Simplifying Improper Fractions

Example 2Divide: 32 ! 98730 R 2732 ! 9879627027We begin by breaking the division into the smallerdivision problem 32 ! 98. Instead of thinking, “Howmany 32s are in 98?” we can use the first-digit trickand think, “How many 3s are in 9?” We see “32 ! 98”but we think “3 ! 9.” We try 3 as an answer. Sincewe are really finding 32 ! 98, we write the 3 abovethe 8 of 98. Then we multiply 3 by 32, subtract, andbring down.Now we begin the new division 32 ! 27. Sincethere is not even one 32 in 27, we write “0” inthe answer; then we multiply and subtract. Thereare no digits to bring down, so we are finished.The answer is 30 R 27. We can check our answerby multiplying 30 by 32 and then adding theremainder, 27.32 30960 27 remainder987 (check)Example 3Loma Vista School expects an enrollment of 868 students. Theprincipal wants to have about 24 students and one teacherper classroom. About how many teachers are needed for thestudents at Loma Vista School?We will use compatible numbers to estimate the number of teachersneeded. We could round 24 down to 20, but 24 is closer to 25, sowe choose 25. Now we round 868 to a number compatible with25. Since we rounded 24 up to 25, we round 868 up to 875. Wethink of 875 as 800 75. Every 100 is four 25s, so 800 25 is 32.Since 75 is three 25s, we find that 875 25 35. Loma VistaSchool needs about 35 teachers.LessonUse compatible numbers to estimate the quotient in problemsa and b.300 10 30b. 21 ! 253240 20 12c. 31 ! 40313d. 12 ! 25321 R 1e. 12 ! 3002523 ! 51022 R 4a. 11 ! 253Divide:One hundred forty-four players signed up for soccer. Ifthe players are separated into 12 equal teams, how manyplayers will be on each team? 12 players606Saxon Math Intermediate 5

Divide. Use the first-digit trick to help with the “divide” step.h. 22 R 22I. 22 R 5j. 20 R 20l. 34 R 2n. 31 R 3o. 22 R 8p. 61 R 9h. 30 ! 682k. 22 ! 924n. 21 ! 654Written Practice* 1.(31, 32)42i. 32 ! 709j. 43 ! 880l. 22 ! 750m. 21 ! 126o. 41 ! 9106p. 21 ! 1290Distributed and IntegratedDraw a pair of horizontal line segments. Make them thesame length. Then draw two more line segments to make a quadrilateral.RepresentSamples:and2. D’Ron worked on his homework from 3:30 p.m. to 6 p.m. How manyminutes did D’Ron work on his homework? 150 minutes(28, 49)3.(67)Represent9Write a decimal number equal to the mixed number 3 10. 3.94. If 24 eggs exactly fill 2 cartons, how many eggs will it take to fill 3 cartons?(49)36 eggs* 5. Some 1-inch cubes were used to build this 4-inch cube.(18)How many 1-inch cubes were used? 64 cubes4 in.4 in.4 in.* 6. a. How many apples weighing 13 pound each would it take to total 1 pound?(87)3 applesb. How many apples weighing 13 pound each would it take to total 4 pounds?12 apples* 7. Name this shape. How many edges does it have?(83)pyramid; 8 edges8. Name the shaded portion of this square as a decimalnumber, as a reduced fraction, and as a percent. 0.50; 12; 50%(71)Lesson 92607

