Summary 123 Section 2.1 Integers, Absolute Value, and Opposite Key Concepts The numbers . . . 3, 2, 1, 0, 1, 2, 3, . . . and so on are called integers. The negative integers lie to the left of zero on the number line. 0 1 2 3 4 5 6 Zero Positive numbers The absolute value of a number a is denoted .The value of 0a 0 is the distance between a and 0 on the number line. Two numbers that are the same distance from zero on the number line, but on opposite sides of zero are called opposites. The opposite of a negative number is a positive number. That is, for a positive number, a, a is negative and 1a2 a. 0a 0 6 5 4 3 2 1 Negative numbers Examples Example 1 The temperature 5 below zero can be represented by a negative number: 5. Example 2 a. b. c. Example 3 The opposite of 12 is 1122 12. 05 0 5 013 0 13 00 0 0 Example 4 The opposite of 23 is 1232 23. Section 2.2 Addition of Integers Key Concepts To add integers using a number line, locate the first number on the number line. Then to add a positive number, move to the right on the number line. To add a negative number, move to the left on the number line. Integers can be added using the following rules: Adding Numbers with the Same Sign To add two numbers with the same sign, add their absolute values and apply the common sign. Adding Numbers with Different Signs To add two numbers with different signs, subtract the smaller absolute value from the larger absolute value. Then apply the sign of the number having the larger absolute value. An English phrase can be translated to a mathematical expression involving addition of integers. Examples Example 1 Add 2 142 using the number line. Move 4 units to the left. 8 7 6 5 4 3 2 1 0 1 2 2 142 6 Example 2 a. 5 2 7 b. 5 122 7 Example 3 a. 6 152 1 b. 162 5 1 Start here. Example 4 3 added to the sum of 8 and 6 translates to 18 62 132. Chapter 2 Summary
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