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Mathematics Grade 8W1 - Lesson 3: Multiplying and DividingFractionsV6-10

Important Concepts of Grade 8 MathematicsW1 - Lesson 1.Perfect Squares and Square RootsW1 - Lesson 2. Working with Ratios and RatesW1 - Lesson 3. Multiplying and Dividing FractionsW1 - Lesson 4. Multiplying and Dividing IntegersW1 - Lesson 5. Working with PercentsW1 - ReviewW1 - QuizW2 - Lesson 1. Modelling and Solving Linear Equations Using Algebra TilesW2 - Lesson 2. Solving Linear EquationsW2 - Lesson 3.Graphing and Analyzing Linear RelationsW2 - Lesson 4. Critiquing the Representation of DataW2 - Lesson 5. Probability of Independent EventsW2 - ReviewW2 - QuizMaterialsRequiredProtractorRulerCalculatorNo TextbookRequiredThis is a standalone course.W3 - Lesson 1. Pythagorean TheoremW3 - Lesson 2.Calculating Surface AreaW3 - Lesson 3.Calculating VolumeW3 - Lesson 4.Drawing 3-D ObjectsW3 - Lesson 5. Congruence of PolygonsW3 - ReviewW3 - QuizMathematics Grade 8Version 6Preview/Review W1 - Lesson 3ISBN 1-891894-00-6Publisher: Alberta Distance Learning CentreWritten by: Monica dHamraitReviewed by: Patty RogersonProject Coordinator: Donna SilgardPreview/Review Publishing Coordinating Team:Heather Martel and Nicole MckeandAlberta Distance Learning Centre has an Internet site that you may find useful. The address is as follows: http://www.adlc.caThe use of the Internet is optional. Exploring the electronic information superhighway can be educational and entertaining. However, beaware that these computer networks are not censored. Students may unintentionally or purposely find articles on the Internet that maybe offensive or inappropriate. As well, the sources of information are not always cited and the content may not be accurate. Therefore,students may wish to confirm facts with a second source.ALL RIGHTS RESERVEDCopyright 2010, by Alberta Distance Learning Centre, 4601-63 Avenue, Barrhead, Alberta, Canada, T7N 1P4. Additional copiesmay be obtained from Alberta Distance Learning Centre.No part of this courseware may be reproduced or transmitted in any form, electronic or mechanical, including photocopying (unlessotherwise indicated), recording, or any information storage and retrieval system, without the written permission of Alberta DistanceLearning Centre.Every effort has been made both to provide proper acknowledgement of the original source and to comply with copyright law. Ifcases are identified where this effort has been unsuccessful, please notify Alberta Distance Learning Centre so that appropriatecorrective action can be taken.IT IS STRICTLY PROHIBITED TO COPY ANY PART OF THESE MATERIALS UNDER THE TERMS OFA LICENCE FROM A COLLECTIVE OR A LICENSING BODY.

Preview/Review ConceptsforGrade Eight MathematicsW1 – Lesson 3:Multiplying and DividingFractions

OBJECTIVESBy the end of this lesson, you will be able to: Express a given positive mixed number as an improper fraction and a given positiveimproper fraction as a mixed number Model the process of multiplying fractions using models and numerically Model the process of dividing fractions using models and numerically Apply rules for multiplying and dividing positive fractions, including mixednumbers Solve an expression involving fractions and apply the order of operations Solve problems involving the multiplication and division of fractions and mixednumbersGLOSSARYDenominator – the bottom number ofa fraction, the number of equal sizedparts a whole has been divided into.Factors – the numbers that aremultiplied to give a product. A factorof a given number will divide into thegiven number with no remainder leftover. For example, the 4 and 5 arefactors of 20.Greatest Common Factor (GCF) –the largest factor that is common to aset of numbers. Example, the GCF of12 and 18 is 6 because 6 divides into12 twice and into 18 three times.Improper Fraction – a fraction inwhich the numerator that is greaterthan the denominator.Mixed number – a number representedby a whole number and a fraction.Multiple – a number that is the productof a natural number and anothernumber. For example, the multiplesof 5 are 5, 10, 15, 20, etc.Numerator – the top number of afraction, the number of pieces beingconsidered.Simplify – reducing a fraction intoits lowest terms. This is done bydividing both the numerator anddenominator by the GCF.

