2. Integers Lesson 1a: Integers Integers are whole numbers and their opposites. Negative integers are numbers less than zero. Positive integers are numbers greater than zero. There is a positive integer to complement every negative integer.

3. Addition of Integers Addition of Integers with the same sign: Add the absolute value. The absolute value is the number of units a number is from zero. The sum has the same sign as the number being added. Examples: 5 + 4 = a 9 = a The answer is positive because both 4 and 5 are positive. -5 + -4 = a -9 = a The answer is negative because both -4 and -5 are negative.

4. Addition of Integers Addition of Integers with different signs: Find the difference in absolute values. The sum has the same sign as the number with the greatest absolute value. Examples: 9 + -3 = a 6 = a The integer with the greatest value is 9. 9 is positive therefore the sum is positive. 4 + -8 = a -4 = a The integer with the greatest value is -8. -8 is negative, therefore the sum is negative

5. Example: Add -5 + 7 Number Lines A number line can be helpful when learning to add integers. -6 -5 -4 -3 -2 0 1 2 3 4 5 6 Since you’re adding 7 to -5, you want to start at -5 on the number line. -5 Then you want to draw an arrow going in the positive direction going 7 spaces. 7 spaces Then look at the integer your arrow ends up on. So -5 + 7 = 2

6. Subtraction of Integers To subtract an integer, add its opposite. Example: a = 7 - 10 a = 7 + -10 a = -3 Subtract +10 by adding (+) its opposite, -10 When you add a number’s opposite, the subtraction problem becomes an addition problem. y = 8 - 12 y = 8 + -12 y = -4 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 -4 12 spaces to the left So 8 - 12 = -4

7. Exercises 1. 9 + 6 =141516 If you are correct you will hear a chime 2. -6 + -8 =14 - 1412 3. -4 + -6 + -8 =-8 - 18 4. 8 - -3 =-5 - 11 5. - 4 - -2 =4 -2-2-6

8. Absolute Values of Integers Definition of Absolute Value For any real number a: If a > 0, then |a| = a, and if a < 0, then |a| = opposite of a. Example: |2| = 2 |-2| = 2 1. |-5| =5-5 2. |47| =47 - 47 3. -|25| =25 - 25 4. -|-25| =25 - 25 Click on the correct answer below for each problem. If you hear a chime, then you chose the correct answer.

9. Review: Definition, Rule, or Property Example Definition of Absolute Value For any real number a: If a > 0, then |a| = a, and If a < 0, then |a| = opposite of a. |2| = 2 |-2| = 2 Adding integers with the Same Sign To add integers with the same sign, add their absolute values. Give the sum the same sign as the integers. 3 + 4 = 7 -3 + (-4) = -7 Adding integers with Different Signs To add integers with the different signs, subtract the lesser absolute value from the greater absolute value. Give the result the same sign as the integer with the greater absolute value. -7 + 5 = -2 9 + (-3) = 6 Additive Inverse Property For every number a, a + (-a) = 0. -8 + 8 = 0 Subtraction Rule To subtract a rational number, you can add its additive inverse. For rational numbers a and b, a – b = a + (-b). 8 – (-3) = 8 + 3 = 10 Review