9. Multiple Choice Which of these numbers does not equal 12? DA 0.5B 50%C 6D 0.0512(23)* 10. AB is 40 millimeters. BC is half of AB. CD equals BC. Find AD. 80 millimeters(61)A11. 8.7 6.25(73)14. 8 125(92)14.95 1000(17)* 17. 24 ! 510B21 R 6C12. 12.75 4.2D15. 2100 ! 264(78)57* 18. 3 " 188(91)* 13. 43 648.55(73)(78)* 16. 293 13222 R 7(92)219. 5 ! 15(63)152335* 20.1of 5 1 233* 23.Write a fraction equal to 25 that has a denominator of 10. Add14 1;2. Remember to reduce your answer. 10that fraction to 10* 24.The figure shows the length and width of arectangle. Estimate the area of the rectangle. 12 sq. ft(86)(79, 81)(62, 72)21. 3 # 4(76) 43* 22. 6 1(87) 10513AnalyzeEstimate3 ft 10 in.2 ft 11 in.25.(57)A penny, nickel, dime, and quarter are tossed at the sametime. Which word best describes the following events: likely, unlikely,certain, or impossible?Predicta. All of the upturned faces are heads.unlikelyb. At least one of the upturned faces is heads.c. There is one more heads than there is tails.26.(73)608likelyimpossibleIn the 1988 Summer Olympic games in Seoul,South Korea, U.S. athlete Florence Griffith-Joyner won three goldmedals in track events. “Flo-Jo,” as she was called, finished the200-meter run in 21.34 seconds, breaking the previous Olympicrecord of 21.81 seconds. By how much did Florence Griffith-Joynerbreak the previous Olympic record? 0.47 secondAnalyzeSaxon Math Intermediate 5

27. Use the information below to answer parts a–c.(Inv. 5,62)Sumi, Lupe, and Melanie bought decorations for theparty. The table shows the items they purchased.a.Describe how to estimate the total costof the items. What is your estimate?EstimateRound each price to the nearest dollar and then add; 8.b. What was the total cost of the decorations? 8.64c. If the girls share the cost evenly, how much will each girl pay? 2.88* 28.(Inv. 4)If the sequence below repeats after 5 terms, what are thenext 5 terms? 4, 4, 1, 4, 4Conclude4, 4, 1, 4, 4, . . .* 29.(Inv. 7)The lengths of several suspension bridges inNorth America are shown in this table:RepresentSuspension Bridges(North America)BridgeLocationLength (ft)Tacoma NarrowsTacoma, WA2800Golden GateSan Francisco Bay, CA4200A. Murray MackayHalifax, Nova Scotia1400Name an appropriate type of graph for the data. Explain your choice,and then graph the data. Bar graph; see student work.30. These thermometers show the average daily minimum and maximum(27)temperatures in Auckland, New Zealand, during the month of January.When compared to the lower temperature, how many degrees warmeris the higher temperature? 14 F &&Lesson 92609

LESSON93 Comparative GraphsPower UpfactsmentalmathPower Up I5a. Number Sense: Reduce the fractions 20,5,155and 10.1 1 14, 3, 2b. Powers/Roots: 33 27c. Money: The total fee for 4 children to attend the summercamp was 436. What was the cost per child?(Think: 436 4.) 109d. Percent: What is 50% of 100? . . . 50% of 10?. . . 50% of 1? 50; 5; 50 e. Time: How many years are in a millennium? How manyyears are in half of a millennium? 1000 yr; 500 yrf. Estimation: At the game, 329 fans wore red and 273 fanswore orange. There were 947 fans altogether. Use compatiblenumbers to estimate how many fans did not wear red ororange. Sample: 325 275 600; 950 600 350 fansg. Calculation:13of 6, 2, 1, 5, 1, 64h. Roman Numerals: Write IX in our number system. 9problemsolving61029282Choose an appropriate problem 8 9 solving strategy to solve this problem.2322522 2Bob erased some of the digits in amultiplication problem. He then gave itto Paolo as a problem-solving exercise. He told Paolo that thereare two different possible solutions. Copy Bob’s multiplicationproblem, and find both solutions for Paolo.Saxon Math Intermediate 5

