# Lesson 5-1

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Lesson 5-1Writing Fractions as DecimalsLesson 5-2Rational NumbersLesson 5-3Multiplying Rational NumbersLesson 5-4Dividing Rational NumbersLesson 5-5Adding and Subtracting Like FractionsLesson 5-6Least Common MultipleLesson 5-7Adding and Subtracting Unlike FractionsLesson 5-8Solving Equations with Rational NumbersLesson 5-9Measures of Central Tendency

Five-Minute Check (over Chapter 4)Main Ideas and VocabularyExample 1: Write a Fraction as a Terminating DecimalExample 2: Write a Mixed Number as a DecimalExample 3: Write Fractions as Repeating DecimalsExample 4: Real-World ExampleExample 5: Compare Fractions and DecimalsExample 6: Real-World Example

Write fractions as terminating or repeatingdecimals. Compare fractions and decimals. terminating decimal mixed number repeating decimal bar notation

Write a Fraction as a Terminating DecimalMethod 1 Use paper and pencil.Division ends when theremainder is 0.Answer: 0.0625 is a terminating decimal.

Write a Fraction as a Terminating DecimalMethod 2 Use a calculator.1 16ENTER0.0625Answer: 0.0625 is a terminating decimal.

A. 0.58B. 0.625C. 0.725D. 5.80%D0%C0%BA0%A.B.C.D.ABCD

Write a Mixed Number as a DecimalWrite as the sum of aninteger and a fraction.Add.Answer: 1.25

A. 0.6B. 2.35C. 2.61.2.3.4.0%D. 2.7ABCDABCD

Write Fractions as Repeating DecimalsThe digits 12 repeat.Answer:

Write Fractions as Repeating DecimalsThe digits 18 repeat.Answer:

A.B.1.2.3.4.0%C.D.ABCDABCD

A.B.1.2.3.4.0%C.D.ABCDABCD

SOCCER Camille’s soccer team won 32 out of 44games to make it to the championships. To thenearest thousandth, find the team’s rate of winning.Divide the number of games they won, 32, by thenumber of games they played, 44.Look to the digit to the right of the thousandths place.Round down since 2 5.Answer: Camille’s soccer team won 0.727 of the time.

The results of a poll showed that 16 out of 24students in Ms. Brown’s class would prefer going tothe planetarium rather than the arboretum. To thenearest thousandth, what part of the class preferredgoing to the planetarium?A. 0.007B. 0.667D. 16.24AB0%CDDCAC. 0.700B0%A.0% B. 0%C.D.

Compare Fractions and DecimalsWrite the sentence.In the tenths place, 7 6.Answer:

A. B. C. 0%0%D0%CA0%BD. none of the aboveA.B.C.D.ABCD

GRADES Jeremy got a score ofquiz andon his firston his second quiz. Which grade wasthe higher score?Write the fractions as decimals and then compare thedecimals.Answer: The scores were the same, 0.80.

BAKING One recipe for cookies requiresof a cupof butter, and a second recipe for cookies requiresof a cup of butter. Which recipe uses less butter.A. the first recipeDAD. cannot be determinedAB 0%0%CDC0%C. both use the same amountA.B.0%C.D.BB. the second recipe

Five-Minute Check (over Lesson 5-1)Main Ideas and VocabularyExample 1: Write Mixed Numbers and Integers asFractionsExample 2: Write Terminating Decimals as FractionsExample 3: Write Repeating Decimals as FractionsConcept Summary: Rational NumbersExample 4: Classify Numbers

Write rational numbers as fractions. Identify and classify rational numbers. rational number

Write Mixed Numbers and Integers asFractionsAnswer:Animation:Whole Numbers

Write Mixed Numbers and Integers asFractionsAnswer:

A.A.B.C.D.0%D0%C0%BA0%A.B.C.D.ABCD

B. Write –6 as a fraction.A.B.C.D.0%D0%C0%BA0%A.B.C.D.ABCD

Write Terminating Decimals as FractionsA. Write 0.26 as a fraction or mixed number insimplest form.0.26 is 26 hundredths.Answer:Simplify. The GCF of 26and 100 is 2.

Write Terminating Decimals as FractionsB. Write 2.875 as a fraction or mixed number insimplest form.2.875 is 2 and 875thousandths.Answer:Simplify. The GCF of 875 and1000 is 125.

