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English1.4SpanishMultiplying IntegersIs the product of two integers positive,SSTATESTANDARDSnegative, or zero? How can you tell?MA.7.A.3.1MA.7.A.3.21EXAMPLE: Multiplying Integers with the Same Sign Use repeated addition to find 3 2. Recall that multiplication is repeated addition. 3 2 means to add3 groups of 2. 2 10 2123 245Now you can write3 2 2 2 2 6. 67 So, 3 2 6.2EXAMPLE: Multiplying Integers with Different Signs Use repeated addition to find 3 ( 2). 3 ( 2) means to add 3 groups of 2. 2 7 6 5 2 4 3 2 2 1Now you can write3 ( 2) ( 2) ( 2) ( 2) 01 6. So, 3 ( 2) 6.3ACTIVITY: Multiplying Integers with Different Signs Work with a partner. Use a table to find 3 2.Describe the pattern in the table. Use the pattern to complete the table. 21 20 2 1 2 2 2 3 2So, 3 2 222Chapter 1 4 2 0 .Operations with IntegersNotice the products decreaseby 2 in each row.So, continue the pattern. 2 2: 2 2 3 2: 4 2 1 2: 0 2
EnglishSpanish4ACTIVITY: Multiplying Integers with the Same Sign Work with a partner. Use a table to find 3 ( 2).Describe the pattern in the table. Use the pattern to complete the table. 3 3 2 3 1 3 0 3 1 3 2So, 3 ( 2) 3 9 6 3 Notice the products increaseby 3 in each row.So, continue the pattern. 3 1: 0 3 3 2: 3 3 3 0: 3 3 .Inductive ReasoningWork with a partner. Complete the table.Exercise 3 ( 2) 3 2 3 ( 2)6 32 ( 5) 6 5 5 ( 3)Type of ProductProduct15. 3 2Integers with the same sign26.Integers with different signs37.48.9.10.11.12.Product: Positiveor NegativeIntegers with different signsIntegers with the same sign13. Write two integers whose product is 0.14. IN YOUR OWN WORDS Is the product of two integers positive, negative, orzero? How can you tell?15. Write general rules for multiplying (a) two integers with the same sign and(b) two integers with different signs.Use what you learned about multiplying integers to completeExercises 8 –15 on page 26.Section 1.4Multiplying Integers23
English1.4SpanishLessonLesson TutorialsMultiplying Integers with the Same SignThe product of two integers with the same sign is positive.WordsNumbers 2 3 6 2 ( 3) 6Multiplying Integers with Different SignsThe product of two integers with different signs is negative.WordsNumbersEXAMPLE1 2 ( 3) 6 2 3 6Multiplying Integers with the Same Sign Find 5 ( 6).The integers have the same sign. 5 ( 6) 30The product is positive.The product is 30.EXAMPLE2Multiplying Integers with Different SignsMultiply. b. 7 4a. 3( 4)The integers havedifferent signs. 7 4 283( 4) 12The productis negative.The product is 12.The product is 28.Multiply.Exercises 8 –23 1. 5 52. 4(11)3. 1( 9)4. 7 ( 8) 24Chapter 1 5. 12 ( 2)6. 4( 6)7. 10(6)8. 5 7Operations with Integers
EnglishSpanishEXAMPLE3Using Exponentsa. Evaluate ( 2)2. ( 2)2 ( 2) ( 2)Study Tip 4Place parenthesesaround a negativenumber to raise it toa power.Write ( 2)2 as repeated multiplication.Multiply.b. Evaluate 52. 52 (5 5)Write 52 as repeated multiplication. 25Multiply.c. Evaluate ( 4)3. ( 4)3 ( 4) ( 4) ( 4) 16 ( 4)Write ( 4)3 as repeated multiplication.Multiply. 64Multiply.Evaluate the expression.9. ( 3)2Exercises 32–37EXAMPLE411. 7250 fewer taxisReal-Life ApplicationThe bar graph shows that the number of taxis in service decreasesby 50 each year. Use a model to solve the problem.Total change Change per year012312. 63The bar graph shows the number of taxis a company has inservice. The number of taxis decreases by the same amount eachyear for four years. Find the total change in the number of taxis.Taxis in ServiceNumber of taxis10. ( 2)34 Number of years 50 4Year 200Use 50 for the change per year becausethe number decreases each year.The total change in the number of taxis is 200.13. A manatee population decreases by 15 manatees each year for3 years. Find the total change in the manatee population.Section 1.4Multiplying Integers25
