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Multiplying and Dividing Integers

Multiplying and Dividing Integers. 192. 49. 36. 16. 7. 9. Review. Multiply or divide. 1. 5(8). 40. 2. 6(12). 72. 3. 4. 4. 7. 12. 5. 18(7). 126. 6. Learn to multiply and divide integers. A positive number multiplied by an integer can be written as repeated addition.

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Multiplying and Dividing Integers

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  1. Multiplying and Dividing Integers

  2. 192 49 36 16 7 9 Review Multiply or divide. 1. 5(8) 40 2. 6(12) 72 3. 4 4. 7 12 5. 18(7) 126 6.

  3. Learn to multiply and divide integers.

  4. 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.

  5. 3(–200) = 2(–200) = 1(–200) = 0(–200) = –1(–200) = –2(–200) = –3(–200) = 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. –600 + 200 –400 + 200 –200 + 200 0 The product of two negative integers is a positive integer. 200 400 600

  6. Example: Multiplying and Dividing Integers Multiply or divide. Signs are different. A. –6(4) Answer is negative. = –24 Signs are the same. B. –8(–5) Answer is positive. = 40

  7. –18 –25 2 –5 Example: Multiplying and Dividing Integers Multiply or divide. C. Signs are different. Answer is negative. = –9 D. Signs are the same Answer is positive. = 5

  8. Try This Multiply or divide. Signs are different. A. 5(–2) Answer is negative. = –10 Signs are the same. B. –3(–2) Answer is positive. = 6

  9. –24 –12 3 –2 Try This Multiply or divide. C. Signs are different. Answer is negative. = –8 D. Signs are the same Answer is positive. = 6

  10. Remember! Order of Operations 1. Parentheses 2. Exponents 3. Multiply and divide from left to right. 4. Add and subtract from left to right.

  11. Example: 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

  12. Example: Using the Order of Operations with Integers Simplify. C. –2(14 – 5) Subtract inside the parentheses. = –2(9) Think: The signs are different. = –18 The answer is negative.

  13. Try This Simplify. A. 2(1 – 8) Subtract inside the parentheses. = 2(–7) Think: The signs are different. = –14 The answer is negative. B. 4(–3 – 8) Subtract inside the parentheses. = 4(–11) Think: The signs are different. = –44 The answer is negative.

  14. Try This Simplify. C. –3(6 – 9) Subtract inside the parentheses. = –3(–3) Think: The signs are the same. = 9 The answer is positive.

  15. The order of operations can be used to find ordered pair solutions of integer equations. Substitute an integer value for one variable to find the value of the other variable in the ordered pair.

  16. (1, 2) (0, –1) (–1, –4) (–2, –7) (2, 5) Example 3: Plotting Integer Solutions of Equations Complete a table of solutions for y = 3x – 1 for x = –2, –1, 0, 1, and 2. Plot the points on a coordinate plane. y 10 8 6 4 2 2 4 6 8 10 –7 3(–2) – 1 (–2, –7) x –4 (–1, –4) 3(–1) – 1 10 8 6 4 2 2 4 6 8 10 –1 3(0) – 1 (0, –1) 3(1) – 1 (1, 2) 2 3(2) – 1 (2, 5) 5

  17. (1, –1) (0, –3) (–1, –5) (–2, –7) (2, 1) Try This Complete a table of solutions for y = 2x – 3 for x = –2, –1, 0, 1, and 2. Plot the points on a coordinate plane. y 10 8 6 4 2 2 4 6 8 10 –7 2(–2) – 3 (–2, –7) x –5 (–1, –5) 2(–1) – 3 10 8 6 4 2 2 4 6 8 10 –3 2(0) – 3 (0, –3) 2(1) – 3 –1 (1, –1) 2(2) – 3 (2, 1) 1

  18. –12(5) –10 –36 t Lesson Quiz: Part 1 Perform the given operations. 1. –8(4) –32 2. 6 Evaluate the expressions for the given value of the variable. 3. –4t – 9 for t = –6 15 4. for t = 9 –4

  19. Lesson Quiz: Part 2 5. Complete a table of solutions for y = 4x + 1 for x = –3, –1, 1, and 3. –11 4(–3) + 1 (–3, –11) –3 (–1, –3) 4(–1) + 1 4(1) + 1 (1, 5) 5 4(3) + 1 (3, 13) 13

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