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Multiplying & Dividing Integers Multiplying AND Dividing Integers follow the same rules: If the SIGNS are the SAME, the product or quotient is always POSITIVE. (4)(8) = 32 − 5 ∙ −8 = 40 −81 28 ÷ 4 = 7 −9 =9 If the SIGNS are DIFFERENT, the product or quotient is always NEGATIVE. −5(9) = −45 (3)(−4) = −12 27 ÷ −3 = −9 −60 12 = −5 If you are asked to perform repeated multiplication or division with integers, you must follow the order of operations and work from the LEFT to the RIGHT. −8 ∙ (−3) ∙ (−2) (3)(4)(−1)(−5) 100 ÷ (−2) ÷ 5 24 ∙ (−2) 12(−1)(−5) −50 ÷ 5 −48 −12(−5) −10 60 YOU TRY IT: Find each product or quotient. 7(−5) (−8)(−1) 45 −64 −9 −8 −8(−1)(−4) −81 ÷ 3 ÷ 3 − 11 ∙ 12 −5 ∙ 3 ∙ −2 −5(−8) −10 Multiplying & Dividing INTEGERS on Number Lines Name: _________________________ Any time you see repeated arrows along a number line, you are looking at a multiplication or a division model. It all depends on how you interpret the model verbally. See examples: −6 ÷ 3 = −2 6 ÷3=2 Negative 6 divided into 3 groups Each group has a value of -2 6 divided into 3 groups Each group has a value of 2 _____________________________________________________________________ Negative 15 divided into 5 groups −15 ÷ 5 = −3 Each group has a value of -3 _____________________________________________________________________ 4 ∙ 6 = 24 OR 24 ÷ 4 = 6 (divide into 4 groups or 6 each) 6 ∙ 4 = 24 OR 24 ÷ 6 = 4 (divide into 6 groups of 4 each) Modeling Integer Multiplication and Division Directions: Draw a model for each problem on the number lines provided. Write the answer to each problem on the blank space. 1) −5 ∙ 4 = ________ 2) −15 ÷ −3 = _______ 3) 3 ∙ 4 = ________ 4) −12 ÷ 4 = ________ Directions: Write a multiplication problem AND a division problem for each model given. Number Line Model Multiplication Division Multiplying & Dividing INTEGERS with Chip Models Name: __________________________ *Just like number line models, integer chip models for multiplication and division are very similar. See examples below: −10 ÷ −5 = 2 Negative 10 divided into 5 negative chips each, gives you 2 groups. −10 ÷ 2 = −5 Negative 10 divided into 2 groups, where each group has 5 negative chips. ______________________________________________________________________ - −8 ÷ 4 = −2 Negative 8 divided into 4 groups, where each group has 2 negative chips. −8 ÷ −2 = 4 Negative 8 divided into -2 chips each, gives you 4 groups. ______________________________________________________________________ 3(−2) = −6 3 groups of 2 negatives −6 ÷ 3 = −2 6 negatives divided into 3 groups of -2 each ______________________________________________________________________ YOU TRY IT: Write a multiplication problem AND a division problem represented by the model below: Multiplication: ____________________ Division: ____________________