Use repeated addition to multiply fractions by whole numbers. is shown. is an improper fraction.

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1 Student book pages 0 Multiplying a Whole Number by a Fraction You will need counters Use repeated addition to multiply fractions by whole numbers You can use grids and counters to model fractions What fraction does this diagram represent? Cutout numerator denominator number of counters on the grid number of squares in the grid terms numerator denominator The denominator tells the number of equal parts in whole The numerator tells the number of equal parts that the fraction represents mixed number a number made up of a whole number and a fraction improper fraction a fraction in which the numerator is greater than the denominator You can use grids and counters to model fraction addition A model of is shown There are the grids counters in is an improper fraction Write as a mixed number Redraw the counters in the grids so that the first grid is full There is full grid, plus counters in the second grid, so you can write as if you want to Lesson : Multiplying a Whole Number by a Fraction Copyright 009 Nelson Education Ltd

2 Multiplication and repeated addition are equivalent For example, is equivalent to can be read as sets of Use repeated addition to model Draw counters on the grids to show sets of There are counters in the grids Draw the same number of counters, but this time fill up as many whole grids as you can Rewrite your answer as a mixed number PROBLEM Six pitchers of lemonade are each full How many pitchers of lemonade are there? Use Cutout and counters to model Write the number of pitchers as an improper fraction Move the counters to fill as many grids as you can Rewrite your answer as a mixed number Hint When you add fractions with the same denominator, the denominator stays the same Reflecting So, Use these words to complete the statements below numerator denominator When you multiply a whole number by a fraction, the stays the same To multiply a whole number by a fraction, multiply the whole number by the of the fraction Copyright 009 Nelson Education Ltd Lesson : Multiplying a Whole Number by a Fraction

3 Practising Multiply Write your answer as a fraction and, if it is greater than, as a mixed number or whole number Use a model and show your work a) Hint A fraction is if the numerator is greater than the denominator Is greater than? b) Draw sets of Draw the same number of counters, but this time fill up as many whole grids as you can c) Draw more fifths grids Draw counters on the grids to show sets of _ Is your answer greater than? Lesson : Multiplying a Whole Number by a Fraction Copyright 009 Nelson Education Ltd

4 d) 7 _ Rewrite your answer as a mixed or whole number Hint and are equivalent fractions Hint Write your answer as a mixed or whole number or Try this method to write as a mixed number Complete the division remainder So, or Art class is of an hour each school day How many hours of art does a student have in days? The student has hours of art in days Jason needs of a cup of flour to make batch of bannock How many cups of flour will he need if he decides to make batches of bannock? Jason needs of bannock cups of flour for batches Copyright 009 Nelson Education Ltd Lesson : Multiplying a Whole Number by a Fraction

5 Student book page Exploring Calculating a Fraction of a Fraction You will need a ruler Cutout term Represent one fraction as part of another fraction You can use a fraction strip tower to compare fractions Use the edge of a ruler to identify fractions that are equal in length A strip is the same length as a strip, so List some other fractions that are equivalent to equivalent fractions fractions that are equal in value You can also use a fraction strip tower to represent one fraction as part of another fraction fits into two times So, is half of of Lesson : Exploring Calculating a Fraction of a Fraction Copyright 009 Nelson Education Ltd

6 Aaron is playing a fraction game with his friends The game board is a fraction strip tower Each player picks a card and colours in the fraction that the card represents Aaron coloured,,, and Match the fractions he coloured with the cards he picked Aaron picked these cards of = of = Use Cutout and the edge of a ruler of Which fraction fits into three times? of of Which fraction fits into four times? of of = of Which fraction fits into four times? of of of of = of What is an equivalent fraction for? What is of this equivalent fraction? So, what is of this equivalent fraction? of Which fraction is equivalent to 0? So, of is also equal to Copyright 009 Nelson Education Ltd Lesson : Exploring Calculating a Fraction of a Fraction 7

7 Student book pages Multiplying Fractions Multiply two fractions less than To multiply, you can draw a -by- grid and determine its area Hint means the same as of Use an area model to multiply fractions < PROBLEM Calculate Use a grid Each row is of the grid Each column is of the grid One grid square is of of the grid of the grid is columns Shade of of the grid Area of shaded part (square units) Area of whole -by- grid (square units) PROBLEM Use a grid to calculate 0 Use this -by-0 rectangle to represent whole There are There are rows Each row is columns Each column is of the grid of the grid Shade 0 of the grid 0 Area of shaded part (square units) Area of whole -by-0 grid (square units) Lesson : Multiplying Fractions Copyright 009 Nelson Education Ltd

