2.3 Multiplying And Dividing Rational Numbers

English2.3SpanishMultiplying andDividing Rational NumbersHow can you useoperations with rational numbers in a story?1EXAMPLE: Writing a StoryWrite a story that uses addition, subtractionmultiplication, or division of rationalnumbers. Draw picturesfor your story.There are many possiblestories. Here is an example.Lauryn decides to earnsome extra money. She sets up a lemonade stand. To getcustomers, she uses big plastic glasses and makes a signsaying “All you can drink for 50 !”Lauryn can see that her daily profit is negative. But, she decides to keeptrying. After one week, she has the same profit each day.Lauryn is frustrated. Her profit for the first week is7( 5.75) ( 5.75) ( 5.75) ( 5.75) ( 5.75) ( 5.75) ( 5.75) ( 5.75) 40.25.She realizes that she has too many customers who are drinking a secondand even a third glass of lemonade. So, she decides to try a new strategy.Soon, she has a customer. He buys a glass of lemonade and drinks it.He hands the empty glass to Lauryn and says “That was great. I’ll haveanother glass.” Today, Lauryn says “That will be 50 more, please.” Theman says “But, you only gave me one glass and the sign says ‘All you candrink for 50 !’” Lauryn replies, “One glass IS all you can drink for 50 .”With her new sales strategy, Lauryn starts making a profit of 8.25 perday. Her profit for the second week is7(8.25) (8.25) (8.25) (8.25) (8.25) (8.25) (8.25) (8.25) 57.75.Her profit for the two weeks is 40.25 57.75 17.50. So, Lauryn hasmade some money. She decides that she is on the right track.62Chapter 2Rational Numbers and Equations

EnglishSpanish2ACTIVITY: Writing a StoryWork with a partner. Write a story that uses addition, subtraction,multiplication, or division of rational numbers. At least one of the numbers in the story has to be negative and notan integer. Draw pictures to help illustrate what is happening in the story. Include the solution of the problem in the story.If you are having trouble thinking of a story, here are some common usesof negative numbers. A profit of 15 is a loss of 15. An elevation of 100 feet is a depth of 100 feet below sea level. A gain of 5 yards in football is a loss of 5 yards. A score of 4 in golf is 4 strokes under par. A balance of 25 in your checking account means the account isoverdrawn by 25.3. IN YOUR OWN WORDS How can you use operations with rationalnumbers in a story? You already used rational numbers in your story.Describe another use of a negative rational number in a story.PUZZLE Read the cartoon. Fill in the blanks using 4s or 8s to make theequation true.4.5.( )( )( ) ( )11“Dear Mom, I’m in a hurry. To savetime I won’t be typing any 4’s or 8’s.”Section 2.311 —(8. 4.6) 1.( ) ( )3 —1 — — 0.6. 1.7.1 — — —312 — — 2 2.Multiplying and Dividing Rational Numbers63

English2.3SpanishLessonLesson TutorialsMultiplying and Dividing Rational NumbersWordsTo multiply or divide rational numbers, use the same rules forsigns as you used for integers.Rememberab27ba 13 2 17 3 221221 — — — — —NumbersThe reciprocal of — is —. 124912 94 1 92 4 9898 — — — — — — —EXAMPLE1Dividing Rational Numbers151312Find 5 — 2 —.1513Estimate 5 2 2 —26573 5 — 2— — — 265Write mixed numbers as improper fractions. 3773 — —Multiply by the reciprocal of —. 26 35 7 — 7835Multiply the numerators and the denominators.835 —, or 2 —835The quotient is 2 —.EXAMPLE2Simplify.Multiplying Rational Numbers Find 2.5 3.6. 2.5 3.6The decimals have different signs.150750 9.0 0The product is negative.The product is 9.64Chapter 2Rational Numbers and Equations83512Reasonable? 2 — 2 —

