1. Learning Objective: Chapter 3 - Fractions We will be able to; Add and subtract fractions Add and subtract mixed numbers.

2. Starter: Give these a go…. (d) Exam questions How good are these?!

3. Let’s recap……………….

4. Equivalent fractions spider diagram

5. Cancelling fractions to their lowest terms A fraction is said to be expressed in its lowest terms if the numerator and the denominator have no common factors. Which of these fractions are expressed in their lowest terms? 14 16 20 27 3 13 15 21 14 35 32 15 Fractions which are not shown in their lowest terms can be simplified by cancelling. 7 8 5 7 2 5

6. Mixed numbers and improper fractions When the numerator of a fraction is larger than the denominator it is called an improper fraction. For example, 15 4 is an improper fraction. We can write improper fractions as mixed numbers. 15 4 can be shown as 15 4 = 3 3 4

7. Improper fraction to mixed numbers Convert to a mixed number. 37 8 8 = 8 8 +++ 8 8 8 8 8 8 + 5 8 5 8 1 + 1 + 1 += 1 + = 4 5 8 4 37 ÷ 8 =4 remainder 5 37 8 = 4 5 8 4 This is the number of times 8 divides into 37. 4 This number is the remainder. 5

8. 22 77 33 Mixed numbers to improper fractions Convert to a mixed number. 2 7 3 2 7 3 = 2 7 1 + 1 + 1 + = 7 7 +++ 7 7 7 7 2 7 = 23 7 To do this in one step, = Multiply these numbers together … … and add this number … … to get the numerator. 23 7

9. Using a common denominator 1) Write any mixed numbers as improper fractions. 1 3 4 = 7 4 2) Find the lowest common multiple of 4, 9 and 12. The multiples of 12 are:12,24,36... 36 is the lowest common denominator. What is+ 1 9 ? 1 3 4 + 5 12

10. 3) Write each fraction over the lowest common denominator. 7 4 = 36 ×9×9 ×9×9 631 9 = 36 ×4×4 ×4×4 45 12 = 36 ×3×3 ×3×3 15 4) Add the fractions together. 36 63 + 36 4 + 15 = 36 63 + 4 + 15 = 36 82 = 2 36 10 = 2 18 5 What is+ 1 9 ? 1 3 4 + 5 12 Using a common denominator

11. To calculate:2 3 + 4 5 using a calculator, we key in: a b c 23+a b c 45= The calculator will display the answer as: We write this as 1 15 7 Using a calculator

12. Please turn to page 30 in your Higher Textbook – Attempt Ex3A, beginning at Q4 if you feel that you need practice… – If you are confident with these questions, move directly to Ex 3B/C on pages 30/31

13. Learning Objective: Chapter 3 - Fractions We will be able to; Multiply fractions and mixed numbers Find a fraction of a quantity

14. Try these fabulous questions… (past exam q’s)

15. Starter

16. When we multiply a fraction by an integer we: multiply by the numerator and divide by the denominator For example, 4 9 54 × = 54 ÷ 9 × 4 = 6 × 4 = 24 Multiplying fractions by integers This is equivalent to of 54. 4 9

17. 5 7 12 × ?What is 5 7 12 × = 12 × 5 ÷ 7 = 60 ÷ 7 = 60 7 = 8 4 7 Multiplying fractions by integers

18. Using cancellation to simplify calculations 7 12 What is 16 × ? We can write 16 × as: 7 12 16 1 × 7 12 4 3 = 28 3 = 1 3 9

19. 8 25 What is × 40? We can write × 40 as: 8 25 8 × 40 1 8 5 = 64 5 = 4 5 12 Using cancellation to simplify calculations

20. Multiplying a fraction by a fraction To multiply two fractions together, multiply the numerators together and multiply the denominators together: 3 8 What is × ? 2 5 3 8 4 5 × = 12 40 3 10 = 3 We could also cancel at this step.

21. 5 6 What is × ? 12 25 5 Start by writing the calculation with any mixed numbers as improper fractions. To make the calculation easier, cancel any numerators with any denominators. 12 25 35 6 ×= 7 5 2 1 14 5 = 2 4 5 Multiplying a fraction by a fraction

22. Please turn to page 33 in your Higher Textbook – Attempt Ex3D

23. Learning Objective: Chapter 3 - Fractions We will be able to; Divide fractions and mixed numbers Solve problems involving fractions

24. Starter

25. 3 4 6 ÷ means, ‘How many three quarters are there in six?’ 6 ÷ = 6 × 4 1 4 = 24 So, 6 ÷ = 24 ÷ 3 3 4 = 8 We can check this by multiplying. 8 × = 8 ÷ 4 × 3 3 4 = 6 3 4 What is 6 ÷ ? Dividing an integer by a fraction There are 4 quarters in each whole.

26. 4 5 What is ÷ ? 2 3 To divide by a fraction we multiply by the denominator and divide by the numerator. 4 5 2 3 ÷ can be written as 5 4 2 3 × Swap the numerator and the denominator and multiply. 5 4 2 3 ×= 10 12 = 5 6 Dividing a fraction by a fraction This is the reciprocal of 4 5

27. 6 7 What is ÷ ? 3 5 3 Start by writing as an improper fraction. 3 5 3 18 5 3 5 3 = 5 ÷ 6 7 = 5 × 7 6 3 1 = 21 5 = 1 5 4 Dividing a fraction by a fraction

28. Please turn to page 34 in your Higher Textbook – Attempt Ex3E – These are all grade C questions

29. Learning Objective: Chapter 3 - Fractions We will be able to; Solve problems involving fractions

30. Problems involving fractions In a cinema 2/5 of the audience are women, 1/8 of the audience are men. What fraction are children? 2/5 + 1/8 = 16/40 + 5/40 = 21/40 1 - 21/40 = 40/40 – 21/40 = 19/40 of the audience are children

31. Problems involving fractions A school has 1800 pupils. 860 of them are girls. ¾ of the girls like swimming, 2/5 of the boys like swimming. What is the total number of pupils that like swimming? ¾ x 860 = 645 1800 – 860 = 940 2/5 x 940 = 376 645 + 376 = 1021 pupils like swimming

32. Please turn to page 36 in your Higher Textbook – Attempt Ex3F beginning at Q6 – These are all grade C – Once all exercises are completed, please complete the chapter review on pg 37