Adding Rational Numbers Identity Property of Addition 5

Adding Rational Numbers -Identity Property of Addition: -5 + 0 = -5 0+5=5 -Inverse Property of Addition: 7 + (-7) = 0 -7 + 7 = 0 Rules for Adding Numbers -Adding Numbers with the same signs: Add the numbers and keep the sign of whatever they are. Example: 2 + 8 = 10 -2 + (-8) = -10 -Adding Numbers with different signs: Subtract the numbers and keep the sign of the number with the greater absolute value. Example: -2 + 6 = 4 2 + (-6) = -4

Example 1: Add the following numbers. You can use the number line to help you if you need it. a. ) -5 + (-6) b. ) 12 + (-14) -11 -2 c. ) -4 + 10 d. ) -1 + 1 6 0

Example 2: Use each situation below to write an addition problem. Then solve it. a. ) A foot ball team gains 2 yards and then has a loss of 8. What is the result of the two plays. 2 + (-8) = -6 yards b. ) You lose 15 lbs. and gain back 7. What is the result. -15 + 7 = -8 lbs.

Subtracting Rational Numbers -Subtracting Numbers: to subtract a number, add its opposite and follow the rules for addition. Example: 3 – 5 = 3 + (-5) = -2 3 – (-5) = 3 + 5 = 8 Example 1: Subtract the following sets of numbers. a. ) -4 – (-9) -1 – (-9) = -4 + 9 = 5 c. ) 4 – 5 = 4 + (-5) = -1 b. ) -6 – 2 = -6 + (-2) = -8 d. ) -6 - 10 -6 – 10 = -6 + (-10) = -16

Simplifying inside Absolute Values a. ) b. )

Ch. 2 -3 Multiplying and Dividing Rational Numbers -Identity Property of Multiplication: when you multiply 1 by anything, you get that something back. Example: 1 * (-5) = -5 -5 * 1 = -5 -Multiplication Property of Zero: when you multiply 0 by anything, you get 0. Example: 3 * 0 = 0 0*3=0 -Multiplying Numbers with the same sign: the product of two positive numbers or two negative numbers is always positive. Example: -2 * -3 = 6 2*3=6 -Multiplying Numbers with different signs: the product of a negative number and a positive number is always negative. Example: 4 * -2 = -8 -4 * 2 = -8

Example 1: Evaluate the following expressions below for x = -10 and y = -2. a. ) -2 xy b. ) –(xy) -2(-10)(-2) -[(-10)(-2)] = -40 = -(20) = -20 Example 2: Simplify the following exponential expressions. a. ) (-3)4 Because the negative sign is inside the parentheses, you need to include it when you do your multiplication. -3 * -3 = 81 b. ) -34 Because the negative sign isn’t inside parentheses, you do not need to include it when you do your multiplication and always tag it on at the end. Expressions like this are always negative! 3 * 3 * 3 = -81

-Dividing Numbers with the same sign: the quotient of two positive numbers or two negative numbers is always positive. Example: 6/3 = 2 -6/-3 = 2 -Dividing Numbers with different signs: the quotient of a negative number and a positive number is always negative. Example: 4 * -2 = -8 -4 * 2 = -8