Fraction Operations
CHAPTER6Fraction OperationsGET READY284Math Link2866.1Warm Up2876.1Multiplying a Fraction and a Whole Number 2886.2Warm Up2946.2Dividing a Fraction by a Whole Number2956.3Warm Up3016.3Multiplying Proper Fractions3026.4Warm Up3096.4Multiplying Improper Fractions andMixed Numbers3106.5Warm Up3196.5Dividing Fractions and Mixed Numbers3206.6Warm Up3286.6Applying Fraction Operations329Chapter Review337Practice Test344Wrap It Up!347Key Word Builder348Math Games349Challenge in Real Life350
Name: Date:Answers284MHR Chapter 11: Probability352
Name: Date:Add and Subtract FractionsTo add fractions with the same denominators, add the numerators.2 numerator5 denominatorTo subtract fractions with different denominators, use a common denominator.a common multiple ofeach denominatorWrite the answer in lowest terms. 22 1 6 3Multiples of 2: 2, 4, 6, 8, Factors of 6: 2, 3, 6 21. Add or subtract. Write your answers in lowest terms. 2a)1 1 6 66b)4 3 5 104 8 5 10 2 6 5 10 Get Ready MHR285
Name: Date:Add and Subtract Mixed Numbersmixed number1 3 includes a whole number and a proper fraction e.g., 1 , 2 2 5 improper fraction10 a fraction in which the numerator is greater than the denominator e.g., 8 To subtract or add mixed numbers:Use Regrouping:Use Improper Fractions:23114 24 2442418 1121Write as improper fractions. 4 2Find a commmon denominator. 4 4447 2 1 Subtract the numerators. ( 4 2 ) Add.4 4 4 33 1Write as a mixed number. 6Write as a mixed number.442. Add or subtract. Write your answers in lowest terms.a) Use regrouping.b) Use improper fractions.3 1 - ‐ 1 25211 2 123Find a common denominator.Find a common denominator.- ‐ 11010Subtract the whole numbers. 1 3ÊÁÁÁÁ (3 - ‐ 1) ÁÁÁÁÁÁÁË- ‐ 266Write as improper fractions.ˆ ˉ 66Add the numerators.Subtract the fractions. ÊÁÁÁÁ ÁÁÁÁÁÁÁË- ‐ˆ ˉ 6 6 6Write in lowest terms. 286MHR Chapter 6: Fraction Operations6
Name: Date:Canada’s EcozonesAn ecozone is an areathat has similar plantsand animals.Canada has many ecozones of different sizes.The boundaries between ecozones depend on geography, climate,animals, plants, and human activities.11a) The Pacific marine ecozone coversb) About of the Prairies ecozone area is in210of Canada’s coastline. The Northwest1Saskatchewan, and about of the area is13Atlantic ecozone covers of Canada’sin Alberta. What fraction of the area is in5coastline.Manitoba?Use a common denominator to find theAdd the areas in Alberta andsum of the 2 ecozones.Saskatchewan. Show your work.Common denominator for1 1 10 51 1 2 10 5 2 1 1011and :510Use your answer above to find the area thatcovers Manitoba.Let 1 represent the whole part of theecozone.1 Think 1 6.66 6 Math Link MHR287
Name: Date:6.1 Warm Up1. Write each fraction.a)b)improper fraction:mixed number:2. Draw fraction strips to solve.1 1a) 3 3b)1 1 8 2b)3 1 5 23. Solve. Write your answers in lowest terms.a)1 2 12 3Find a commondenominator.4. Multiply.288a) 2 4 b) 4 5 c) 3 2 d) 5 3 e) 3 3 f) 6 5 MHR Chapter 6: Fraction Operations
Name: Date:6.1 Multiplying a Fraction and a Whole NumberWorking Example 1: Multiply Using a Modelproper fraction5 a fraction in which the denominator is greater than the numerator e.g., 8 5using fraction strips. Write the product in lowest terms.6Find 3 You can model with patternblocks instead of fraction strips.Solution3 5 5 5 5 6 6 6 6Count the shaded parts of the strips:5 5 5 6 6 66Write the answer in lowest terms. 315 62 3So, 3 5 5 .6 2Draw fraction strips to find the product. Write the answer in lowest terms.2 56 6.1 Multiplying a Fraction and a Whole Number MHR289