8 Use a procedure to multiply fractions Look back at your solution to Area of the part of the grid shaded to show of Numerator of the product Product of the numerators of square units Area of the whole -by- grid Denominator of the product Product of the denominators of square units Circle the numbers you multiply to get the numerator of the product Underline the numbers you multiply to get the denominator of the product PROBLEM Calculate Multiply the numerators Multiply the denominators Product of the numerators Product of the denominators PROBLEM Calculate Product of the numerators Product of the denominators Reflecting Which method for multiplying fractions less than do you prefer the area model or the procedure? Explain Copyright 009 Nelson Education Ltd Lesson : Multiplying Fractions 9

9 Practising Draw a model for each multiplication expression Determine the product a) The denominators of the fractions are and, so start with a rectangle units long and units wide Draw this rectangle on the grid Inside this rectangle, shade a rectangle of the length and of the width What fraction of the whole is shaded? b) Draw a -by- rectangle on the grid Shade a rectangle that is c) Draw a -by- rectangle on the grid Shade a rectangle that is or 7 a) Draw a picture to show why = 0 To model, use a -by- rectangle to represent whole Draw this rectangle on the grid Area of rectangle = square units Inside this rectangle, shade a rectangle What fraction of the whole is shaded? = 0 Lesson : Multiplying Fractions Copyright 009 Nelson Education Ltd

10 b) List other pairs of fractions with a product of 0 Write pairs of numbers that are factors of the numerator and denominator of 0 Pair A Pair B = = = 0 = Hint To write a fraction in lower terms, divide the numerator and denominator by a common factor Matthew s bed takes up of the width of his bedroom and of the length What fraction of the floor area does the bed use up? Solution: Use the procedure to determine of Multiply the numerators and the denominators or Matthew s bed takes up of the floor area Some examples of : a pitcher of lemonade that is full Describe a situation where you might multiply Use one of these or your own ideas to describe a situation where you might calculate of of a project still to do of a class of students Copyright 009 Nelson Education Ltd Lesson : Multiplying Fractions

11 Student book page 7 Exploring Estimating Fraction Products Estimate to predict whether a fraction product is closer to 0, _, or Brian and Preston are playing a spinner game They spin twice and multiply They score point if the product is closest to 0, point if it is closest to, and points if it is closest to Hint What is the simplest fraction that describes the shaded area? Predict whether each product is closer to 0,, or Write in lowest terms Is closest to 0,, or? Write fractions equivalent to 0,, and with a common denominator of _ Compare the numerator of your answer and the numerators of the equivalent fractions for 0,, and Is closest to 0,, or? How do you know? Lesson : Exploring Estimating Fraction Products Copyright 009 Nelson Education Ltd

12 9 0 Write equivalent fractions with a common denominator of Is 9 0 closest to 0,, or? 9 0 Write equivalent fractions with in the denominator 0 Is 9 0 closest to 0,, or? Is 9 0 closest to 0,, or? Is closest to 0,, or? Is closest to 0,, or? What happens when you multiply fractions close to 0? What happens when you multiply fractions close to? Copyright 009 Nelson Education Ltd Lesson : Exploring Estimating Fraction Products

13 Student book pages Multiplying Fractions Greater Than Multiply mixed numbers and improper fractions whole Use an area model to multiply fractions > You can use a grid to model Use a grid with rows Use a grid with columns A -by- rectangle represents whole So, each grid square represents Number of shaded grid squares Fraction each grid square represents PROBLEM Use a grid to calculate Use a grid with rows rows represent whole Use a grid with columns columns represent whole Shade a 7-by- rectangle on the grid Label the sides of the rectangle and Outline a -by- rectangle to show whole There are grid squares inside this rectangle, so each grid square represents Number of shaded grid squares Fraction each grid square represents Lesson : Multiplying Fractions Greater Than Copyright 009 Nelson Education Ltd

