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Math 64 2.1 "Introduction to Integers" Objectives: * Represent real-life situations with integers. * Compare integers and graph integers on a number line. * Find the absolute value of a number. * Find the opposite of a number * Read bar graphs containing integers. Preliminaries: Thus far in this text, all numbers have been 0 or greater than 0. Numbers greater that 0 are called positive numbers. However, sometimes situations exist than cannot be represented by a number greater that 0. For example: Negative Temperatures are recorded as: Zero Positive below zero zero above zero The stock market will show as: a loss no change a gain Altitude can be measured as: below sea level sea level above sea level Business will report: losses no gain pro…ts Extending the number line to the left of 0 allows us to picture negative numbers, which are numbers that are less than 0. ————————————————————————————————————————————————— Graphing Integers Graphing Points on a Number Line: 1: Draw a horizontal line and choose some point on the line. Label this point as 0. 2: Using 0 as reference label all the integers. 3: For each point (number) that must be graphed draw a solid circle on the number line that corresponds to the required point. Example 1: (Graphing sets of Integers) Graph the following sets of integers on a number line. a) A = f 3; 1; 1; 3g b) B = f 5; 2; 0; 3; 8g Comparing Integers We can compare integers by using a number line. 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. Page: 1 Notes by Bibiana Lopez Prealgebra by Elayn Martin-Gay 2.1 Symbols for Order: Symbol Meaning Symbol < Meaning > Example 2: (Using > and <) Insert the appropriate symbol in the blank to make each statement true. a) 3 e) 0 0 1 b) 5 f) 7 2 4 c) 6 6 g) 8 10 d) 9 15 h) 10 20 Example 3: (True or false statements ) Determine whether each statement is true or false. a) 0 = 0 b) 9< 10 c) 5 5 d) 11 12 Finding the Absolute Value of a Number De…nition: "Absolute Value" The absolute value ( j j ) of a number is the number’s distance from 0 on the number line. Example 4: (Finding absolute value of integers) Find the following absolute values. a) j+3j b) j 1j c) j0j d) j 8j Example 5: (Using >, < and = ) Insert the appropriate symbol in the blank to make each statement true. a) j 5j 5 b) j2j 2 c) 12 j 12j d) j 9j j9j Example 6: (Finding absolute value of integers) Mark each statement as true or false. a) 15 = j15j b) j 2j = j2j c) j 20j Page: 2 20 d) 16 > j 16j Notes by Bibiana Lopez Prealgebra by Elayn Martin-Gay 2.1 Finding Opposites De…nition: "Opposites" If a is a number, then ( a) = a: Note: The opposite of 0 is 0 (itself !) Example 7: (Finding opposites of integers) Find the opposite of: a) 10 b) +12 c) 7 Reading Bar Graphs Containing Integers Example 8: (Application) The graph below shows the average temperature (in Fahrenheit) of the eight planets, excluding the newly classi…ed "dwarf planet," Pluto. Notice that a negative temperature is illustrated by a bar below the horizontal line representing 0 F; and a positive temperature is illustrated by a bar above the horizontal line representing 0 F: a) Which planet has the lowest average temperature? b) Which planet has the highest average temperature? Page: 3 Notes by Bibiana Lopez