New ConceptComparative graphs can be used to display two or more setsof related data.Example 1The average daily high temperatures in January and July for fivecities is displayed in the comparative vertical bar graph below.Average Daily High TemperaturesThinking SkillBar graphs usuallydo not have agreat number ofbars. Why not?Any number of barsis possible.Sample: It becomesdifficult to comparea great number ofbars; a graph withmany bars would bevery large.Temperature ( F)AnalyzeHow many barscan a bar graphhave?806040January2000JulyRome,ItalyCaracas, Sydney,Venezuela AustraliaParis,FranceTokyo,Japana. In which city was the average July high temperaturehighest?b. In which city was the average January high temperaturelowest?c. Which city had the smallest range between thesetemperatures? Do you know why?Visit www.SaxonMath.com/Int5Activities foran online activity.d. For which city is the average January high temperaturegreater than the average July high temperature? Do youknow why?a. The tallest dark blue bar appears above Rome, Italy. Theaverage July high temperature is about 89 F in Rome.b. The shortest light blue bar appears above Paris, France. Theaverage January high temperature is about 42 F in Paris.c. The smallest difference in heights of the bars occurs aboveCaracas, Venezuela. Caracas is near the equator, andtemperatures in locations near the equator do not vary muchthroughout the year.d. We look for the city that has a light blue bar that is taller than itsdark blue bar. We find Sydney, Australia. Australia is warmer inJanuary than in July because it is south of the equator. South ofthe equator, January is in the summer and July is in the winter.Lesson 93611

Example 2PopulationWe can use a double-line graph to show how two or morethings change in relation to one another. For example, thedouble-line graph below shows the change in population of thecities of Austin and Pittsburgh from 1950 to 2000. The legend tothe right tells which line belongs to which ,000LegendAustinPittsburgh1950 1960 1970 1980 1990 2000Yeara. Approximately what was Austin’s population in 1970?b. Approximately how much did Pittsburgh’s populationdecrease between 1950 and 2000?a. The line graph with solid dots represents Austin’s population.For 1970, the dot is about halfway between 200,000 and300,000, which means the population was about 250,000.b. In the 50-year period, Pittsburgh’s population declined fromabout 700,000 to about 350,000. Subtracting, we find thatthe decrease was approximately 350,000.700,000 350,000 350,000Lesson Practicea.Paragraphsper Storya. Chinara, Alice, Terrell, and Manuel each wrote two stories.The number of paragraphs per story is shown in the tablebelow:ChinaraAliceTerrellManuelStudentStory 1Story 2Chinara88Alice36Terrell67Manuel710Make a comparative horizontal bar graph to show thescores. There should be two bars for each student.612Saxon Math Intermediate 5

b. For a science project, Mia and Lonnie each planted a seed.A record of the height of each seedling is shown below.Display the data in a double-line graph. See student work.Written Practice* 1.(77, 85)Week 1Week 2Week 3Week 4Mia’s Seedling1 cm5 cm11 cm20 cmLonnie’s Seedling2 cm4 cm10 cm16 cmDistributed and IntegratedThe saying “A pint’s a pound the world around” means thata pint of water weighs about a pound. About how much does 2 quartsof water weigh? about 4 poundsEstimate2. At a grocery store, apples are sold by the pound. What is the cost of4 pounds of apples if 3 pounds costs 2.55? 3.40(49)3. If 300 marbles will fill a carton, how many marbles will make thecarton 12 full? 150 marbles(46)4. Name the shaded portion of this group as a decimalnumber, as a reduced fraction, and as a percent.(71)0.5; 12; 50%* 5. a.(87)How many plums weighing 15 pound each would it take tototal 1 pound? 5 plumsAnalyzeb. How many plums weighing 15 pound each would it take to total3 pounds? 15 plums6.(8)RepresentWrite the following sentence using digits and symbols:When nine is subtracted from twelve, the difference is three. 12 9 32* 7. Compare: 2 of 3 3 !3(86)38. Multiple Choice If 3n 18, then 2n 5 equals which of thefollowing? BA 23B 17C 31D 14(49)Lesson 93613

* 9. A cube has 12 edges. How many edges does a hexagonal(89)prism have? 18* 10. Multiple Choice Which of these angles appears to be aright angle? DA AOBB BOCC CODD AOC(31, 61)* 11.(91)354"25581#8* 12.1(90)4 25* 14. 1 18(87)O565#1619. 10 56 (70)* 21. 31 ! 970(92)7.47* 16. 1 1(87) 5102518. ( 20 6.55) 5(13, 26)20. 6 78 900 5.60(18, 29)22. 92 # 2931 R 965* 15. 8 ! 5(90) 1010817. 12.34 (5.67 0.8)(79)(41)(78)2 2.69421,20078Write fractions equal to 34 and 16 that have denominators of 12.9 2 11Then add the fractions. 12; 12; 12Analyze24. Look at the picture below. Then answer parts a–c.(53, 72)cm 1a. How long is the rectangle?23453 cmb. The rectangle is 1 centimeter longer than it is wide. What is theperimeter of the rectangle? 10 cmc. What is the area of the rectangle?614DA4 12(24, 73)* 23.13.4Saxon Math Intermediate 56 sq. cmCB