14 Write each product you calculated as a mixed number remainder So, remainder So, Use a procedure to multiply fractions > Calculate Step : Write as an improper fraction Here are methods you can use Shade the fraction strip to show OR Write as an improper fraction Then add Step : Multiply Step : Write the product as a mixed number 0 0 R Combine the steps in the procedure above ( ) OR So, 0 0 Hint If a fraction is <, its numerator is less than its denominator Reflecting How can you tell that the product of fractions less than will always be less than? Copyright 009 Nelson Education Ltd Lesson : Multiplying Fractions Greater Than

15 Practising Calculate each product a) Write as an improper fraction OR b) Use the grid to model Then calculate the product Solution:, so use a grid with rows, so use a grid with columns Shade a 7-by- rectangle on the grid The rows show fourths 7 rows show 7, so rows show, or whole The columns show thirds 7 columns show 7, so columns show, or whole So, a -by- rectangle represents whole Outline a rectangle that represents whole There are grid squares inside this rectangle, so each grid square represents Number of shaded grid squares Fraction each grid square represents Write the product as a mixed number Lesson : Multiplying Fractions Greater Than Copyright 009 Nelson Education Ltd

16 0 Tai calculated He multiplied the whole number parts together and then the fraction parts together to get an incorrect product of a) Explain why estimation would not help Tai realize that he made a mistake To estimate, which whole numbers are close to and? What is the product of your estimate? Why would estimation not help Tai realize that he made a mistake? b) How could you show Tai that his answer is incorrect? Write and as improper fractions Hint If a number is even, it is divisible by Divide the numerator and denominator of your answer by a common factor to write the improper fraction in lower terms Hint Think of situations where you see fractions, such as in recipe books Write the product as a mixed number Describe a situation at home in which you might multiply by Copyright 009 Nelson Education Ltd Lesson : Multiplying Fractions Greater Than 7

17 Student book pages 7 Dividing Fractions by Whole Numbers Use a sharing model to represent the quotient of a fraction divided by a whole number Use grids and counters to divide a fraction 9 You can think of dividing as sharing 0 tells you the share size if people share 9 0 of something You can use a grid and counters to model 9 0 A -by- grid represents the denominator (0) Place 9 counters on the grid to represent the numerator (9) Circle the 9 counters to divide them into equal groups Each person would have counters out of PROBLEM Calculate Draw counters on the -by- grid to represent Can you divide counters into equal groups? Write a fraction equivalent to, with a numerator that can be divided into equal groups Draw counters on a -by- grid to represent this fraction Circle the counters to divide them into equal groups Each of the groups represents of the grid Lesson : Dividing Fractions by Whole Numbers Copyright 009 Nelson Education Ltd

18 Multiply by a fraction to divide a fraction Divide Multiply of of Dividing by is the same as taking of the number Divide 9 Multiply of of 9 9 Dividing by is the same as taking of the number Multiply to divide Reflecting Use to explain how a division of a fraction by a whole number can be done as a multiplication Copyright 009 Nelson Education Ltd Lesson : Dividing Fractions by Whole Numbers 9

19 Practising Divide Show your work a) 9 Use a grid and counters to represent 9 Draw a grid to represent whole ( 9 9 ) 9 Draw a grid this size Draw counters on the grid to represent 9 Circle the counters to divide them into equal groups There are counters in each group Each of the groups represents of the grid 9 b) 9 Can you divide counters into groups? Write a fraction equivalent to 9, with a numerator that can be divided into equal groups _ 9 The denominator of a fraction shows the number of parts in whole Draw a grid to represent whole Draw counters on the grid to represent the equivalent fraction To calculate, you can think of sharing counters out of between people Each person would have of the counters 9 0 Lesson : Dividing Fractions by Whole Numbers Copyright 009 Nelson Education Ltd

20 Kevin used of a can of paint to cover walls How much of a can did he use for each wall? Solution: Write a division sentence to represent this problem? To divide by, you can multiply by Kevin used of a can of paint for each wall Hint 9 a) Create a problem you might solve by dividing by Think of something you could have of Divide it between people or things b) Solve your problem Copyright 009 Nelson Education Ltd Lesson : Dividing Fractions by Whole Numbers

