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Lesson 2-1 and Lesson 2-2 Adding and Subtracting Integers I Can… Add two integers. Add more than two integers. Subtract integers. Evaluate expressions containing variables. Algebra Tiles We will use PINK tiles to represent NEGATIVE #s -1 We will use BLUE tiles to represent POSITIVE #s 1 Example 1 -1 + ( -2) -1 -1 -1 = -3 Example 2 3 + ( -2) 1 1 -1 -1 1 =1 Example 1: Adding Integers on a Number Line Find 2 + (-5) ① Always start at zero. ② Move RIGHT for a positive number. ③ Move LEFT for a negative number. Adding Integers with the Same Sign Words Examples To add integers with the same sign: 1. Add their absolute value. 2. Give the result the same sign. -5 + (-2) = -7 6+3=9 Example 2: Add Integers with the Same Sign Find – 4 + (-5) Adding Integers with Different Signs Words Examples To add integers with different signs: 1. Subtract their absolute value. 2. Give the result the same sign as the integer with the greater absolute value. + (-2) = 5 +2= 5 Example 3: Add Integers with Different Signs Find – 8 + 3 Find 10 + (-4) Example 4: Use Integers to Solve a Problem During the night, the average temperature on the moon is -140°C. By noon, the average temperature has risen 252°C. What is the average temperature on the moon at noon? Words The temperature at night is -140°C. It increases 252°C by noon. What is the temperature at noon? Variables Let x= the temperature at noon. Equation temperature at night plus increase by noon equals temperature at noon Additive Inverse Property Two numbers with the same absolute value but different signs are called opposites. An integer and its opposite are also called additive inverses. Additive Inverse Property Words The sum of any number and its additive inverse is zero. Symbols x + (-x) = 0 Example 6 + (-6) = 0 Example 5: Add 3 or more Integers 9 + (-3) + (-9) -4 + 6 + (-3) + 9 Whiteboard Practice Adding Integers 5 + (-6) = -1 8+5 = 13 -8 + (-9) = -17 -3 + 9 =6 -11 + 5 = -6 6 + (-9) + 9 =6 -9 + 16 + (-10) = -3 -41 + 25 + (-10) = -26 Ι 18 + (-13) Ι =5 Ι -25 + (-12) Ι =37 Subtracting Integers Words To subtract an integer, add its additive inverse. Symbols a – b = a + (-b) Example 5 – 9 = 5 + (-9) or -4 -2 – 7 = -2 + (-7) or -9 Example 6: Subtract a Positive Integer 8 - 13 -4 - 10 Example 7: Subtract a Negative Integer 7 – (−3) −2 − (−4) Example 8: Evaluate Algebraic Expressions Evaluate a – b + c if a = 15, b = 5, and c = −8 Evaluate s − t if s = −9 and t = −3 Example 9: Subtract Integers to Solve a Problem The table shows the record high and low temperatures recorded in selected states through 1999. What is the range, or difference between the highest and lowest temperatures, for Virginia? State Lowest Temp. °F Highest Temp °F Utah −69 117 Vermont −50 105 Virginia −30 110 Washington −48 118 West Virginia −37 112 Wisconsin −54 114 Wyoming −66 114 Whiteboard Practice Subtracting Integers -13 - 9 = -22 20 – (−15) = 35 −1 − (−10) =9 −16 − (−3) = −13 Evaluate m − (−2) if m =4 =6 Evaluate x – y if x = −14 and y = −2 = −12 Evaluate x – y – z if x = -3, y = 8, and z = -12 =1