4» « Date: Multiplying a Whole Number by a Fraction. Name: = Use repeated addition to multiply fractions by whole numbers.
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1 4» «Name:. Multiplying a Whole Number by a Fraction Use repeated addition to multiply fractions by whole numbers.. a) Write 4 x as a repeated addition sentence = b) Draw a model to calculate the answer. To multiply a whole number by a fraction, you can: Multiply using grids and counters. x means the same as sets Multiply. Write your answer as a fraction and as a a) 7 x - = 5 or b) 4 X 5 =. How much farther are jumps of g on a number line than jumps of g? Explain Math class is g h for three days of each school week. How many hours of math class does a student have in one week? x or Each square represents, so the squares covered with counters * represent -f. Multiply using a number line. Calculate x using a number line. Write the product both as an improper fraction and as a whole or mixed number. x = x 4 fifths = fifths - y o r 5 0 Chapter : Fraction Operations Copyright O 009 by Nelson Education Ltd.
2 . Multiplying Fractions. Draw a fraction strip model to determine the product ofjxi Match each expression with its product in the box to the right. a) b) 0 d) n V 4 X 5 i 5 5 X - 8*5 4 8 X 9 ii) iii) 5 0 iv) To multiply x, you can: Use a fraction strip model Model and divide each fifth into thirds '" r Then, to show f of each section, colour of the thirds. n in v _ 8_ * 5 5 Use a grid model. Calculate the area of a rectangle I of a unit wide and of a unit long. 5 : *. a) Shade the grid to show why X = 5. The coloured rectangle has x = squares, so its area is square units. v * 5 ~~ 5 b) List two other pairs of fractions with a product of x x Multiply. You can multiply the numerators and the denominators. For example, x X5 _ 5 Chapter : Fraction Operations Copyright 009 by Nelson Education Ltd.
3 Exploring Estimating Fraction Products. Estimate. Which products are close to?. 5 4., a) x is close to x 9. b) x is close to 4 c) x is close to , d) x is close to % IO. Estimate. Which products are close to 0?,. a) x is close to 9 x x To estimate the product of two fractions, use the following guides: The product of two fractions close to is close to. X = The product of two fractions close to \ is close to \. v - * ~ 4 The product of two fractions close to 0 is close to 0. 0X0 = 0 For example, x is close to because \ is close to. b) x - is close to x X 4 ' S t 0 J % 5 8. d) x is close to x. Estimate. Circle the products close to \. 5 7» a) x 5 u l C ). 4 9 X 7 d - x - Copyright 009 by Nelson Education Ltd. Chapter : Fraction Operations
4 Multiplying Fractions Greater than Estimate each product.? a) - x - is close to x b) - x - is close to X 5 8. Multiply the following using an area model. a) ^ x ^ To multiply mixed fractions, you can: Use an area model. For example, to calculate the area of a rectangle I- units long and \ units wide: whole 4 b) o o c X A 5 4 = 4 x - e or x q. Multiply using improper fractions. a) b) o o 5 X = 4 X X or or The product of three improper fractions is j- What could the three fractions be? 5 X There are squares in a whole, so each square is g. There are 0 squares in the coloured rectangle. Another way to record this is + + =, or, or There are two wholes and 8 other squares in the coloured rectangle. Multiply improper fractions. Write each mixed number as an improper fraction and multiply as you would with proper fractions. 5X5 = X5 _ 4 X 5 " X - 0 _ 4 Chapter : Fraction Operations Copyright 009 by Nelson Education Ltd.
5 r Dividing Fractions by. O Whole Numbers Use a sharing si model to represent the quotient of a fraction divided by a whole number.. Use a model to show 4 = g. To divide a fraction by a whole number, you can: Think of it as sharing.. a) How can you solve h- 5 using multiplication of fractions? _ X b) Explain why this works.. Divide = _ b) yh-4 5 of a room has to be painted. painters are going to share the job. What fraction of the room will each painter complete if they all paint at the same rate? For example, -r- tells you the share size if people share 5 of something. You cannot share equally among three people, so write an equivalent fraction. _ are in each group,. o _ so = 5- Multiply by a fraction. For example, as off, or 5 x = ^. is the same Divide using an equivalent fraction, where the numerator is a multiple of the whole number. For example, ^ = ^^- _ ~ 5 Copyright 009 by Nelson Education Ltd. Chapter : Fraction Operations 5
6 .7 Estimating Fraction Quotients r - Interpret and estimate the quotient of fractions less than.. Estimate the quotient as a whole number. 5 a) + is close to 5 b) + is close to 7 9 To estimate a quotient of fractions less than, you can: Compare fractions by multiplying. For example, estimate +.. Estimate. Which quotients are between and 5? 8 a) is close to 8 b) + is close to c) - T ^ i s close to d) + is close to. Why might you estimate * ^ by dividing by \l 5 5 X j =, which is close to g. -7- g is close to 5. Use fraction strips to visualize the quotient. For example, to see how relates to g, see how many times g fits into. It looks like it fits about 5 times. 4. How do you know that + is less than? Compare using equivalent fractions. c, 4 _ 5 For example, g = 45 and g = is about 5 times greater than 5, so g * g is close to 5. Chapter : Fraction Operations Copyright 009 by Nelson Education Ltd.
