Chapter 2 – Properties of Real Numbers 2.2 – Addition of Real Numbers

Today we will learn how to: Today we will learn how to: Add real numbers using a number line or addition rules Add real numbers using a number line or addition rules Use addition of real numbers to solve real-life problems Use addition of real numbers to solve real-life problems

2.2 – Addition of Real Numbers We can add real numbers with movements on a number line We can add real numbers with movements on a number line Add positive numbers by moving to the right Add positive numbers by moving to the right Add negative numbers by moving to the left Add negative numbers by moving to the left

2.2 – Addition of Real Numbers Example 1 Example 1 Use a number line to find the sum Use a number line to find the sum 7 + (-3) 7 + (-3)

2.2 – Addition of Real Numbers Example 2 Example 2 Use a number line to find the sum: -2 + (-3) + 6 Use a number line to find the sum: -2 + (-3) + 6

2.2 – Addition of Real Numbers RULES OF ADDITION RULES OF ADDITION TO ADD TWO NUMBERS WITH THE SAME SIGN TO ADD TWO NUMBERS WITH THE SAME SIGN Add their absolute values Add their absolute values Attach the common sign Attach the common sign Example: Example:

2.2 – Addition of Real Numbers RULES OF ADDITION RULES OF ADDITION TO ADD TWO NUMBERS WITH OPPOSITE SIGNS: TO ADD TWO NUMBERS WITH OPPOSITE SIGNS: Subtract the smaller absolute value from the larger absolute value Subtract the smaller absolute value from the larger absolute value Attach the sign of the number with the larger absolute value Attach the sign of the number with the larger absolute value Example: 3 + (-9) Example: 3 + (-9)

2.2 – Addition of Real Numbers PROPERTIES OF ADDITION PROPERTIES OF ADDITION COMMUTATIVE PROPERTY COMMUTATIVE PROPERTY The order in which two numbers are added does not change the sum. The order in which two numbers are added does not change the sum. a + b = b + a a + b = b + a Example : 3 + (-2) = (-2) + 3 Example : 3 + (-2) = (-2) + 3

2.2 – Addition of Real Numbers PROPERTIES OF ADDITION PROPERTIES OF ADDITION ASSOCIATIVE PROPERTY ASSOCIATIVE PROPERTY The way you group three numbers when adding does not change the sum The way you group three numbers when adding does not change the sum (a + b) + c = a + (b + c) (a + b) + c = a + (b + c) Example: (-5 + 6) + 2 = -5 + (6 +2) Example: (-5 + 6) + 2 = -5 + (6 +2)

2.2 – Addition of Real Numbers PROPERTIES OF ADDITION PROPERTIES OF ADDITION IDENTITY PROPERTY IDENTITY PROPERTY The sum of a number and 0 is the number The sum of a number and 0 is the number a + 0 = a a + 0 = a Example: = -4 Example: = -4

2.2 – Addition of Real Numbers PROPERTIES OF ADDITION PROPERTIES OF ADDITION PROPERTY OF ZERO (INVERSE PROPERTY) PROPERTY OF ZERO (INVERSE PROPERTY) The sum of a number and its opposite is 0 The sum of a number and its opposite is 0 a + (-a) = 0 a + (-a) = 0 Example: 5 + (-5) = 0 Example: 5 + (-5) = 0

2.2 – Addition of Real Numbers Example 3 Example 3 Find the sum /3 + 1/ /3 + 1/3

2.2 – Addition of Real Numbers Example 4 Example 4 On a standardized test, students receive a score of +1 for each correct answer and -1 for each incorrect answer. Those questions that are left blank are given a zero. In order to get a grade above average on the test, a student’s total score must be above 35. Would the following students score above average on the test? Sylvia: 7 incorrect, 12 blank, 41 correct Sylvia: 7 incorrect, 12 blank, 41 correct Nathan: 8 incorrect, 5 blank, 47 correct Nathan: 8 incorrect, 5 blank, 47 correct

2.2 – Addition of Real Numbers Example 5 Example 5 A child care center had the following monthly results after comparing income and expenses. Add the monthly profits and losses to find the overall profit or loss during the four- month period. March $7, April -$1, May -$9, June$12,043.65

2.2 – Addition of Real Numbers HOMEWORK Page 75 #12 – 50 even, 62 – 69