Mathematics Grade 8Preview/Review Concepts W1 - Lesson 3W1 – Lesson 3: Multiplying and Dividing FractionsMaterials required: Paper, Pencil, and CalculatorReview: Converting between Improper Fractions and MixedNumbersTo change a mixed number into an improper fraction, multiply the denominator by thewhole number and add the numerator. This value becomes the numerator in the improperfraction. The denominator in the mixed number is the same denominator you use in theimproper fraction.First, multiply thedenominator by thewhole numberFor example: 21 3 2 1 7 333Second, add thenumerator.To change an improper fraction into a mixed number, reverse the process outlined above.Determine how many times the denominator goes into the numerator and this valuebecomes the whole number. The remainder becomes the numerator in the fraction. Thedenominator remains the same.For example:9 2 and there is one left over491 244This is the remainder.Developed by Alberta Distance Learning Centre .1

Mathematics Grade 8Preview/Review Concepts W1 - Lesson 3Part 1: Multiplying FractionsWhen you multiply fractions, what you are really doing is finding a fraction of a fraction.Fractions can be multiplied using the area model.Use the area model to multiply2 1 .3 5First use a square to represent2vertically.3Then, represent1horizontally on the same square.5The shaded squares that overlap represent the numerator of the answer. The totalnumber of parts in the square represents the denominator.In this case, the numerator would be 2, and the denominator would be equal to 15.Thus,2 1 2 .3 5 152 . Developed by Alberta Distance Learning Centre

Mathematics Grade 8Preview/Review Concepts W1 - Lesson 3When multiplying fractions numerically, remember these steps:Step 1: Convert any mixed numbers into improper fractions.Step 2: Simplify the numerators and denominators. To do this, divide the numerators anddenominators by a common factor.Step 3: Multiply the numerators.Step 4: Multiply the denominators.Step 5: If an improper fraction results, change it into a mixed number.Example 13 1 3 1 4 2 4 23 8Example 21 37 3 2 3 43 47 31 31 4Cancel out the 3's.7 11 47 43 14 Developed by Alberta Distance Learning Centre .3

Mathematics Grade 8Preview/Review Concepts W1 - Lesson 3Example 377 5 5 88 17 5 8 135 83 48Example 41110 21 3 5343 45710 21 42135 7 1 235 21 172 When you simplify the expression before youstart multiplying the result will always be inlowest terms.Practice Questions1.3 3 54 . Developed by Alberta Distance Learning Centre

Preview/Review Concepts W1 - Lesson 32.5 2 6 33.3 35 5 84.121 2 25Mathematics Grade 8Developed by Alberta Distance Learning Centre .5

Mathematics Grade 8Preview/Review Concepts W1 - Lesson 3Part 2: Dividing FractionsWhen you divide 12 by 3, you are determining how many groups of 4 are in 12. When 12is divided into groups of 4, the result is 3. Dividing fractions uses a similar method.You can divide fractions using a number line.Let’s use 5 groups of11 20 as an example. When dividing 5 by, you must determine how many441are in 5.41414140There are 20 groups ofThus, 5 1414141141414214141414141431414414141451in 5.41 20 .4When dividing fractions numerically, remember these steps:Step 1: Convert any mixed numbers into improper fractions.Step 2: Multiply the first term by the reciprocal of the second term. The reciprocal is the“flip” of the fraction or number.Step 3: Multiply the numerators.Step 4: Multiply the denominators.Step 5: If an improper fraction results, change it into a mixed number.6 . Developed by Alberta Distance Learning Centre

Mathematics Grade 8Preview/Review Concepts W1 - Lesson 3Example 133 1 2 44 23 1 4 23 8The reciprocal of 2 is12Example 212 212 5 51 26 12 5 121Multiply by the reciprocalof the second term6 51 1 30 Example 33 13 5 7 57 13 5 7 115 71 27Developed by Alberta Distance Learning Centre .7

Mathematics Grade 8Preview/Review Concepts W1 - Lesson 3Example 44318 27 2 3 787818 8 7 27 2188 727 32 87 316 21 Practice Questions2 31.8 2.5 4 128 . Developed by Alberta Distance Learning Centre

Preview/Review Concepts W1 - Lesson 33.2 1 7 54.232 1 54Mathematics Grade 8Developed by Alberta Distance Learning Centre .9