Name: Date:Working Example 2: Multiply Using a DiagramFind 3 2. Write the product in lowest terms.5Solution3 2 2 2 5 5 5Model the fractions using a number line.The denominator is 5.So, you need 5 equal parts between each whole number.You could draw rectanglesinstead of using a number line.2 2 2 5 5 5So, 3 52 6 .5 5Draw a diagram to find each product.a) 2 232 2 3 3290MHR Chapter 6: Fraction Operationsb) 3 343 3 3 4 4 4
Name: Date:Working Example 3: Apply Multiplication With FractionsA spider has 8 legs.3An ant has as many legs as a spider.4How many legs does an ant have?Solution333of 8 means 8 or 8 .4443An ant has of the number of legs of a spider.4Use repeated addition on the number line to show 8 3.4You could draw rectangles.The answer isSo, 8 3 4An ant has.legs.Jenelle is making a recipe that needs 6 cups of flour.2She wants to make of the recipe.3How many cups will she need to use?Write a multiplication statement: 6 Model the multiplication on the number line.Jenelle needscups of flour.6.1 Multiplying a Fraction and a Whole Number MHR291
Name: Date:1. The diagram models 3 6.5a) The diagram represents b) Use the number line to model the same equation.c) Circle the model you like to use. FRACTION STRIPS or NUMBER LINE.Give 1 reason for your answer.2. Write the multiplication statement that each diagram shows.a) b)292 MHR Chapter 6: Fraction Operations
Name: Date:3. Write the multiplication statement that each number line shows.a)b)4. Write the multiplication statement that each model shows.a)1 whole161312b)5. Draw a diagram to find each product.a) 4 12b) 3 710Of means to multiply.6. The width of a Canadian flag is1of its length. The length of the flag is 4 m long.2What is the width of the flag?4 Sentence:6.1 Multiplying a Fraction and a Whole Number MHR293
Name: Date:7. A minibus has room for 12 people. The bus is 3full. How many people are on the minibus?43 4Sentence:8. a) Write a word problem for1 8.4b) Show how to solve your problem.One quarter of Canada’s 20 ecozones are marine ecozones. They include parts of the oceans.The rest of Canada’s ecozones are terrestrial ecozones (land, rivers, lakes, and wetlands).a) How many marine ecozones does Canada have?One quarter 20 Number of ecozones 204 Canada hasmarine ecozones.b) How many terrestrial ecozones does Canada have?Number of ecozones 20Marine ecozones 20 – marine ecozones terrestrial ecozones20 –Canada has294 terrestrial ecozones.MHR Chapter 6: Fraction OperationsUse your answerfrom part a).
Name: Date:6.2 Warm Up1. Write the multiplication statement for each diagram.a)b) c) d) 2. Draw a diagram to solve.a) 4 38b)7 123. Divide.a) 15 5 b) 30 6 c) 40 2 d) 6 3 e) 12 4 f) 21 7 6.2 Warm Up MHR295
Name: Date:296MHR Chapter 6: Fraction Operations
Name: Date:6.2 Dividing a Fraction by a Whole NumberWorking Example 1: Divide Using a ModelFind1 3.4SolutionUse a fraction strip to showThe fraction strip shows thatEach of the 3 equal parts of1:41into43 equal parts.Divide each13is equal to.4121is4:121 3 4Use fraction strips to find the answer.3 343.4Shade the fraction strip to showDivide each3 41into 3 equal parts.412Each of the 3 equal parts of3 3 412or43is412or4.6.2 Dividing a Fraction by a Whole Number MHR297
Name: Date:Working Example 2: Divide Using Diagrams2 4. Write your answer in lowest terms.3SolutionFindDraw and label a number line that shows thirds.To model division by 4, divide each thirdintoequal parts.There are 12 parts in the whole, so each part isUse brackets to divide2into 4 equal parts.3Each of the 4 parts isorSo,2 4 361212.1.6.Use a number line to find each quotient. Write your answers in lowest terms.1 521 Label the number line to show .2 Divide each half into 5 equal parts to show division by 5.There are Use brackets to divide298parts in the whole, so each part is1into 5 equal parts. Each of the 5 parts is2MHR Chapter 6: Fraction Operations.