7 .8 Dividing Fractions by Measuring Divide fractions using models and using equivalent fractions with a common denominator.. Calculate using common denominators. a } _. 4 8 r r a. Calculate each quotient using equivalent fractions. To divide two fractions, you can: Determine the number of times the divisor fits into the dividend using fraction strips and a common denominator. For example, to calculate + :. a) ' Compare using equivalent fractions. I. Sally has L of apple juice in the fridge. Each glass holds g L. a) Set up a division statement to calculate how many glasses of apple juice Sally can pour.. ' ' -r or b) Solve your statement. How many glasses of apple juice can Sally pour? 4. Does order matter when you divide fractions? Explain. Copyright 009 by Nelson Education Ltd. Chapter : Fraction Operations 7
8 Jams: q Dividing Fractions Using a. / Related Multiplication Divide fractions using a related multiplication.. Calculate. _ d) + = ' 0 X X or or = X or. Write =, <, or > in each box. Calculate the quotients that are greater than. al b) c) d) 0 4L> ' 0 7 8! * 7 8 ' ' ' 4 5 or To divide two fractions, you can: Multiply by the reciprocal. The reciprocal is the fraction that results from switching the numerator and denominator. For example, is the reciprocal of f. Calculate using the reciprocal. 4 _ v 9 9 ~ * 4 _ 8 - = l^orlj. Why does it make sense that f is greater than f? 4. Jack delivers newspapers as his part-time job. It takes 5 \ min to deliver one newspaper. a) How many newspapers can Jack deliver in 0 min? b) How many newspapers can Jack deliver in 45 min? c) How many newspapers can Jack deliver in \ h? Chapter : Fraction Operations Copyright 009 by Nelson Education Ltd.
9 .0 Order of Operations Use the order of operations in calculations involving fractions.. Calculate using the rules for order of operations. ) (, \ + X j 7.. \ i.f 5. n = 4_ + ' V7 " ) 4 J ( 4 /5 d ) ^ U X j 4 j x 7 + The order of operations is: Perform the operations in the brackets first. Divide and multiply from left to right. Add and subtract from left to right. Write the answer as a mixed number. For example: I v i x? 5 * 0 + = f - x 0 T _, ~ 0 *" = ^ - 7, 0 _ _ 47 7 _ 0 o r 0 Divide. Multiply. Subtract. Add. X 8 + = 0 Place brackets to make this equation true. o x = Copyright 009 by Nelson Education Ltd. Chapter : Fraction Operations 9
10 . Communicate about Multiplication and Division Describe situations involving multiplying and dividing fractions and mixed numbers.. a) Create and solve a problem in which you calculate g X. b) Explain why multiplying these numbers is appropriate for the problem. To describe situations involving multiplying and dividing fractions and mixed numbers, use the following Communication Checklist: Communication Checklist El Did you explain each step? Zl Did you justify your conclusions? Ei Did you use models to make your thinking clear? c) How do you know your answer is reasonable?. Use words and these grids to explain why of is the same as of.. Explain why you can calculate 4 using each method below. Use the Communication Checklist as part of your answer. a) Divide equivalent fractions with the same denominator. b) Multiply by the reciprocal. 0 Chapter : Fraction Operations Copyright 009 by Nelson Education Ltd.
11 Chapter Test Yourself Circle the letter of the correct answer.. Calculate x. A. 8 B. C. D.. Calculate \ of. B. C. Both A and B D. Neither A nor B. What is the missing fraction? IS I of 5- A. B ^ 4. Calculate 4 x yg. Express your answer in lowest terms. A. 8 B. 5. Estimate which product is closer to. 0 B. x C. x 4 ^ X. Calculate 4-X4-. Express your answer in lowest terms A. 5 B. C. 0 D s 7. Calculate g x j. Express your answer in lowest terms A. B. C. D. 5 Copyright 009 by Nelson Education Ltd. Chapter : Fraction Operations
12 D a t e : Chapte r JL Test Yourself continued O 8. Calculate ^ 9 9. Estimate the quotient + \ as a whole number. A. B. 5 C. D Calculate! _ 8 A B C. D. A " 8 5. Calculate^ +. Q A 4 B C - D ^ B C D ' 0 ' 4 ' 45 V ^. What is the missing number in the following equation? + U ; X U j 4 5 \ / _ \ A. 4 B. 04 C. 44 D. 4. Calculatef - f x ( + ^). A _ 5 B 5 C "Z T 4. Calculate + \ + x 8. A. 9 B. 8 C. D. ± Chapter : Fraction Operations Copyright O 009 by Nelson Education Ltd.
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