 7 The absolute value of a number is the number’s distance from 0 on the number line. The symbol for absolute value is . 2 is 2 because 2 is 2 units from 0. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -2 is 2 because -2 is 2 units from 0. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Martin-Gay, Prealgebra, 5ed 8 Helpful Hint 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. 0 0 zero -6 6 a positive number Martin-Gay, Prealgebra, 5ed 9 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 -6 -5 -4 -3 -2 -1 5 units 0 1 2 3 4 5 6 5 and -5 are opposites Martin-Gay, Prealgebra, 5ed 10 5 is the opposite of -5 and -5 is the opposite of 5. The opposite of 4 - (4) = The opposite of -4 - is -4 is written as -4 is 4 is written as (-4) = 4 - (-4) = 4 If a is a number, then - (-a) = a. Martin-Gay, Prealgebra, 5ed 11 Helpful Hint Remember that 0 is neither positive nor negative. Therefore, the opposite of 0 is 0. Martin-Gay, Prealgebra, 5ed 12