Name: Date:So,1 5 2.6.2 Dividing a Fraction by a Whole Number MHR299
Name: Date:Working Example 3: Apply Division With Fractions3of a jar of sauce on 6 servings of pasta.4He used the same amount of sauce on each serving.What fraction of the jar of sauce did he use on each serving?Mustafa usedSolution3 6.4Label the number line to show quarters.FindTo show division by 6, divide each quarter into 6 parts.There areparts in the whole, so each part isUse brackets to divide3into 6 equal parts.4Each of the 6 parts isSo,3 6 42424.Write in lowest terms. 33 248 3Mustafa used3008of a jar of sauce on each serving.MHR Chapter 6: Fraction Operations24.
Name: Date:Four students equally sharedFind1 21of a cake. What fraction of the cake did each student eat?2. Label the number line to show halves. Divide each half intoThere areparts in the whole. Each part is Use brackets to divideSo,1 21. a) Modelequal parts to show the division.1into2.equal parts. 1 2 using fraction strips or a number line.21 2 2b) What did you use to solve the question? Circle FRACTION STRIPS or NUMBER LINE.Give 1 reason your choice.6.2 Dividing a Fraction by a Whole Number MHR301
Name: Date:2. Find the quotient using fraction strips.a)1 24b)1 33 Divide the strip into quarters.1 Shade .4 Divide each quarter into 2 equal parts.There areEach part isparts in the whole.8. So,1 2 41 3 383. Find each quotient using a number line.a)3 25b)1 42 Label the number line to show fifths. Divide each fifth into 2 equal parts.There arethe whole, so each part isSo,302.3into 2 equal parts.5 Use brackets to divideEach part isparts in1.3 2 5MHR Chapter 6: Fraction OperationsSo,1 4 2.
Name: Date:4. Two different fish curries, dhopa and molee curry, are made with coconut.1of a coconut to make22 servings of dhopa.What fraction of a coconut is in eachserving?a) You needb) You need1coconut to make 4 servings of2molee.What fraction of a coconut is in eachserving?1 2 ?2Draw a fraction strip to solve. ?Draw a number line to solve.1 21 2 22full.3Four students share the juice equally.What fraction of the full container does each student get?5. A container of orange juice is Sentence:The Montane Cordillera and Boreal Cordillera ecozones have almost equal areas.1Together, the 2 ecozones equal aboutof the area of Canada.10What fraction of the area of Canada does each of these ecozones cover?1 2 10Sentence:6.2 Dividing a Fraction by a Whole Number MHR303
Name: Date:6.3 Warm Up1. Draw diagrams to solve.a)1 36c) 5 b)25d) 6 2. Decide whether each fraction is closer to 0,Use the number line to help you.a)353is closer to5c)232is closer to3.d).131, or 1.2b)787is closer to83 24161is closer to63. Multiply.304a) 4 2 b) 5 3 c) 12 2 d) 7 6 MHR Chapter 6: Fraction Operations.