21 7 Student book pages 7 7 Estimating Fraction Quotients Interpret and estimate the quotient of fractions less than Participants last year The fraction of students in a school who participate in school sports has increased from to Is closer to double or triple? Fit one fraction into the other fraction You can divide to find out how many times fits into Estimate Participants this year Shade and on the fraction strips About how many times does fit into? times So, is close to Is about double or triple? Compare fractions using equivalent fractions Double is Triple is Hint To find a common denominator, compare the multiples of the denominators Which of the fractions above is closer to? To compare, common denominator The denominators of, and, rewrite the fractions using a,, and are,, and Circle the lowest common denominator of and, 0,, 0,, 0,, 0,,,,,, 0,,,, 7, Lesson 7: Estimating Fraction Quotients Copyright 009 Nelson Education Ltd

22 Write equivalent fractions with a common denominator = 0 = = Is 0 0 or 0 closer to 0? is closer So, is or closer to? is closer = = is close to, so fits into about times is close to PROBLEM Estimate 7 9 Shade 7 9 and on the fraction strips fits into 7 9 about times So, 7 9 is close to PROBLEM Estimate using common denominators One common denominator is Write equivalent fractions About how many times does fit into? Compare the numerators of the equivalent fractions Hint a b c dividend divisor quotient When the dividend is greater than the divisor, the quotient is less than Reflecting fits into about times, so fits into about times So, is close to is about The quotient,, is greater than is about The quotient,, is less than When will a quotient be less than? Copyright 009 Nelson Education Ltd Lesson 7: Estimating Fraction Quotients

23 A useful fact The quotient of fractions with the same denominator is the same as the quotient of the numerators a n b n a b Example: Think of it this way: fits into the same number of times as fits into Practising Estimate each quotient as a whole number a) and = = 0 = b) c) The denominators are the same, so is close to So, is close to Circle a common denominator of and,,,,, Write a fraction equivalent to using the common denominator that you circled Compare the numerators of the equivalent fraction and so fits into about times, is close to 0 Circle a common denominator of and 0,,,, 0, 0, 0, 0, Write equivalent fractions with this denominator Compare the numerators fits into about times, so 0 is close to Lesson 7: Estimating Fraction Quotients Copyright 009 Nelson Education Ltd

24 CUP / / / cup, / of a cup full / cup Amber needs of a cup of berries to make a Saskatoon berry soup She can find only a -cup measure About how many times will she have to fill the cup to have the right amount of berries? Solution: Start by restating the problem: How many times does fit into? Finding a common denominator Method : Compare the multiples of the denominators,, 9,,,,,, Method : Use the product of the denominators Hint a b c dividend divisor quotient This means, what is? Estimate the quotient Shade the fraction strips to show and fits into about times, so is close to Rewrite and with a common denominator Compare the numerators of the equivalent fractions = = fits into about times So, 0 is close to Amber will have to fill the cup about times How do you know that is less than? Solution: Shade the fraction strips to show and Look at the quotient Which is less, the dividend or the divisor? Look at your answer to the Reflecting question at the bottom of page How do you know that is less than? Copyright 009 Nelson Education Ltd Lesson 7: Estimating Fraction Quotients

25 Student book pages 7 0 Dividing Fractions by Measuring You will need Cutout scissors Divide fractions using models and using equivalent fractions with a common denominator Misa exercises for of an hour several times a week How many times does Misa have to exercise if she wants to exercise for a total of h every week? Use a model to divide fractions Use the fraction strips on Cutout A Line up whole fraction strips to represent hours B Line up strips along the whole strips How many complete strips fit in whole strips? C Add a fraction of to match the length of whole strips exactly Did you add of, of, OR of? D You used of the strips, plus a of strip to match the length of whole strips So, how many times do fit into? times E How many times does Misa have to exercise to achieve her goal of h? times Lesson : Dividing Fractions by Measuring Copyright 009 Nelson Education Ltd

26 Use equivalent fractions with a common denominator to divide fractions Complete the table Step : Identify a common denominator Calculate Step : Write the fractions as equivalent fractions with the common denominator Step : Divide the numerators of the equivalent fractions or Calculate Calculate Rename as _ Reflecting or equivalent mixed number Hint a b c Before answering this question, review your answer to the Reflecting question at the bottom of page Why is greater than? dividend divisor quotient Use the words dividend and divisor in your answer Copyright 009 Nelson Education Ltd Why is less than? Lesson : Dividing Fractions by Measuring 7