A. Write 0.84 as a fraction or mixed number insimplest form.A.B.C.D.0%1.2.3.4.ABCDA B C DBCD

B. Write 3.625 as a fraction or mixed number insimplest form.A.B.C.D.0%1.2.3.4.ABCDA B C DBCD

Write Repeating Decimals as FractionsWrite 0.39 as a fraction in simplest form.N 0.3939. . .Let N represent the number.100N 100(0.3939. . .) Multiply each side by 100because two digits repeat.100N 39.39Subtract N from 100N to eliminate the repeating part,0.3939. . .

Write Repeating Decimals as Fractions100N – N 100N – 1N or 99NDivide each side by 99.Simplify.Answer:Check13 33ENTER0.3939393939

A.0%B.C.D.1.2.3.4.A B C DABCDBCD

Classify NumbersA. Identify all sets to which the number 15 belongs.Answer: 15 is a whole number, an integer, and arational number.

Classify NumbersC. Identify all sets to which the number0.30303030 belongsAnswer: 0.30303030 is a nonterminating, repeatingdecimal. So, it is a rational number.

A. Identify all sets to which –7 belongs.A. whole number, integer,rationalB. whole number, integerAB 0%CDDCD. integerA0%A.0% B. 0%C.D.BC. integer, rational

A. whole number, rationalB. integer, rationalC. not rationalAB 0%CDDCAD. rationalB0%A.0% B. 0%C.D.

C. Identify all sets to which 0.24242424 belongs.A. whole number, rationalB. integer, rationalC. not rationalABCD0%DA.0%B.C.D.C0%BD. rationalA0%

Five-Minute Check (over Lesson 5-2)Main Ideas and VocabularyKey Concept: Multiplying FractionsExample 1: Multiply FractionsExample 2: Multiply Negative FractionsExample 3: Multiply Mixed NumbersExample 4: Real-World ExampleExample 5: Multiply Algebraic FractionsExample 6: Real-World Example

Multiply positive and negative fractions. Use dimensional analysis to solve problems. dimensional analysis

Multiply FractionsMultiply the numerators.Multiply the denominators.Answer:Simplify. The GCF of 10and 40 is 10.

A.B.D.A.0%B.C.D.ABCD0%D0%BA0%CC.

Multiply Negative FractionsDivide 2 and 4 by their GCF, 2.Multiply the numerators andmultiply the denominators.Answer:Simplify.

A.B.C.D.0%1.2.3.4.ABCDABCD

Multiply Mixed NumbersDivide by the GCF, 3.Multiply.Answer:Simplify.

A.B.C.D.0%1.2.3.4.ABCDABCD

DONATIONS Rasheed collected cash donations forunderprivileged children every October. ThisOctober he collected 784. Last year he collectedas much. How much did Rasheed collect lastOctober?To find how much Rasheed collected last Octobermultiply 784 by

Divide by the GCF, 8.Multiply.Simplify.Answer: Rasheed collected 490 last October.

SHOPPING Melissa is buying a sweater originallypriced for 81. The sweater is discounted byFind the amount of the discount.A. 64.00B. 54.00C. 50.670%D0%C0%BD. 27.00A0%A.B.C.D.ABCD

Multiply Algebraic FunctionsThe GCF of q2 and q is q.Answer:Simplify.

A.B.C.0%0%D0%CA0%BD.A.B.C.D.ABCD

RUNNING TRACK The track at Cole’s school ismile around. If Cole runs one lap in two minutes,how far (in miles) does he run in 30 minutes?

Distance rate timeDivide by the commonfactors and units.Multiply.Simplify.Answer:

A.B.C.0%D0%C0%BD.A0%A.B.C.D.ABCD

Five-Minute Check (over Lesson 5-3)Main Ideas and VocabularyKey Concept: Inverse Property of MultiplicationExample 1: Find Multiplicative InversesKey Concept: Dividing FractionsExample 2: Divide by a Fraction or Whole NumberExample 3: Divide by a Mixed NumberExample 4: Divide by an Algebraic FunctionExample 5: Real-World Example

Divide positive and negative fractions usingmultiplicative inverses. Use dimensional analysis to solve problems. multiplicative inverses reciprocals

Find Multiplicative InverseA.The product is 1.Answer:

Find Multiplicative InverseB.Write as an improperfraction.The product is 1.

A.A.B.C.D.0%D0%C0%BA0%A.B.C.D.ABCD

B.A.B.C.0%0%D0%CA0%BD.A.B.C.D.ABCD

Divide by a Fraction or Whole NumberA. Find each quotient. Write in simplest form.Divide by the GCF, 5.Answer:Simplify.

Divide by a Fraction or Whole NumberB. Find each quotient. Write in simplest form.Write 3 asMultiply.Answer:.

A.0%B.C.D.ABCD1.2.3.4.ABCD

Divide by a Mixed NumberRename the mixednumbers as improperfractions.Divide by common factors.Answer:Simplify.