Name: Date:6.3 Multiplying Proper FractionsWorking Example 1: Multiply Using Paper FoldingFind1 3 .2 5SolutionFold a rectangular piece of paper into fifths along its length.3Open the paper and shade of it.5Fold the paper in half across its width.Open the paper and draw slanted lines on half of it.Count the rectangles. There areequal rectangles.How many are shaded and have slanted lines?1 3 2 510Find each product using paper folding.a)1 1 4 2b)2 2 3 3 Fold paper into quarters along its length.1 Shade .4 Fold paper in half across its width.Draw a line to show the fold. Draw slanted lines on half of it.There areequal rectangles. How many are shaded and haveslanted lines?1 1 4 26.3 Multiplying Proper Fractions MHR305
Name: Date:Working Example 2: Multiply Using DiagramsFind2 1 . Write the product in lowest terms.3 2SolutionDraw a rectangle.Draw lines to divide its length into thirds.Draw a line to divide the width of the rectangle in half.2of the rectangle is grey6and has slanted lines.2 1 2 3 2 6 2 1 6 3 So,2 1 1 .3 2 3Find each product using diagrams.Write your answers in lowest terms.a) Find1 1 .2 2b) Find1 3 .3 4 Divide the length in half.1 Shade .2 Divide the width in half. Draw slanted lines on the top half.1 1 number of shaded parts with lines 2 2total number of parts 306MHR Chapter 6: Fraction OperationsWrite in lowest terms.
Name: Date:Working Example 3: Multiply Using a RuleEstimate and calculate8 5 .15 6SolutionEstimate:Is18closer to 0, , or 1?2158 1 15 251Is closer to 0, , or 1?625 168 5 15 61 121 2Calculate:8 5 15 68 5 Multiply the numerators 15 6 Multiply the denominators 90Write in lowest terms. 10 9 10Plot on a number line.The answer is reasonable because it is close tothe estimate of2.An estimate is reasonable if itis close to the actual answer.6.3 Multiplying Proper Fractions MHR307
Name: Date:Estimate and calculate. Write your answers in lowest terms.3 2 5 9Estimate:IsCalculate:31closer to 0, , or 1?52 3 5Is3 2 5 9 21closer to 0, , or 1?922 9 Multiply the numerators Multiply the denominators 33 2 5 9 Write in lowest terms. 31. Brendan calculated3 2 6 . Brendan made a mistake.5 5 5a) What mistake did he make?b) Find the correct answer.308MHR Chapter 6: Fraction Operations
Name: Date:Use paper foldingto help you.2. Find the products by drawing diagrams.a)5 1 6 2b)3 5 4 6 Divide the length in sixths.5 Shade .6 Divide the width in half. Draw slanted lines on the top half.5 1 number of shaded parts with lines 6 2total number of parts 3. Estimate and calculate3 2 . Write your answers in lowest terms.8 3Estimate:Calculate:2 33 83 2 8 3 3 2 8 3 Write in lowest terms.6.3 Multiplying Proper Fractions MHR309
Name: Date:4. Calculate. Write your answers in lowest terms.a)3 3 4 4b)5 3 6 811of an apple pie in her fridge. She ate of it.24What fraction of the whole pie did she eat?5. Tamar had1 21Sentence:1of the people in the world live in Canada or the United States.201Of the people who live in Canada or the United States, aboutlive in Canada.10What fraction of people in the world live in Canada? Show your work.6. About Sentence:310MHR Chapter 6: Fraction Operations
Name: Date:1of his time sleeping.31While he is asleep, he dreams for of the time.47. Marius spendsa) What fraction of the time is Mariusdreaming?b) How many hours a day is Marius dreaming?Show your work.Fraction from part a) number of hours 1of the area of Canada.101The Pacific Maritime ecozone covers about of British Columbia.5What fraction of the area of Canada does the Pacific Maritimeecozone cover? Show your work.British Columbia is about Sentence:6.3 Multiplying Proper Fractions MHR311