27 Important note: You can multiply numbers in any order But with division, the order in which you divide the numbers in matters For example,, but Take care to write the fractions in the correct order in your calculations Practising Calculate each quotient using equivalent fractions a) Hint To find a common denominator, identify the least common multiple of the denominators,,,,,,,, b) Use these steps to rename the mixed number as an improper fraction Step : Multiply the whole number by the denominator of the fraction Step : Add the result to the numerator ( ) + A common denominator of and is Write the quotient as a mixed number remainder Lesson : Dividing Fractions by Measuring So, the quotient can be written as 0 Copyright 009 Nelson Education Ltd

28 c) Rename the mixed number as an improper fraction ( ) + A common denominator of and is Write your answer as a mixed number remainder So, the quotient can be written as d) Explain how you calculated the quotient I wrote _ fractions with a _ denominator I looked at the _ of the equivalent fractions to determine how many times fit into Copyright 009 Nelson Education Ltd Lesson : Dividing Fractions by Measuring 9

29 9 Student book pages Dividing Fractions Using a Related Multiplication Divide fractions using a related multiplication large can of paint holds as much as small ones Allison has large cans of paint How many small cans of paint can she fill with large cans? Allison Allison? Use a related multiplication to divide Each small can is of a large can term reciprocal the fraction that results from switching the numerator and the denominator is the reciprocal of = is the reciprocal of To see how many small cans can be filled with large cans of paint, you need to divide by To divide by a fraction, just multiply by the reciprocal Show this by completing the equations below and and and The reciprocal of is 0 Lesson 9: Dividing Fractions Using a Related Multiplication Anita s large cans of paint will fill small cans Copyright 009 Nelson Education Ltd

30 Multiply by the reciprocal to divide PROBLEM Nikita has 7 of a large can of paint Each small can is of a large can How many small cans of paint can she fill? Nikita? PROBLEM A medium-sized can of paint holds as much paint as large can Misa has 7 large cans of paint How many medium-sized cans of paint can she fill? Solution: You need to calculate Estimate the quotient Solution: You need to calculate 7 Use fraction strips to estimate the quotient fits into 7 about times, so 7 is close to Calculate the quotient Multiply 7 by the reciprocal of, which is is close to Calculate the quotient Write 7 as an improper fraction 7 Then, multiply by the reciprocal of 7 or or or equivalent mixed number full can and 7 of a large can of paint 7 of a large can of paint will fill small cans will fill medium-sized cans Reflecting Do you prefer to use a model, equivalent fractions, or multiplying by the reciprocal to divide fractions? Explain Copyright 009 Nelson Education Ltd Lesson 9: Dividing Fractions Using a Related Multiplication

31 Writing fractions in lowest terms Use divisibility rules or a factor tree to identify factors Practising Calculate Write your answers in lowest terms Write improper fractions as mixed numbers Hint a) 9 9 A number is divisible by 9 if the sum of the digits is divisible by 9 b) or Hint or c) 7 or So,,,, and are all factors of d) Rahul has of a container of trail mix He is filling snack packs that each use of a container How many snack packs can Rahul make? Solution: Determine how many times fits into Rahul can make Lesson 9: Dividing Fractions Using a Related Multiplication snack packs Copyright 009 Nelson Education Ltd

32 Why does it make sense that 7 is greater than 7? Explanation: When you divide by, it is the same as multiplying by Is this reciprocal less than or greater than? _ When you multiply any number n by a number greater than, the product is than n Explain again in your own words Divisibility rules Even numbers are divisible by A number is divisible by if the sum of the digits is divisible by If a number is divisible by both and, it is divisible by Calculate Write your answers as mixed numbers or whole numbers a) 9 b) 7 c) 7 7 d) Copyright 009 Nelson Education Ltd Lesson 9: Dividing Fractions Using a Related Multiplication

33 0 Student book pages 9 Order of Operations Use the order of operations in calculations involving fractions Rules for Order of Operations Evaluate the contents of brackets first Divide and multiply from left to right Add and subtract from left to right Use BDMAS to remember the order B Brackets D _ M _ A _ S _ A Underline the operation that should be completed first Use the order of operations with fractions B Add brackets so that the multiplication will be done last C Calculate using the rules for order of operations ( ) ( ) ( ) ( ) 0 7 D Work through the example on the next page Underline the part of the expression that you are working on in each line of the equation Lesson 0: Order of Operations Copyright 009 Nelson Education Ltd

