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Multiplying and Dividing Integers We are learning to…multiply and divide integers by looking for patterns. Thursday, May 25, 2017 Multiplication of Integers -8 Evaluate: -2 + -2 + -2 + -2 = ________ Multiplication Repeated addition is the same thing as:__________________ 4(-2) ...so -2 + -2 + -2 + -2 can be written:________ -12 Evaluate: -4 + -4 + -4 = ______________ Multiplication Repeated addition is the same thing as:__________________ . 3(-4) ..so -4 + -4 + -4 can be written:________ Multiplication of Integers -35 Evaluate: -7 + -7 + -7 + -7 + -7 = ______________ 5(-7) ...Rewrite as a multiplication problem:_________ -24 Evaluate: -12 + -12 = ______________ 2(-12) ...Rewrite as a multiplication problem:_________ -5 Evaluate: -1 + -1 + -1 + -1 + -1 = ______________ 5(-1) ...Rewrite as a multiplication problem:_________ Multiplication of Integers I know that: (positive number) × (negative number) = Negative Number _______________________________________. Commutative The ______________________________ property of multiplication allows me to multiply in any order. So I also know that (negative number) × (positive number) = Negative Number _______________________________________. Evaluate the expressions below. When your entire group is finished share your solutions. Multiplication of Integers Negative Negative Negative × Positive = _______________ and Positive × Negative = _______________ Negative If the signs in a multiplication problem are different the solution is:_______________ I know that a: Positive positive × positive = ______________ Negative (+)(–) = ______________ Now follow the pattern: Negative (–)(+) = ______________ Positive (+)(+) = ______________ So… I know that a: Positive (–)(–) = ______________ Positive negative × negative = _________________________ Positive If the signs in a multiplication problem are the same the solution is:_______________ 7(-8) = _____ A. B. C. D. 56 -56 -1 -15 -6(-7) = _____ A. B. C. D. 49 -42 -13 42 -9(3) = _____ A. B. C. D. 27 -6 -36 -27 Which of the following statements is NOT true? A. B. C. D. A negative multiplied by a negative is a positive product. A positive multiplied by a negative is a negative product. A negative multiplied by a negative is a negative product. A negative multiplied by a positive is a negative product. Division of Integers a c ______ b _______ a The Division Algorithm: If b c then ______ Example 1: Negative divided by a Positive: 40 40 -8 -8 5 40 ______ so… ______ ? or… 5 5 Negative Negative divided by a positive will always result in a:______________ Division of Integers a c ______ b _______ a The Division Algorithm: If b c then ______ Example 2: Positive divided by a Negative: 63 ? 9 or… 63 -7 ______ 9 -7 (9) 63 so… ______ Negative Positive divided by a negative will always result in a:______________ Division of Integers a c ______ b _______ a The Division Algorithm: If b c then ______ Example 2: Negative divided by a Negative: 42 ? 7 42 6 6 (7) 42 so… ______ or… 7 ______ Positive Negative divided by a negative will always result in a:______________ Division of Integers Wait a minute…these look familiar! Multiplication These are the same rules as:____________________________ Negative If the signs in a division problem are different the solution is:______________ Positive If the signs in a division problem are the same the solution is:_____________ Evaluating Integer Expressions Thursday, May 25, 2017 48 Evaluate: 6 A. B. C. D. 8 -8 7 -9 Evaluate: A. B. C. D. 21 -20 -22 -21 105 5 Evaluate: A. B. C. D. -7 7 8 -6 77 11 Evaluating Integer Expression Today you will use the Order of Operations and your knowledge about integer operations to simplify some complex expressions. Order of Operations: Parentheses Exponents Multiplication and Division Addition and Subtraction Evaluate: 2 4 6 1 3 5 A. B. C. D. -14 -30 20 -8 Evaluate: 7(3) 2 5 8 A. B. C. D. 315 -105 3 -76 2