Name: Date:6.4 Warm Up1 2 3 4, , , , 11 2 3 41. Change the improper fraction to a mixed fraction.a)52 11111 22222 2 2 43d)641212 c)b)532. Change the mixed number to an improper fraction.a)2 312b)1d) 3143 3 2 3 3 3 c) 123334MHR Chapter 6: Fraction Operations12
Name: Date:6.4 Multiplying Improper Fractions and Mixed NumbersWorking Example 1: Multiply Mixed Numbers Using a ModelFind 213 1 .24A mixed number is made up ofa whole number and a fraction.SolutionDraw a rectangle.Draw lines to separate eachmixed fraction into a wholenumber and a proper fraction.Show the area of eachpart in the diagram.Calculate the area of each part.2 2 1 1 12344 1 3 2 4 83 21 121 1 3 2 2 8 1 1 3 (2 1) 2 2 8 Add the areas together: 2 1 3 3 1 4388443 888Add the whole numbers.Find a common denominator.Add the numerators.Change to a mixed fraction.386.4 Multiplying Improper Fractions and Mixed Numbers MHR313
Name: Date:So, 2133 1 4 .248314MHR Chapter 6: Fraction Operations
Name: Date:Find each product using a model.11a) 1 123b) 2 Label the outer edges of the diagram. Label the inside of the diagram. Calculate the area of each part.11 144 Label the outer edges of the diagram. Label the inside of the diagram. Calculate the area of each part.1 1 1 1 21 1 1 2 3 Add all the areas together. Add all the areas together. 6.4 Multiplying Improper Fractions and Mixed Numbers MHR315
Name: Date:Working Example 2: Multiply Mixed Numbers Using a RuleEstimate and calculate 411 2 . Write the product in lowest terms.23SolutionEstimate:Calculate:Round each mixed number to theclosest whole number.Write the mixed numbers as improper fractions.441 5212 3 25 2 So, 411 2 23.21 2 3, , . 11 2 31 2 2 2 2 1 2 2 2 2 2 21 33 3 133Multiply the improper fractions.411 9 7 2 23 2 3 2 3 Multiply the numerators Multiply the denominators 6Write in lowest terms. 363 62 3 10316MHR Chapter 6: Fraction Operations1220 10 .2211So, 10 .22
Name: Date:Estimate and calculate.111 3102Estimate:1Calculate:Change to improper fractions.1 1013 2 So, 111 10 11 3 .102 13 2 Multiply the improper fractions.1 11 3102 Multiply the numerators Multiply the denominators 6.4 Multiplying Improper Fractions and Mixed Numbers MHR317
Name: Date:11 3 like this:241 1 11112 3 6 and , so 2 3 6 .2 4 82481. Henri multiplied 2a) What mistake did Henri make?b) What is the correct answer?2. Write each improper fraction as a mixed number.a)1133 3 3318176b)MHR Chapter 6: Fraction Operations 5656
Name: Date:3. Write each mixed number as an improper fraction.a)4 34b)4 4 4 4 34278 78 44. Use a model to find each product.11a) 1 15211b) 1 223 Draw rectangle to solve. Draw rectangle to solve. Label the diagram parts. Multiply each area. Label the diagram parts. Multiply each area. Add all the areas together. Add all the areas together.6.4 Multiplying Improper Fractions and Mixed Numbers MHR319
Name: Date:5. Estimate and calculate. Write your answers in lowest terms.a)4 10 5 7b) 2Estimate:Estimate:10 3 1774 512 15310 7 So, 4 10 .5 7Calculate:Calculate:4 10 57 Multiply the numerators Multiply the denominators Write in lowest terms. Is yourcalculation closeto your estimate? 320MHR Chapter 6: Fraction Operations
Name: Date:6. Two and a half laps of a running track equal 1 km.How many laps equal 3 km?3 Write the mixed number as an improper fraction.Multiply the improper fractions.Write in lowest terms.Sentence:11hours of daylight, it was sunny for of the time.23How many hours was it sunny?7. On a day in Winnipeg with 10Sentence:6.4 Multiplying Improper Fractions and Mixed Numbers MHR321
