1. Fractions Re-cap2 Mathematics

2. Which is bigger or ? 3 8 5 12 To compare two fractions convert them to fractions with the same denominator. First we need to find the lowest common multiple of 8 and 12. The lowest common multiple of 8 and 12 is24. Now, write and as equivalent fractions over 24. 3 8 5 12 3 8 = 24 ×3 9 and 5 12 = 24 ×2 10 so, 3 8 5 12 < Using equivalent fractions

3. Ordering fractions

4. 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.

5. 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

6. 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

7. 4 5 What is ÷ ? 2 3 To divide by a fraction we flip the second fraction and multiply. 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

8. 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

9. Dividing fractions

10. When fractions have the same denominator it is quite easy to add them together and to subtract them. For example, 3 5 + 1 5 = 3 + 1 5 = 4 5 We can show this calculation in a diagram: += Adding and subtracting fractions

11. 7 8 – 3 8 = 7 – 3 8 = 4 8 Fractions should always be cancelled down to their lowest terms. 1 2 = 1 2 We can show this calculation in a diagram: – = Adding and subtracting fractions

12. Fractions with different denominators Fractions with different denominators are more difficult to add and subtract. For example, What is 5 6 – 2 9 ? – 15 18 – 4 = = 15 – 4 18 = 11 18

13. 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

14. 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