A.B.1.2.3.4.0%C.D.ABCDABCD

Divide by an Algebraic FractionDivide by common factors.Answer:Simplify.

A.B.C.0%0%D0%CA0%BD.A.B.C.D.ABCD

Write as improper fractions.Divide by common factors.Simplify.

Check Use dimensional analysis to examine the units.Divide bycommon units.Simplify.The result is expressed as gallons.

A.B.D.AB0%CDDCA0%BC.A.B. 0%0%C.D.

Five-Minute Check (over Lesson 5-4)Main IdeasKey Concept: Adding Like FractionsExample 1: Add FractionsExample 2: Add Mixed NumbersKey Concept: Subtracting Like FractionsExample 3: Subtract FractionsExample 4: Subtract Mixed NumbersExample 5: Add Algebraic Fractions

Add like fractions. Subtract like fractions.

Add FractionsEstimate 1 1 2The denominators are thesame. Add the numerators.Answer:Simplify and rename as amixed number.Compared to the estimate, the answer is reasonable.

A.B.A0%BCDD0%BD.A0%A.0%B.C.D.CC.

A.B.C.D.0%1.2.3.4.ABCDABCD

Subtract FractionsThe denominators are thesame. Subtract thenumerators.Answer:Simplify.

A.0%B.C.D.1.2.3.4.ABCDABCD

Subtract Mixed NumbersWrite the mixed numbers asimproper fractions.Subtract the numerators.Answer:Simplify.

A.B.C.0%0%D0%CA0%BD.A.B.C.D.ABCD

Five-Minute Check (over Lesson 5-5)Main Ideas and VocabularyExample 1: Find the LCMExample 2: The LCM of MonomialsExample 3: Find the LCDExample 4: Compare FractionsExample 5: Order Rational Numbers

Find the least common multiple of two or morenumbers. Find the least common denominator of two or morefractions. multiple common multiples least commonmultiple (LCM) least commondenominator (LCD)Interactive Lab:Least Common Multiple

Find the LCMFind the LCM of 168 and 180.NumberPrime Factorization Exponential Form1682 2 2 3 723 3 71802 2 3 3 522 32 5The prime factors of both numbers are 2, 3, 5, and 7.Multiply the greatest power of 2, 3, 5, and 7 appearingin either factorization.LCM 23 32 5 7 2520Answer: The LCM of 168 and 180 is 2520.

Find the LCM of 144 and 96.A. 24B. 144C. 288A B C0%DA0%BCDC DD. 13,824B0%A.0%B.C.D.

The LCM of MonomialsFind the LCM of 12x2y2 and 6y3.Find the prime factorization ofeach monomial.Highlight the greatest powerof each prime factor.Multiply the greatest power ofeach prime factor.Answer: The LCM of 12x2y2 and 6y3 is 12x2y3.

Find the LCM of 18ab3 and 24a2b.A. 6abB. 9a2b30%C. 72a2b3D. 432a3b41.2.3.4.ABCDABCD

Find the LCDWrite the prime factorizationof 8 and 20.Highlight the greatest powerof each prime factor.Multiply.Answer:

Compare FractionsThe LCD of the fractions is 3 5 7 or 105. Rewritethe fractions using the LCD and then compare thenumerators.

A. B. D. none of the aboveAB 0%CDDCA0%A.0% B. 0%C.D.BC.

Order Rational NumbersFOOTBALL Dane’s football team usually practicesforThe table below shows how manyhours from normal they practiced each day thisweek. Order the practices from shortest to longest.

Order Rational NumbersStep 1 Order the negative fractions first. The LCD of 6and 8 is 24.

Order Rational NumbersStep 2 Order the positive fractions. The LCD of 3 and 4is 12.Answer: Sincethe order of thepractices from shortest to longest isWednesday, Monday, Thursday, and Tuesday.

WEATHER The table shows therainfall of four months compared tothe overall yearly average ofinches of rainfall for Columbus,Ohio. Order the months from leastrainfall to most rainfall.A. Jul, Apr, Jan, OctB. Jan, Oct, Jul, AprD. Jan, Oct, Apr, Jul0%0%D0%CA0%BC. Oct, Jan, Apr, JulA.B.C.D.ABCD

Five-Minute Check (over Lesson 5-6)Main IdeasKey Concept: Adding Unlike FractionsExample 1: Add Unlike FractionsExample 2: Add Fractions and Mixed NumbersKey Concept: Subtracting Unlike FractionsExample 3: Subtract Fractions and Mixed NumbersExample 4: Real-World Example

Add unlike fractions. Subtract unlike fractions.