Name: Date:8. Andreas has 18.2times as much as Andreas.3How much money does Bonnie have?3times as much as Bonnie.5How much money does Cheryl have?a) Bonnie has 1b) Cheryl has 1c) How much money do they have altogether?Sentence:1of the area of Canada.269The Northern Arctic ecozone is about 3times as big as the Hudson Plains ecozone.10What fraction of the area of Canada does the Northern Arctic ecozone cover?The Hudson Plains ecozone covers19 32610Write the mixed number as an improper fraction.Multiply the fractions.Sentence:322MHR Chapter 6: Fraction Operations
Name: Date:6.5 Warm Up1. Write each fraction as a mixed number.a)185b)2332. Write each mixed number as an improper fraction.a) 337b) 13113. Write each set of fractions with a common denominator.a)12 1, 15 3,b)5 7, 2 8d)12 9, 9 6,Multiples of 15: 15, 30, 45, 60, Multiples of 3: 3, 6, 9, 12, 15, 18, The lowest common multiple isc)3 1, 4 6,.,4. Divide.a) 12 2 b) 40 8 c) 13 1 d) 24 3 6.5 Warm Up MHR323
Name: Date:6.5 Dividing Fractions and Mixed NumbersWorking Example 1: Divide Using DiagramsFind2 1 .3 4Solution12s are in .43 Divide 1 rectangle into 3 parts. Shade 2 of the parts. Divide another rectangle into 4 parts.12The diagrams show that the number of s in is between 2 and 3.4312A common denominator of and is.43So, divide a rectangle into twelfths. Shade the parts up to the dotted line.8In , there are 2 whole groups of122 1223 2 or, plus of another group.3 433312 Draw diagrams to see how manyFind3 1 using diagrams.4 3 Shade 3 parts of the first rectangle. Draw a dotted line from the end of the shaded partthrough the other 2 rectangles.13and is34 Divide the third rectangle into twelfths. Shade the parts up to the dotted line.A common denominator of Count the number of shaded parts:of4, plus12So,3244.12. In9, there are12of another group. There are3 1 4 3MHR Chapter 6: Fraction Operationsor4whole groupswhole groups of.3.12
Name: Date:Working Example 2: Divide Using a RuleEstimate and calculate.a)7 1 84SolutionEstimate:7.8 Draw a diagram divided into quarters.7 Draw a dotted line from to the next diagram.8 Draw a diagram showingThe number of quarters in7is between 3 and8. So,7 11 3 .842reciprocal flip the fraction to switch the numerator and denominator23 example: the reciprocal of is32Calculate:Method 1: Divide Using a CommonDenominatorMethod 2: Divide Using MultiplicationTo divide by a fraction, multiply by its reciprocal.7 1 8 4Find a common denominator. 7 88Divide the numerators.7 2Write in lowest terms.7 1 8 47 4 8 1 flip the numeratorand denominator8 428 7 8 2 41 326.5 Dividing Fractions and Mixed Numbers MHR325
Name: Date: 332612MHR Chapter 6: Fraction Operations
Name: Date:b) 213 324SolutionEstimate:132 3 and 3 4 .24132 3 3 424 4Calculate:Method 1: Divide Using a CommonDenominator2132 3242Method 2: Divide Using MultiplicationWrite as improper fractions.1 2 2 1 2 2 2 213 324Write as improper fractions. 25 4 2 1515.4Write as a reciprocal. 23 4 4 4 33 4 4 4 4 4 Write in lowest terms.30 10 45 15 2 410 15 44 15Find a common denominator.30 Divide the numerators. 10Write in lowest terms.36.5 Dividing Fractions and Mixed Numbers MHR327
Name: Date:Estimate and calculate.a)32843 5 10b) 312 163Estimate:Estimate:Calculate:Calculate:MHR Chapter 6: Fraction Operations
Name: Date:Working Example 3: Apply Division With FractionsBaby teeth are replaced by adult teeth as people get older.5Children have as many teeth as adults do. Children have 20 teeth.8How many teeth do adults have?You could also divide usingcommon denominators.Solution5 20 520 58 1 8Divide 20 by to find the number of adult teeth.8160 5 5Multiply by the reciprocal.20 888 20 1Check:Use multiplication to check the division.5 3285 32 Multiply the numerators 8 1 Multiply the denominators8160 32Adults have teeth.8 201of the tray.6How many servings are in 3 trays of lasagna?One serving of lasagna is3 6Multiply by the reciprocal.Check your answer.1 6 1 61 There areservingsof lasagna in 3 trays of lasagna. 6.5 Dividing Fractions and Mixed Numbers MHR329
