Chapter 2 – Properties of Chapter 2 – Properties of Real NumbersReal Numbers

2.2 – Addition of Real Numbers2.2 – Addition of Real Numbers

2.2 – Addition of Real Numbers2.2 – 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 Add real numbers using a number line or addition

rulesrules

Use addition of real numbers to solve real-life Use addition of real numbers to solve real-life problemsproblems

2.2 – Addition of Real Numbers2.2 – Addition of Real Numbers

We can add real numbers with movements on We can add real numbers with movements on a number linea number line Add positive numbers by moving to the rightAdd positive numbers by moving to the right Add negative numbers by moving to the leftAdd negative numbers by moving to the left

2.2 – Addition of Real Numbers2.2 – Addition of Real Numbers

Example 1Example 1 Use a number line to find the sumUse a number line to find the sum 7 + (-3)7 + (-3) -8 + 2-8 + 2

2.2 – Addition of Real Numbers2.2 – Addition of Real Numbers

Example 2Example 2 Use a number line to find the sum: -2 + (-3) + 6Use a number line to find the sum: -2 + (-3) + 6

2.2 – Addition of Real Numbers2.2 – Addition of Real Numbers

RULES OF ADDITIONRULES OF ADDITION TO ADD TWO NUMBERS WITH THE TO ADD TWO NUMBERS WITH THE SAME SAME

SIGNSIGN Add their absolute valuesAdd their absolute values Attach the common signAttach the common sign Example: -4 + -5Example: -4 + -5

2.2 – Addition of Real Numbers2.2 – Addition of Real Numbers

RULES OF ADDITIONRULES OF ADDITION TO ADD TWO NUMBERS WITH TO ADD TWO NUMBERS WITH OPPOSITE OPPOSITE

SIGNS:SIGNS: Subtract the smaller absolute value from the larger Subtract the smaller absolute value from the larger

absolute valueabsolute value Attach the sign of the number with the larger absolute Attach the sign of the number with the larger absolute

valuevalue Example: 3 + (-9)Example: 3 + (-9)

2.2 – Addition of Real Numbers2.2 – Addition of Real Numbers

PROPERTIES OF ADDITIONPROPERTIES OF ADDITION COMMUTATIVE PROPERTYCOMMUTATIVE PROPERTY

The order in which two numbers are added does not The order in which two numbers are added does not change the sum.change the sum.

a + b = b + aa + b = b + a Example : 3 + (-2) = (-2) + 3Example : 3 + (-2) = (-2) + 3

2.2 – Addition of Real Numbers2.2 – Addition of Real Numbers

PROPERTIES OF ADDITIONPROPERTIES OF ADDITION ASSOCIATIVE PROPERTYASSOCIATIVE PROPERTY

The way you group three numbers when adding does The way you group three numbers when adding does not change the sumnot 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 Numbers2.2 – Addition of Real Numbers

PROPERTIES OF ADDITIONPROPERTIES OF ADDITION IDENTITY PROPERTYIDENTITY PROPERTY

The sum of a number and 0 is the numberThe sum of a number and 0 is the number a + 0 = aa + 0 = a

Example: -4 + 0 = -4Example: -4 + 0 = -4

2.2 – Addition of Real Numbers2.2 – Addition of Real Numbers

PROPERTIES OF ADDITIONPROPERTIES OF ADDITION PROPERTY OF ZERO (INVERSE PROPERTY)PROPERTY OF ZERO (INVERSE PROPERTY)

The sum of a number and its opposite is 0The sum of a number and its opposite is 0 a + (-a) = 0a + (-a) = 0

Example: 5 + (-5) = 0Example: 5 + (-5) = 0

2.2 – Addition of Real Numbers2.2 – Addition of Real Numbers

Example 3Example 3

Find the sumFind the sum -0.7 + 1.9 + 0.7-0.7 + 1.9 + 0.7 -3 + 2/3 + 1/3-3 + 2/3 + 1/3

2.2 – Addition of Real Numbers2.2 – Addition of Real Numbers

Example 4Example 4

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

2.2 – Addition of Real Numbers2.2 – Addition of Real Numbers

Example 5Example 5A child care center had the following monthly results after A child care center had the following monthly results after

comparing income and expenses. Add the monthly profits comparing income and expenses. Add the monthly profits and losses to find the overall profit or loss during the four-and losses to find the overall profit or loss during the four-month period.month period.

MarchMarch $7, 982.43$7, 982.43

AprilApril -$1, 820.62-$1, 820.62

MayMay -$9, 219.56-$9, 219.56

JuneJune $12,043.65$12,043.65

2.2 – Addition of Real Numbers2.2 – Addition of Real Numbers

HOMEWORKHOMEWORK

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