Add Unlike FractionsUse 4 7 or 28 as thecommon denominator.Rename each fraction withthe common denominator.Answer:Add the numerators.

A.B.0%0%0%D0%CABCDBD.A.B.C.D.AC.

Add Fractions and Mixed NumbersA.Estimate: 1 0 1The LCD is 2 3 5or 30.Rename each fractionwith the LCD.Answer:Compare to theestimate. Is the answerreasonable?

Add Fractions and Mixed NumbersB.Write the mixednumbers as improperfractions.Rename fractionsusing the LCD, 24.Simplify.

A.A.B.C.D.0%1.2.3.4.ABCDABCD

B.A.B.C.D.0%1.2.3.4.ABCDABCD

Subtract Fractions and Mixed NumbersA.The LCD is 16.Rename using the LCD.Answer:Subtract.

Subtract Fractions and Mixed NumbersB.Write as improperfractions.Rename using the LCD.Simplify.Answer:Subtract.

A.A.B.C.D.0%1.2.3.4.ABCDABCD

B.A.0%B.C.D.1.2.3.4.ABCDABCD

Explore You know the total distance Juyong joggedand the distances on two days.

RenameLCD, 20.Simplify.with the

GARDENING Howard’s tomato plants grew a total ofinches during the first three weeks aftersprouting. If they grewweek andinches during the firstinches during the second week, howmuch did they grow during the third week aftersprouting?B.0%0%DD.0%CC.A0%BA.A.B.C.D.ABCD

Five-Minute Check (over Lesson 5-7)Main IdeaExample 1: Solve by Using Addition and SubtractionExample 2: Solve by Using DivisionExample 3: Solve by Using MultiplicationExample 4: Real-World Example

Solve equations containing rational numbers.

Solve by Using Addition and SubtractionA. Solve m 8.6 11.2.m 8.6 11.2m 8.6 – 8.6 11.2 – 8.6m 2.6Answer: 2.6Write the equation.Subtract 8.6 from eachside.Simplify.

A. Solve 4.2 x – 9.5A. –5.3B. 1.37C. 5.3ABCD0%DA.0%B.C.D.C0%BD. 13.7A0%

B.A.B.D.A.0%B.C.D.ABCD0%D0%CA0%BC.

Solve by Using DivisionSolve 9a 3.6. Check your solution.Write the equation.Divide each side by 9.Answer:Simplify. Check the solution.

Solve –6m –4.8. Check your solution.A. –0.8B. 0.80%C. 1.2D. 28.81.2.3.4.ABCDABCD

Solve by Using MultiplicationWrite the equation.Answer:Simplify. Check the solution.

A.B.0%C.D.1.2.3.4.ABCDABCD

CEREAL Torrey eatsand anothercup of cereal each morningcup as a snack after school. If one boxof cereal contains 10 cups of cereal, how many dayswill the box last?

Wordscups times the number equals 10 cupsper dayVariableEquationof daysof cerealLet d the number of days d 10Write the equation.Renamefraction.as an improper

Multiply each side bySimplify.Answer: The box of cereal will last approximately

Each morning Michael buys a cappuccino for 4.50and each afternoon he buys a regular coffee for 1.25. If he put aside 30 to buy coffee drinks, howmany days will the money last?A. 3 daysB. 5 daysC. 6 days0%D0%C0%BD. 9 daysA0%A.B.C.D.ABCD

Five-Minute Check (over Lesson 5-8)Main Ideas and VocabularyKey Concept: Measures of Central TendencyExample 1: Real-World ExampleConcept Summary: Using Mean, Median, and ModeExample 2: Choose an Appropriate MeasureExample 3: Real-World ExampleExample 4: Standardized Test Example

Use the mean, median, and mode as measures ofcentral tendency. Choose an appropriate measure of centraltendency and recognize measures of statistics. measures of central tendency mean median mode

A. MOVIES The revenue of the 10 highest grossingmovies as of 2004 are given in the table. Find themean, median, and mode of the revenues.Answer: The mean revenue is 266.8 million.

To find the median, order the numbers from least togreatest.163, 173, 176, 187, 249, 261, 279, 371, 373, 436There is an evennumber of items.Find the mean ofthe two middlenumbers.Answer: The median revenue is 255 million. There isno mode because each number in the setoccurs once.

B. OLYMPICS The line plotshows the number of goldmedals earned by eachcountry that participated inthe 2002 Winter Olympicgames in Salt Lake City, Utah.Find the mean, median, andmode for the gold medalswon.Answer: The mean is 3.16.