Name: Date:3 2 .4 3Is Mike’s method correct? Circle YES or NO.Give 1 reason for your answer.1. Mike solvedMike’s Work:3 2 4 34 2 3 38 92. Find5 1 using diagrams.8 4 Divide 1 rectangle into 8 parts.Shade 5 parts. Draw a dotted line from the end of theshaded part through the other 2 rectangles. Divide the second rectangle into 4 parts. A common denominator of 8 and 4 is Divide the third rectangle into eighths. Shade the parts up to the dotted line.5 1 8 4 330.In12Write as an improper fraction.MHR Chapter 6: Fraction Operations5, there are whole groups821of , plus of another group.82
Name: Date:3. Divide using a common denominator.a)3 9 5 10 b) 1Find a commondenominator. 1 5 2 611 2 Divide thenumerators. 2 Write as animproper fraction.2 Find a commondenominator for2 and 6. Divide thenumerators.Write in lowestterms. 2 4. Divide using multiplication.a)3 4 4 5 3 4b) 1Write as a reciprocal.25 236Write asimproperfractions. 6.5 Dividing Fractions and Mixed Numbers MHR331
Name: Date:1of an hour to perform.4How many performers are there in a 2-h show?5. In a comedy show, each performer has2 2 214There are6. It takes 2performers in 2 h.1cups of flour to make 1 cake. How many cakes can you make with 15 cups of flour?2Sentence:The wettest part of the Prairies ecozone is the Manitoba Plain.The average yearly amount of precipitation is about 70 cm.4This amount of precipitation is 2 of the amount in the dry grasslands.5What is the average annual precipitation in the grasslands?Precipitation is waterthat falls as rain, snow,sleet, or hail.470 25Sentence:332MHR Chapter 6: Fraction Operations
Name: Date:6.6 Warm UpBrackets, multiply or divide,then add or subtract.1. Use the order of operations to calculate.a)4 7 – 10b) – 10 c)7–2 3Multiply. 7–Multiply.Subtract. Subtract.8 (3 – 1)d)10 – (2 6) 2 8 Brackets. 10 – Multiply. 10 – 2Brackets.Divide. 1 2 using a common5denominator.2. a) Divideb) Divide 5 reciprocal.4by multiplying by the93. Change mixed numbers to improper fractions.a) 313 b) 2 25 6.6 Warm Up MHR333
Name: Date:6.6 Applying Fraction OperationsWorking Example 1: Use the Order of OperationsCalculate using the order of operations.Brackets, multiply or divide,then add or subtract.1 1a) 2 4 2Solution1 1 4 22 4 1 1 1 22 Divide by multiplying the reciprocal.12Multiply.82 Write in lowest terms.b)1 (9 – 2)3Solution1 (9 – 2)31 3 233413Brackets.Multiply.7 3Write as a mixed fraction.MHR Chapter 6: Fraction Operations71
Name: Date:c) 21 31 1 1 4 44 1 1 Solution44 2 1 33 1 4 4 2 1 31 1 1 4 44 21 4 2 4 34 4 113Write the mixed number as an improper fraction.Multiply by the reciprocal.Write in lowest terms.12a) 4 – 2 4 4 1 9 4 4 4 414 Add the whole numbers.Add the fractions.35b) 22 11 51 –2 84Multiply bythe reciprocal.4 1 Find a commondenominator. 6.6 Applying Fraction Operations MHR335
Name: Date:Working Example 2: Apply Fraction OperationsBev earns 25/h as a machine operator.When she works more than 40 h in a week, she earns time-and-a-half.How much does Bev earn for working 46 h in a week?To earn time-and-a-half means to be paid for 11h when you work for 1 h.2SolutionMethod 1: Calculate in StagesBev works 40 h at her regular pay of 25/h.Amount earned at regular rate: 40 25 How many hours does she work at time-and-a-half? 46 – 40 6 h at time-and-a-half ? h at regular ratetime-and-a-half 1 1216 12Write as an improper fraction:2 1 3 2 2 2 6 63 12 2 96 h at time-and-a-half 9 h at regular rateAmount earned at time-and-a-half: 9 25 Total earnings amount earned at regular rate amount earned at time-and-a-half 225 Bev earns 336for working 46 h in a week.MHR Chapter 6: Fraction Operations