b. What is the period of the sequence?E,E(Inv. 4)E* 25. a. Write the next three terms of the repeating sequence below.,4rotation,E,EE,Ec. What transformation is shown in the sequence?,E,,,, .Refer to the spinner to answer parts a–c.26. a. If you spin this spinner 60 times, about how many timeswould you expect it to stop on 2? about 15 times(Inv. 9)12b. What percent of the spinner’s face is region 2? 25%c. What decimal part of the spinner’s face is region 3?0.5327. Montana became a state in 1889, which was 98 years after Vermont(49)became a state. Utah became a state 105 years after Vermont. In whatyear did Utah become a state? 189628.(21, 62)A physical education teacher must divide a class of31 students into four teams. If possible, the same number of studentsare to be on each team. What is a reasonable estimate of the numberof students that will be on each team? Explain your answer. 8 students;Estimatesample: I used compatible numbers; since 31 is close to 32 and 32 is divisible by 4, areasonable estimate is 32 4, or 8 students.29. The famous Austrian composer Wolfgang Amadeus Mozart was born(35)in 1756. About how many years ago was he born? Explain why yourestimate is reasonable. Sample: about 250 years ago; 2000 1750 250* 30. A square field that is one hectare is 10,000 square meters. Describe(78)how to use a calculator to find the length of each side of the field. Howlong is each side? Enter 10,000 and press the square root key; 100 meters.EarlyFinishersReal-WorldConnectionBryce surveyed students at his school to see if they enjoyedcertain activities. The chart below shows the results of the survey.Display the data in a double-line graph. Be sure to label your graphappropriately. See student ll4025Camping4535Lesson 93615

LESSON94 Using Estimation WhenDividing by Two-DigitNumbersPower UpfactsmentalmathPower Up l3a. Number Sense: Reduce the fractions 15,b. Fractional Parts:c. Fractional Parts:1323of 155of 1510d. Percent: 50% of 155,15and 10.151 1 25, 3, 37 12e. Geometry: A soccer ball represents which geometric solid?spheref. Estimation: Choose the more reasonable estimate for themass of a soccer ball: 15 oz or 15 kg. 15 ozg. Calculation: 281, 5, 1, 4, 1, 4, 30h. Roman Numerals: Write 20 in Roman numerals. XXproblemsolvingChoose an appropriate problem-solving strategy to solvethis problem. Two cups equal a pint, and two pints equal a quart.Two quarts equal a half gallon. Two half gallons equal one gallon.A quart of milk was poured out of a full gallon container. Howmany pints of milk were still in the container? 6 pintsNew ConceptIn Lesson 92, we learned a method to help us divide by two-digitnumbers. The problems in that lesson were chosen so that usingthe first digit to guess the division answer would work. However,this method does not always work. In this lesson we will learnanother strategy for two-digit division.616Saxon Math Intermediate 5

