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Study Guide: Integers and Integer Operations Name: Integer: a counting number, zero, or the opposite of a counting number […-2, -1, 0, 1, 2…] NOT a fraction, decimal, or percent -2.5, ¾ , 35% Integers are used to represent everyday situations in word problems. positive situations negative situations above below deposit withdraw rise fall gain loss after before increase decrease Adding Integers Model the addition of integers using zero pairs. Zero Pair: the pairing of a positive with a negative; has a value of zero 1 2 3 represent each integer with counters remove zero pairs record value of remaining counters Formulated Rules: positive + positive = always positive negative + negative = always negative 5+3=8 -5 + -3 = -8 positive + negative = ? If there are more positives, the answer will be positive. If there are more negatives, the answer will be negative. 5 + -3 = 2 -5 + 3 = -2 In other words… 1 identify the larger number 2 the sign (positive or negative) of the larger number will be the sign of the answer 3 subtract the numbers Example: 12 + -15 = ? Subtract 15 – 12 = 3 so the answer is -3. Practice: 8 + -5 = ? The larger numbers is 15, which is negative… therefore, the answer will be negative. (Are there more positives or negatives?) (How many more?) Answer: ____ Subtracting Integers Use the KISS method to turn the subtraction problem into an addition problem. Then, add the numbers accordingly. KISS = Keep It, Switch, Switch (add the opposite) Examples: 10 – 18 = ____ -7 – 2 = ____ 8 – (-7) = ____ -3 – (-11) = ____ 10 + -18 = -8 -7 + -2 = -9 8 + (+7) = 15 -3 + (+11) = 8 Multiplying and Dividing Integers Formulated Rules: same signs (get along) positive ∙ positive = positive negative ∙ negative = positive 12 ∙ 4 = 48 -9 ∙ -3 = 27 different signs (do not get along) negative ∙ positive = negative positive ∙ negative = negative -5 ∙ 6 = -30 2 ∙ -11 = -22 * Use same rules for division 10 ÷ 7 = 70 -8 ÷ -6 = 48 -9 ÷ 5 = -45 3 ÷ -6 = -18 Practice Complete the following equations. Draw a picture to model some of your work! 1. -3 + -10 = _____ 2. 4 + -12 = _____ 3. -5 + -5 = _____ 4. 2 – 8 = _____ 5. 5 – (-4) = _____ 6. -13 – 3= _____ 7. 3 ● (-5) = _____ 8. -2(-12) = _____ 9. -4 ● 8 = _____ 10. -72 ÷ 9 = _____ 11. 55 ÷ (-5) = _____ 12. -24 = _____ -2