EnglishSpanishExercises1.4Help with Homework1. WRITING What do you know about the signs of two integers whose product is(a) positive and (b) negative?2. WRITING How is ( 2)2 different from 22?Tell whether the product is positive or negative without multiplying.Explain your reasoning.4. 5( 7)3. 4( 8) 5. 3 (12)Tell whether the statement is true or false. Explain your reasoning.6. The product of three positive integers is positive.7. The product of three negative integers is positive.6) 39 (- 3) 3 (- 9) 4 (- 1)9 (-Multiply.12 8. 6 410. 2(8)9. 7( 3) 11. 3( 4) 12. 6 713. 3 914. 8 ( 5)16. 5(10)17. 13(0)18. 9 919. 15( 2)22. 7( 14)23. 11 ( 11) 20. 10 1121. 6 ( 13) 15. 1 ( 12) 24. JOGGING You burn 10 calories each minute you jog. What integer representsthe change in your calories after you jog for 20 minutes?25. EROSION A shoreline in Volusia County recedes 9 feet each year. What integerrepresents the change in the shoreline after 4 years?Multiply. 28. 3( 5)( 4)26. 3 ( 8) ( 2)27. 6( 9)( 1)29. 7( 3)( 5)30. 6 3 ( 6)31. 3 ( 12) 033. ( 1)334. 82 Evaluate the expression.3 32. ( 4)2 35. 62 36. 52 437. 2 ( 3)3ERROR ANALYSIS Describe and correct the error in evaluating the expression.38.26 Chapter 139. 2( 7) 14Operations with Integers 102 100
EnglishSpanishALGEBRA Evaluate the expression when a 2, b 3, and c 8.40. ab41. a2c 42. ab3 acNUMBER SENSE Find the next two numbers in the pattern.43. 12, 60, 300, 1500, . . .44. 7, 28, 112, 448, . . .45. GYM CLASS You lose four points each time you attend gym classwithout sneakers. You forget your sneakers three times. Whatinteger represents the change in your points?46. AIRPLANE The height of an airplane during a landing is given by22,000 ( 480t), where t is the time in minutes.a. Copy and complete the table.b. Estimate how many minutesit takes the plane to land.Explain your reasoning.Time5 min10 min15 min20 minHeight47. INLINE SKATES In June, the price of a pair of inline skates is 165.The price changes each of the next three months.a. Copy and complete the table.MonthPrice of Skates 165June165July165 ( 12) August165 2( 12) September165 3( 12) b. Describe the change in the price of the inline skates foreach month.c. The table at the right shows the amount of money yousave each month to buy the inline skates. Do you haveenough money saved to buy the inline skates in August?September? Explain your reasoning.48.Amount SavedJune 35JulyAugust 55 45September 18Two integers, a and b, have a product of 24. What is the leastpossible sum of a and b?Divide. SKILLS REVIEW HANDBOOK49. 27 950. 48 651. 56 452. 153 953. MULTIPLE CHOICE What is the prime factorization of 84?()SKILLS REVIEW HANDBOOKA 22 32 B 23 7 C 33 7 Section 1.4D 22 3 7 Multiplying Integers27
Section 1.4 Multiplying Integers 23 Inductive Reasoning Work with a partner. Complete the table. Exercise Type of Product Product Product: Positive or Negative 5. 3 2 Integers with the same sign 6. 3 ( 2) Integers with different signs 7. 3 2 Integers with different signs 8. 3 ( 2) Int
