You will need • fraction strips • grid paper • coloured pencils 9.5 Multiplying Fractions GOAL Multiply two fractions less than 1. Learn about the Math About 1 of Canadians who are 12 and older 10 downhill ski. About 2 of these skiers are between 5 the ages of 12 and 24. fraction of the Canadian ? What population between the ages of 12 and 24 downhill ski? Example 1: Using a fraction strip model The fraction of Canadians between the ages of 12 and 24 who downhill ski is 2 of 1. What fraction is this? 5 10 Jordan’s Solution 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 I used fraction strips to model 2 of 1. 5 I divided 1 10 10 into 5 equal sections and coloured 2 of the sections. I divided each 1 the same way to 10 determine the size of each section. I made 5 10 50 sections. Only 2 sections were coloured. So, 2 of 1 is 2. 5 2 50 10 50 1 since every 2 sections of 1 25 50 can be combined to make 1 section of 1. 1 2 2 of 10 50 5 1 25 About 1 of Canadians between the ages of 12 and 24 downhill ski. 25 25 300 Chapter 9 NEL Example 2: Using a grid model to determine a fraction of a fraction Calculate 2 1. 5 10 Sheree’s Solution 10 To calculate the area of a rectangle, you multiply the two dimensions. The area of a rectangle 5 units wide and 10 units long is 5 10. So, 2 1 must be the area of a rectangle that 5 5 Area 5 10 1 10 10 is 2 of a unit wide and 1 of a unit long. 10 5 I used a 5-by-10 grid to help me see the fifths and tenths. There are 5 10 or 50 sections. 2 5 The purple rectangle is 1 wide and 2 long. It is 2 of the whole. 10 2 50 50 5 can be written in simplest form as 1. 25 2 1 21 5 10 5 10 2 50 1 25 Reflecting 2 5 1 10 2 5 1 10 1. Calculating of is the same as calculating . How does Sheree’s solution show this? 2. How can you use a model to determine the numerator and denominator of a product? 3. Write a rule for multiplying two fractions less than 1. NEL Fraction Operations 301 Work with the Math Example 3: Multiplying fractions less than 1 About 2 of the students in Windham Ridge School are in Grades 7 and 8. About 5 of these 3 8 students are girls. What fraction of the students in the school are girls in Grades 7 and 8? Solution A: Using fraction strips Solution B: Using an area model This model shows 5 of 2. Divide 2 into 8 3 Colour a 3-by-8 rectangle to show 5 by 2. 3 8 1 3 1 12 1 12 1 3 1 12 1 12 1 12 1 12 1 3 1 12 1 12 1 12 1 12 1 12 3 5 2 52 8 3 83 10 24 5 12 8 equivalent sections, and colour 5 of the sections. 1 12 So, 5 of the students are girls in Grades 7 5 2 5 8 3 12 12 and 8. So, 5 of the students are girls in Grades 7 12 and 8. A Checking B 4. What multiplication expression does each model represent? a) 1 4 1 4 1 4 1 4 Practising 7. What multiplication expression does each model represent? a) 1 8 1 1 1 1 1 1 1 1 1 1 1 1 12 12 12 12 12 12 12 12 12 12 12 12 b) 1 4 1 4 1 8 1 8 1 4 1 8 1 8 1 4 1 8 1 8 1 8 b) c) 3 4 2 5 5. Draw a model for . Use your model to determine the product. 2 11 6. About of Canadian downhill skiers are from British Columbia. Recall that about 1 10 of Canadians downhill ski. What 8. Draw a model for each multiplication expression. Determine the product. 1 3 1 2 c) a) 2 8 6 5 4 1 3 2 b) d) 5 3 4 6 fraction of all Canadians are downhill skiers from British Columbia? 302 Chapter 9 NEL 15. a) Recall that a2 a a and a3 a a a. Calculate each power for a 2. 9. Match each expression with its product. 7 5 a) 10 6 8 1 3 4 b) 15 6 8 9 3 7 2 9 c) 10 12 6 10 4 14 d) 7 15 3 i) a2 iii) a4 b) Why does a higher power of 2 result in 3 a lower product? 1 3 10. Matthew’s bed takes up of the width of his bedroom and 3 of the length. What 5 fraction of the area of the floor does Matthew’s bed take up? 2 3 ii) a3 16. How does the product of two fractions less than 1 compare with the two fractions being multiplied? Is the product greater than, less than, or equal to each fraction? How do you know? 17. a) Calculate 0.4 0.3. b) Rename each decimal as a fraction, and multiply. What do you notice? 5 8 11. Jessica is awake of the day. She spends of this time at home. a) What fraction of the day is Jessica awake at home? b) How many hours is Jessica awake at home? C Extending 3 4 18. More than of Americans eat ice cream at least once a month. About 3 of these 10 12. a) Complete this pattern, and continue it for three more products. 1 4 ■ 2 1 2 ■ 2 1 1 ■ 2 1 1 ■ 2 2 b) How does this pattern explain the product of 13. a) 1 2 1 ? 2 Draw a picture to show that 2 3 6. 5 8 40 people eat vanilla ice cream. a) What fraction of Americans eat vanilla ice cream at least once a month? b) According to recent statistics, there are about 300 million Americans. About how many of them eat vanilla ice cream at least once a month? 19. a) What is the probability of landing in the red B A section? b) Why does it make sense that the 2 3 2 7 40 c d ■ ■ 14. Daniel said that . Complete the missing fraction, and explain your thinking. NEL A B a a2 2 9 20. What is the value of a in ? product of 6. a b B A probability is 1 1? b) List two other pairs of fractions with a A 21. What is the product of 1 2 2 3 4 … 99? 3 4 5 100 Fraction Operations 303

© Copyright 2018