Integers and Absolute Value

Integers are whole numbers and their opposites. Remember…. Integers are whole numbers and their opposites. -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5

Terms associated with Integers Negative Positive Below Bonus Goes down Above BC Profit Withdrawal AD Lost/Loss Goes up Descending Increase Decrease Deposit Ascending

Operations with Integers Addition Subtraction Multiplication Division Equals Sum Difference Product Quotient Is Plus Decreased by Twice Per Equal More than Less than Multiplied Divided Increased by Minus Times Separate In all Each

Operations with Integers Addition with Same Sign Integers Positive + Positive = Positive 5 + 4 = 9 Negative + Negative = Negative (- 7) + (- 2) = - 9

Operations with Integers Addition with Different Sign Integers Use the sign of the larger number and subtract (- 7) + 4 = -3 Larger number is 7 so 7 – 4 = 3 The answer is negative because there are more negatives

1. 6 + (-9) = 2. (- 3) + 7 = 3. 5 + ( -3) =

1. 6 + (-9) = - 3 2. (- 3) + 7 = 4 3. 5 + ( -3) = 2

Subtraction of a Negative Is really addition of a positive Use Keep it, Change it, Opposite This concept changes any subtraction to addition of the opposite Ex: 9 – (-4) -15 – (-20) 9 + 4 -15 + 20 9 + 4 = 13 -15 + 20 = 5

Operations with Integers Multiplication and Division Positive & Positive = Positive Negative & Positive = Negative Negative & Negative = Negative

Absolute Value – measures the distance a number is from zero |-6| = 6

Simplify |9| + |-9|

Simplify |9| + |-9| |9| + |-9| = 9 + 9 = 18

Simplify |13| - |-2|

Simplify |13| - |-2| |13| - |-2| = 13 – 2 = 11

Evaluate the expression |x| - 7 if x = - 13

Example 4: Evaluate the expression |x| - 7 if x = - 13 = 13 – 7 = 6