Using the first-digit trick for 19 ! 59 , we follow this process:Reading MathWe know ourguess is too largewhen the numberwe are subtractingis greater than thenumber we aresubtracting from.We see:We think:We try the guess, butthe guess is too large:?19 ! 5951! 5519 ! 5995Our guess, 5, is incorrect because there are not five 19s in 59.Our guess is too large. So we will estimate. To estimate, wementally round both numbers to the nearest 10. Then we use thefirst-digit trick with the rounded numbers.We see:19 ! 59We round:We think:We try:20 ! 6032! 63R219 ! 59572ExampleDivide: 19 ! 595Thinking SkillVerifyWhy do we writethe digit 3 in thetens place of thequotient?We are dividing59 tens.We begin by breaking the division into the smallerdivision problem 19 ! 59 . We round to 20 ! 60 and. We guess 3, so wefocus on the first digits, 20 ! 60write the “3” above the 9 of 59. Then we multiply3 by 19, subtract, and bring down. The nextdivision is 19 ! 25. We may estimate to help usdivide. We write “1” in the answer; then we multiplyand subtract.31 R 619 ! 5955725196The answer is 31 R 6. To check our answer, we multiply 31 by 19and add the remainder, which is 6.Lesson Practicea. 41 R 13d. 31 R 1e. 17 R 13h. 43 R 8Divide:a. 19 ! 792b. 30 ! 600d. 29 ! 900e. 48 ! 829f. 29 ! 121041 R 21h. 18 ! 782i. 39 ! 120030 R 30g. 28 ! 8963220c. 29 ! 1214R5Lesson 94617

Written Practice* 1.(80)Distributed and IntegratedWrite all of the prime numbers less than 50 that end with thedigit 1. 11, 31, 41List2. What number is missing in this division problem?(20)192 8 243. Sofia ran 660 yards in 3 minutes. At this rate, how many yards wouldshe run in 6 minutes? 1320 yards(49)4.(71)Represent9Write a decimal number equal to the mixed number 4 10. 4.95. Seventy-six trombone players led the parade. If they marched in4 equal rows, how many were in each row? 19 trombone players(21)6. a. A dime is what fraction of a dollar?(87)110b. How many dimes are in 1?10 dimesc. How many dimes are in 4?40 dimes* 7. Multiple Choice Which of the following means, “How many 19s are(92)in 786?” BA 19 786B 786 19C 19 786D 786 19* 8. a. How many 41 s are in 1?4b. How many 13 s are in 1?3(87)9. What word names this shape?(83)cone* 10. Multiple Choice If LN is perpendicular to JM, then JNLis what type of angle? BA acuteB rightC obtuseD straightK(31, 61)618Saxon Math Intermediate 5LJMN

11. 63.75 1.48 59 5(70)12. 1010 (101 10)(24) 70.8213. 3.48 7919(17)14. 252 6259 ! 786* 15. 19(78)(94)* 16. 236 ! 264* 18. 5 ! 5 ! 5(91) 66 6* 20. Reduce: 8(90)1222. 1 of 3(76) 34* 24.(Inv. 6,Inv. 8)(94)31 R 22* 19. 5 " 3 2 1262 12(86, 91)121. 3 # a2 # b 1 14423(24, 63)14Write a fraction equal to 23 that has a denominator of 12.8 1. Remember to reduce the answer. 12Subtract that fraction from 11;412AnalyzeThe graph below shows Jeff’s height from ages 9 to 14.Use this graph to answer parts a and b.InterpretJeff’s Height6866Height (in inches)23.(79, 81)41 R 7* 17. 38 ! 120014(78) 24.366462605856549101112Jeff’s Age (in years)1314a. How many inches did Jeff grow between the ages of 12and 14? 7 inchesb. At what age was Jeff 5 feet tall?12Lesson 94619

* 25. The sides of this square are one yard long. Since 1 yardequals 3 feet, the sides are also 3 feet long. Refer to thisfigure to answer parts a–c.3 ft(45, 72)3 fta. Multiple Choice Which of these terms does notdescribe the figure? CA rectangleB parallelogramC pentagonD regular quadrilateral1 yd1 ydb. What is the perimeter of the square in feet? What is the perimeterin yards? 12 ft; 4 ydc. What is the area of the square in square feet? What is the area insquare yards? 9 sq. ft; 1 sq. yd26. a. Compare: 1 yd 3 ft(72, 74)b. Compare: 1 sq. yd 9 sq. ft27.(43)In a fifth grade class,

Oct 09, 2017 · 8! 1 3 8" 2 10 8 2 10 8" 32 8 32 8" 31 4 Justify Use fractions to explain why 2 10 8 3 2 8. AActivityctivity Modeling Improper Fractions Materials needed: fraction manipulatives saved from Investigations 2 and 3 Use your fraction manipulatives to model each problem below. Write the mixed number or whole