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2-3 Multiplying and Dividing Integers Problem of the Day Complete the pyramid by filling in the missing numbers. Each number is the sum of the numbers in the two boxes below it. –4 –8 –7 2 Course 3 –9 4 –1 5 8 –3 2-3 Multiplying and Dividing Integers Learn to multiply and divide integers. Course 3 2-3 Multiplying Insert Lesson HereIntegers andTitle Dividing A positive number multiplied by an integer can be written as repeated addition. 3(–200) = –200 + (–200) + (–200) = –600 From what you know about adding and subtracting integers, you can see that a positive integer times a negative integer is negative. Course 3 2-3 Multiplying Insert Lesson HereIntegers andTitle Dividing You know that multiplying two positive integers together gives you a positive answer. Look for a pattern in the integer multiplication at right to understand the rules for multiplying two negative integers. Course 3 3(–200) = –600 2(–200) = –400 1(–200) = –200 0(–200) = 0 + 200 + 200 + 200 –1(–200) = 200 The product of two negative –2(–200) = 400 integers is a positive –3(–200) = 600 integer. 2-3 Multiplying Insert Lesson HereIntegers andTitle Dividing MULTIPLYING AND DIVIDING TWO INTEGERS If the signs are the same, the sign of the answer is positive. If the signs are different, the sign of the answer is negative. Course 3 Love/Hate Love to Love ++=+ Love to Hate +-=- Hate to Love -+=- Hate to Hate --=+ 2-3 Multiplying and Dividing Integers Additional Example 1A & 1B: Multiplying and Dividing Integers Multiply or divide. A. –6(4) = –24 B. –8(–5) = 40 Course 3 Signs are different. Answer is negative. Signs are the same. Answer is positive. 2-3 Multiplying and Dividing Integers Additional Example 1C & 1D: Multiplying and Dividing Integers Multiply or divide. C. –18 2 = –9 D. Course 3 Signs are different. Answer is negative. –25 –5 Signs are the same =5 Answer is positive. 2-3 Multiplying and Dividing Integers Try This: Example 1A & 1B Multiply or divide. A. 5(–2) = –10 B. –3(–2) =6 Course 3 Signs are different. Answer is negative. Signs are the same. Answer is positive. 2-3 Multiplying and Dividing Integers Remember! Order of Operations 1. Parentheses 2. Exponents 3. Multiply and divide from left to right. 4. Add and subtract from left to right. Course 3 2-3 Multiplying and Dividing Integers Additional Example 2A & 2B: Using the Order of Operations with Integers Simplify. A. 3(–6 – 12) Subtract inside the parentheses. = 3(–18) Think: The signs are different. = –54 The answer is negative. B. –5(–5 + 2) Subtract inside the parentheses. = –5(–3) Think: The signs are the same. = 15 The answer is positive Course 3 2-3 Multiplying and Dividing Integers Additional Example 2C: Using the Order of Operations with Integers Simplify. C. –2(14 – 5) Course 3 Subtract inside the parentheses. = –2(9) Think: The signs are different. = –18 The answer is negative. 2-3 Multiplying and Dividing Integers Try This: Example 2A & 2B Simplify. A. 2(1 – 8) = 2(–7) Think: The signs are different. = –14 The answer is negative. B. 4(–3 – 8) Course 3 Subtract inside the parentheses. Subtract inside the parentheses. = 4(–11) Think: The signs are different. = –44 The answer is negative. 2-3 Multiplying and Dividing Integers Try This: Example 2C Simplify. C. –3(6 – 9) Course 3 Subtract inside the parentheses. = –3(–3) Think: The signs are the same. =9 The answer is positive. 2-3 Multiplying andTitle Dividing Insert Lesson HereIntegers Lesson Quiz: Part 1 Perform the given operations. 1. –8(4) –32 2. –12(5) 6 –10 Evaluate the expressions for the given value of the variable. 3. –4t – 9 for t = –6 15 4. –36 for t = 9 –4 t Course 3 2-3 Multiplying andTitle Dividing Insert Lesson HereIntegers Lesson Quiz: Part 2 5. Complete a table of solutions for y = 4x + 1 for x = –3, –1, 1, and 3. x y (x, y) –3 4(–3) + 1 –11 (–3, –11) –1 4(–1) + 1 –3 (–1, –3) (1, 5) 5 1 4(1) + 1 4(3) + 1 (3, 13) 13 3 Course 3 4x + 1