EnglishSpanishEXAMPLEStandardized Test Practice35Which number, when multiplied by —, gives a product3between 5 and 6?14A 6 14B 3 — C — D 3 Use the guess, check, and revise method.Guess 1: Because the product is positive and the known factor isC .negative, choose a number that is negative. Try Choice 14 1 ( 5)4 3( )53512 — — — —Guess 2: The result of Choice C is not between 5 and 6. So,B.choose another number that is negative. Try Choice 14( )53134( )53 13 ( 5)4 36512512 3 — — — — — — 5 —5125 — is between 5 and 6. So, the correct answer is B .Multiply or divide.EXAMPLE4( )122.— 2 —3.( )4. 1.8( 5.1)5. 6.3( 0.6)6.( 1.3)213231 32 —Real-Life ApplicationAccount PositionsStock( )1. — —65Exercises 10 – 33Original ValueCurrent ValueChangeA600.54420.15 180.39B391.10518.38127.28C380.2299.70 280.52An investor owns stocks A, B, and C.What is the mean change in value ofthe stocks? 180.39 127.28 ( 280.52)3 333.633mean ——— — 111.21The mean change in value of the stocks is 111.21.7. In Example 4, the change in value of stock D is 568.23.What is the mean change in value of the four stocks?Section 2.3Multiplying and Dividing Rational Numbers65

EnglishSpanishExercises2.3Help with Homework1. WRITING How is multiplying and dividing rational numbers similarto multiplying and dividing integers?Find the reciprocal.252. —1693. 3135. 2—4. —Tell whether the expression is positive or negative without evaluating.( )3108156. — —( )12147. 1— — 8.16 2.728. 6.2 8.189. —6) 39 (- 3) 3 (- 9) 4 (- 1)9 (-Divide. Write fractions in simplest form.710( )(14251 10. — —384527( )8911. — —41114. 2— ( 7)15. 10 — 4—18. 3.45 ( 15)19. 0.18 0.03)891512. — —13. — 2016. 9 7.217. 8 2.220. 8.722 ( 3.56)21. 12.42 ( 4.8)Multiply. Write fractions in simplest form.223291326. 3 —4323. — —7 ( 2 —10 )30. 8(0.09)( )( )143 22. — —27.2 33 1— 31. 9.3 ( 5.1)56( )( )8151424. — —25. 2 1—28. 0.4 ( 0.03)29. 0.05 ( 0.5) 32. 95.2 ( 0.12)33. ( 0.4)3ERROR ANALYSIS Describe and correct the error.34. 35. 2.2 3.7 8.14 14324132122 — — — — — 636. HOUR HAND The hour hand of a clock moves 30 every15hour. How many degrees does it move in 2— hours?37. SUNFLOWER SEEDS How many 0.75-pound packagescan be made with 6 pounds of sunflower seeds?66Chapter 2Rational Numbers and Equations 30

EnglishSpanishEvaluate.39. 2.85 6.2 2238. 4.2 8.1 ( 1.9)59( ) ( )23353441. 1— — 2—5640. 3.64 5.3 1.53( ) ( )2 2 3 1 — 2—34 31342. 3 — — 2 —43. —3544. OPEN-ENDED Write two fractions whose product is —.305045. FENCING A farmer needs toenclose two adjacent rectangularpastures. How much fencing doesthe farmer need?2yd95yd83446. GASOLINE A 14.5-gallon gasoline tank is — full. How many gallons will it taketo fill the tank?47. BOARDWALK A section of a boardwalk is made using 15 boards. Each board is149 — inches wide. The total width of the section is 144 inches. The spacing betweeneach board is equal. What is the width of the spacing between each board?48. RUNNING The table shows the changes in the times(in seconds) of four teammates. What is the mean change?149.234TeammateChange1 2.432 1.8530.614 1.455Consider ( 2) , ( 2) , ( 2) , ( 2) , ( 2) ,and ( 2)6.a. Evaluate each expression.b. What pattern do you notice?c. What is the sign of ( 2)49?Add or subtract.50. 6.2 4.7SECTION 2.251. 8.1 ( 2.7)95(71052. — 2—)54. MULTIPLE CHOICE What are the coordinates of thepoint in quadrant IV?SECTION 1.6A ( 4, 1) B ( 3, 3) C (0, 2) D (3, 3) ( )564953. 4— 3—y4A32C1 4 3 2BDO 2 3124 x3FE 4Section 2.3Multiplying and Dividing Rational Numbers67

Section 2.3 Multiplying and Dividing Rational Numbers 63 Work with a partner. Write a story that uses addition, subtraction, multiplication, or division of rational numbers. A t least one of the numbers in the story has to be negative and not an integer. Draw pictures to help illustrate what is happening in the story. Include the solution of the problem in the story.