Name: Date:Method 2: Evaluate One ExpressionBev’s regular rate of pay is 25/h. For 6 h at time-and-a-half, Bev is paid 11 2h.1 An expression of her total earnings is: 25 40 1 6 2 1 25 40 1 6 2 25 40 3 6 25 40 2 1 25 40 2 25 49 1225Bev earns 2 1 3 2 2 2Brackets first. 6 Write the mixed number as an improper fraction.Multiply the numbers in the bracket. 18 18 2 9240 9 49Add.Multiply.for working 46 h in a week.Ron earns 15/h as a security guard.When he works more than 35 h in 1 week, he earns time-and-a-half.How much does Ron earn for working 43 h in a week?Ron worked 35 h at regular pay. Amount earned at regular pay: 35 15 Hours worked at time-and-a-half: 43 – 35 8 112Amount earned at time-and-a-half:Total earnings 15 6.6 Applying Fraction Operations MHR337
Name: Date: 1 1 21. Mia missed the lesson
Fraction Operations GET READY 284 Math Link 286 6.1 Warm Up 287 6.1 Multiplying a Fraction and a Whole Number 288 6.2 Warm Up 294 6.2 Dividing a Fraction by a Whole Number 295 6.3 Warm Up 301 6.3 Multiplying Proper Fractions 302 6.4 Warm Up 309 6.4 Multiplying Improper Fractions and Mixed Numbers 310 6.5 Warm Up 319
FRACTION REVIEW A. INTRODUCTION 1. What is a fraction? A fraction consists of a numerator (part) on top of a denominator (total) separated by a horizontal line. For example, the fraction of the circle which is shaded is: 2 (parts shaded) 4 (total parts) In the square on the right, the fraction shaded is 8 3 and the fraction unshaded is 8 5
1. Look at the fraction. Is it an improper fraction or a mixed number? 2. Write the fraction in the correct column (either improper fraction or mixed number). 3. Use fraction circles to help convert the improper
visualization of the fraction sum and visualization of an equivalent sum. 4. Give each pair of students a copy of the Fraction Sum Sheet. Display the following fraction problems, and instruct student pairs to work with their fraction strips to find the sums and to record the equivalent
Folding Fraction Strips (4th) L1-2a 4.NF.1 Explain why a fraction a/b is equivalent to a fraction (a x n)/(b x n) by using visual models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to reco
SOM1 0.01 Initial fraction of SOM1 in total organic carbon f SOM2 0.02 Initial fraction of SOM2 in total organic carbon f SOM3 0.1 Initial fraction of SOM3 in total organic carbon F FeRB 2 10-6 Initial fraction of Fe reducers in total organic carbon F Mega 10-6 Initial fraction of acetoclastic methanogens in total organic carbon F MegH 10
This fraction can be simplified to 14 3 2. 104 36 This fraction can be simplified to 26 9 3. 3192 924 This fraction can be simplified to 38 11 Practice #2 Answers 1. 15 9 This fraction can be simplified to 5 3 2. 52 70 This fraction can be simplified to 26 35
Fraction Scoot Multiplication Scoot 3 What fraction of the squares are inside the circle? Multiplication Scoot 2 What fraction of the marbles are black? Fraction Scoot 1 Super Teacher Worksheets - www.superteacherworksheets.com Practice moving from desk to desk before playing the actual game.
Applying GCF and LCM to Fraction Operations Reteach How to Multiply a Fraction by a Fraction 2 3 i 3 8 2 3 i 3 8 6 Multiply numerators. 2 3 i 3 8 6 24 Multiply denominators. 66 24 6 1 4 Divide by the greatest common factor (GCF). The GCF of 6 and 24 is 6. How to Add or Subtract