Mathematics Grade 8Preview/Review Concepts W1 - Lesson 3Part 3: Applying Order of OperationsWhen calculating the answer to an expression with many mathematical operations youmust follow the order of operations. Use the acronym BEDMAS to help you.Complete theseoperations,divisions ormultiplicationin order from left to onadditionsubtractionComplete these operations,addition or subtractionin order from left to right.Example 133 1 4Evaluate the following expression 4 5 5Answer:Step 1: Since there are no brackets present, evaluate the exponent.33 1 4 4 5 5 314 4 125 510 . Developed by Alberta Distance Learning Centre

Preview/Review Concepts W1 - Lesson 3Mathematics Grade 8Step 2: Complete the division.314 4 125 531 5 4 125 45131 4 25 125 4 31 4 100Step 3: Complete the addition.31 4 100751 100 10076 10019 25 Developed by Alberta Distance Learning Centre .11

Mathematics Grade 8Preview/Review Concepts W1 - Lesson 3Example 2 5 1 2 1 Evaluate the following expression 1 . 7 2 3 4 Answer:Step 1: Solve the operations in the first set of brackets. 5 1 2 1 1 7 2 3 4 5 2 2 1 1 7 1 3 4 10 2 1 1 7 3 4 Step 2: Solve the operations in the second set of brackets. 10 2 1 1 7 3 4 10 5 1 7 3 4 10 20 3 7 12 12 10 23 7 12 Step 3: Solve the operations in the second set of brackets. 10 23 7 12 5 10 23 7 126 5 23 7 6115 4231 24212 . Developed by Alberta Distance Learning Centre

Preview/Review Concepts W1 - Lesson 3Mathematics Grade 8Practice Questions1.1 1 1 2 7 22. 2 5 10 3 6 9 2Developed by Alberta Distance Learning Centre .13

Mathematics Grade 83.Preview/Review Concepts W1 - Lesson 33 2 1 2 8 3 6 514 . Developed by Alberta Distance Learning Centre

Preview/Review Concepts W1 - Lesson 3Mathematics Grade 8Lesson 3: Assignment1.5 1 6 32.9 1 10 63.44 2 74.4 32 5 85.721 2 856.73 3 124Developed by Alberta Distance Learning Centre .15

Mathematics Grade 87.3 1 5 48.5 2 6 39.8 1Preview/Review Concepts W1 - Lesson 31 410.2 13 5 511.35 2 812.1101 3 11216 . Developed by Alberta Distance Learning Centre

Mathematics Grade 8Preview/Review Concepts W1 - Lesson 31 413.2 14.6 3 1315.9 3 11Solve the following problems involving fractions. All the answers must be in lowest terms,include the units, and written in complete sentences.16.1An elastic band will stretch to be 4 8 times its original size. If the elastic back is102cm long, to what length will it stretch?3Developed by Alberta Distance Learning Centre .17

Mathematics Grade 817.Preview/Review Concepts W1 - Lesson 3Captain Dianne is in her canoe and notices it has 20container that holds 31L of water in it. She has a21L of water. How many scoops of water will must she3make to bail all the water out of her canoe?18.8How many complete pieces of ropemetres long can be cut from a roll of rope that9is 36 metres long?18 . Developed by Alberta Distance Learning Centre

Preview/Review Concepts W1 - Lesson 319.Mathematics Grade 8Corbin and Sheila are in the widget-selling business together. Since Shelia investedmore money into the business than Corbin did, she is entitled to3of the profits.5For every widget they sell, they earn 18.50 in profit. How much will Corbin get foreach widget that is sold? Express the answer as a fraction and in dollars.20.1 3 1 2 4 8 Developed by Alberta Distance Learning Centre .19

Mathematics Grade 8Preview/Review Concepts W1 - Lesson 3321.2 1 3 2 22.211 5 320 . Developed by Alberta Distance Learning Centre

Preview/Review Concepts W1 - Lesson 323.Mathematics Grade 82 9 3 3 2 3 10 5 7Developed by Alberta Distance Learning Centre .21

Mathematics Grade 824.Preview/Review Concepts W1 - Lesson 33 8 3 5 3 5 9 4 6 22 . Developed by Alberta Distance Learning Centre

Part 2: Dividing Fractions When you divide 12 by 3, you are determining how many groups of 4 are in 12. When 12 is divided into groups of 4, the result is 3. Dividing fractions uses a similar method. You can divide fractions using a number line. Let’s use 1 5 20 4 as an example. When dividing

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