34 9 ( ) 9 ( ) 9 ( 9 ( ) 9 or ) Step : Evaluate the contents of brackets first Write as an improper fraction You can only add or subtract fractions with a common denominator Write and as equivalent fractions with a common denominator A common denominator is You do not need these brackets anymore Step : Next, divide Divide by multiplying by the reciprocal Use mental math to calculate the product Step : Now, subtract Write and as equivalent fractions with a common denominator A common denominator for and is Write the improper fraction as a mixed number Reflecting Calculate Use mental math ( ) ( ) Why do we need rules for the order of operations? Copyright 009 Nelson Education Ltd Lesson 0: Order of Operations

35 Hint Underline the part of the expression that you are working on in each step Work out equivalent fractions at the side, and then substitute them into the expression Practising Calculate using the rules for order of operations a) b) 0 0 c) Hint Identify a common denominator for,, and Lesson 0: Order of Operations Copyright 009 Nelson Education Ltd

36 Hint Write mixed numbers as improper fractions before you evaluate the expression Calculate 9 Add brackets to the expression so that the multiplication will be done last Evaluate the new expression a) b) Copyright 009 Nelson Education Ltd Lesson 0: Order of Operations 7

37 Student book pages 9 9 Communicate about Multiplication and Division Describe situations involving multiplying and dividing fractions and mixed numbers Misa created a problem that required division of by Read Misa s explanation of why her problem required that division, and why it could also be solved using multiplication Jeff s mom was installing new baseboards in a room She had a lot of strips of wood Most were one length, and there were a few shorter ones that were of that length She had to fill a space that required of the longer strips If she decided to use the shorter strips, how many of them would she need? I know that one meaning of division is how many of one thing fit into another I decided to use that meaning I picked a problem about strips of wood I made sure one strip was as long as a certain distance and the other strip was times as long as that same distance I know that one way to solve a division question involving fractions is to multiply by the reciprocal So to solve the problem I created, I could use multiplication of fractions Describe multiplication and division situations Should multiplication or division be used to solve each problem below? Explain your reasoning A Mary plans to read books this summer She can read of a book each day How many days will it take Mary to read all of her books? Circle one: multiplication division Explanation: The problem asks how many times fits into Lesson : Communicate about Multiplication and Division Copyright 009 Nelson Education Ltd

38 B Jack needs to measure cups of flour He only has a -cup measure How many cups of flour does he need? Circle one: multiplication division Explain _ C Joe is building a rectangular flower garden m long and m wide What is the area of Joe s garden? Circle one: multiplication division Explain _ D A waterfront property is of a kilometre long If this property is split into equal sections, how long will each section be? Circle one: multiplication division Explain _ Match the problems to the fraction expressions A B C D Reflecting Describe a type of problem that you would use multiplication to solve Describe a type of problem that you would use division to solve Copyright 009 Nelson Education Ltd Lesson : Communicate about Multiplication and Division 9

39 Communication Checklist Did you explain each step? Did you justify your conclusions? Did you use models to make your thinking clear? Practising Use words and these grids to explain why of is the same as of First grid: Each row represents and each column represents The model shows of Second grid: Each row represents and each column represents The model shows of There are squares in total on each grid The shaded parts each represent of the grid So, of is the same as of How can you use fraction multiplication to explain why 0 = 0? Explanation: 0 is 0 and 0 = 0 is sets of 0 Model this by shading the fraction strips The model shows that there are tenths altogether So, 0 = 70 Lesson : Communicate about Multiplication and Division Copyright 009 Nelson Education Ltd

40 7 a) Why can you calculate 0% of by multiplying? Explanation: 0% means out of 00 or OR OR Substitute and for 0% and 0% of 0% b) Do you think this is the easiest way to calculate the percent? Explain = = = _ = Copyright 009 Nelson Education Ltd Fabienne said that she now understands why she needs to multiply the numerator and denominator of a fraction by the same amount to get an equivalent fraction Explain her reasoning, at the left Explanation: What happens when you multiply a number by? If the numerator and the denominator of a fraction are equal, what does the fraction represent? Does the value of a fraction change when you multiply it by a fraction that represents? Will the fraction that results still represent the same part of a whole? Lesson : Communicate about Multiplication and Division 7

41 Cutout Cutout Copyright 009 Nelson Education Ltd

42 Copyright 009 Nelson Education Ltd Cutout Cutout

43 Cutout whole whole whole whole / / / / / / / / / / / / / / / / / / / of / / of / / of / Cutout Copyright 009 Nelson Education Ltd