There are 24 numbers. The median number is theaverage of the 12th and 13th numbers.Answer: The median is 2.The number 0 occurs most frequently in the set of data.Answer: The mode is 0.

A. TEST SCORES The test scores for a class of ninestudents are 85, 93, 78, 99, 62, 83, 90, 75, 85. Find themean, median, and mode of the test scores.A. mean, 73.9; median, 85;mode, no modeB. mean, 83.3; median, 85;mode, 85D. mean, 83.3; median, 62;mode, 85AB 0%CDDCA0%BC. mean, 750; median, 62;mode, 85A.0% B. 0%C.D.

B. FAMILIES A survey ofschool-age children shows thefamily sized displayed in theline plot. Find the mean,median, and mode.A. mean, 5.1; median, 5;mode, 3, 4, 5, 6, 8B. mean, 102; median, 5;mode, 5C. mean, 6.05; median, 6;mode, 60%D0%C0%BD. mean, 4.3; median, 5.5;mode, 4.5A0%A.B.C.D.ABCD

Choose an AppropriateMeasureSURVEYS Eleanor took a poll in her class to seehow many times her classmates had visited thelocal amusement park during summer vacation.What measure of central tendency best representsthe data?The data is: 5, 0, 2, 3, 2, 4, 1, 2, 1, 3, 8, 2, 2, 0.Since there is an extreme value of 8, the median wouldbest represent the data.0, 0, 1, 1, 2, 2, 2, 2, 2, 3, 3, 4, 5, 8Answer: The median is 2. This is also the mode.

BOWLING Jenny’s bowling scores are 146, 138, 140,142, 139, 138, and 145. Which measure of centraltendency best represents the data?A. mean0%B. medianC. mode1.2.3.4.ABCDAD. cannot be determinedBCD

QUIZ SCORES The quiz scores for students in amath class are 8, 7, 6, 10, 8, 8, 9, 8, 7, 9, 8, 0, and 10.Which measure of central tendency best representsthe data? Then find the measure of centraltendency.The data value 0 appears to be an extreme value. So,the median and mode would best represent the data.0, 6, 7, 7, 8, 8, 8, 8, 8, 9, 9, 10, 10Answer: The median and mode are 8.

Check You can check whether the median bestrepresents the data by finding the mean with andwithout the extreme value.mean with extreme valuemean without extreme valueThe mean without the extreme value is closer to themedian. The extreme value decreases the mean byabout 0.7. Therefore, the median best represents thedata.

BIRTH WEIGHT The birth weights of ten newbornbabies are given in pounds: 7.3, 8.4, 9.1, 7.9, 8.8, 6.5,7.9, 4.1, 8.0, 7.5. Tell which measure of centraltendency best represents the data. Then find themeasure of central tendency.A. mean, 7.53B. median, 7.91.2.3.4.0%C. mode, 7.9D. cannot be determinedABCDABCD

SALARIES The monthly salaries for the employeesat Bob’s Book Store are: 1290, 1400, 1400, 1600, 2650. Which measure of central tendencyshould Bob’s Book Store’s manager use to shownew employees that the salaries are high?A modeB medianC meanD cannot be determinedRead the Test ItemTo find which measure of central tendency to use, findthe mean, median, and mode of the data and select thegreatest measure.

Solve the Test ItemMode: 1400Median: 1290, 1400, 1400, 1600, 2650Answer: The mean is the highest measure, so theanswer is C.

EXERCISE The number of hours spent exercisingeach week by women are: 1, 6, 4, 2, 1, and 8. Whichmeasure of central tendency should a person use toshow that women do not spend enough timeexercising?A. modeB. medianD. cannot be determined0%DAB0%CDCA0%BC. meanA.B.0%C.D.

Five-Minute ChecksImage BankMath ToolsWhole NumbersLeast Common Multiple

Lesson 5-1 (over Chapter 4)Lesson 5-2 (over Lesson 5-1)Lesson 5-3 (over Lesson 5-2)Lesson 5-4 (over Lesson 5-3)Lesson 5-5 (over Lesson 5-4)Lesson 5-6 (over Lesson 5-5)Lesson 5-7 (over Lesson 5-6)

Lesson 5-1 Writing Fractions as Decimals Lesson 5-2 Rational Numbers Lesson 5-3 Multiplying Rational Numbers Lesson 5-4 Dividing Rational Numbers Lesson 5-5 Adding and Subtracting Like Fractions Lesson 5-6 Least Common Multiple Lesson 5-7 Adding and Subtracting Unlike Fractions Lesson 5-8 Solving Equations with Rational Numbers