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15 5 15 3 x 5 15 15 15 15 Cancelling down gives 9 = 3 x 3 = 3 15 3 x 5 5 NB: an alternative method would have been to cancel down 12/15 to 4/5 initially leaving an easier sum of 4/5 – 1/5 = 3/5 Multiplication of Fractions It may help to understand multiplication if you interpret the ‘x’ sign as ‘of’. Hence: 1 x 2 means 1 of 2 = 1 2 5 2 5 5 The calculation involves multiplying both numerators and both denominators then cancelling down: Eg: 1 x 2 = 1 x 2 = 21 = 1 2 5 2 x 5 105 5 4 x 2 = 4 x 2 = 8 5 3 5 x 3 15 7 x 3 = 7 x 3 = 21 11 8 11 x 8 88 Note that when multiplying, you can cancel down during the sum as well as at the final stage – it often makes the calculation easier: Eg: 31 x 2 = 2 13 31 13 41 x 3 = 1 x 31 = 1 x 1 = 1 9 82 93 2 3 2 6 5 x 61 = 5 x 1 = 5 244 7 4 x 7 28 Dividing Fractions The trick with division of fractions is to turn the second fraction upside down and then to multiply: Eg. 2 ¸ 1 = 2 x 5 = 10 3 5 3 1 3 Note that this answer can also be written as 31/3 2 ¸ 4 = 21 x 5 = 5 7 5 7 42 14 2 ¸ 7 = 2 x 8 = 16 3 8 3 7 21 Improper Fractions An improper fraction is one where the numerator is larger than the denominator, eg. 10/3 To convert this to a mixed number (one combining a whole number and a fraction), think of 10/3 in the following way: 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 3 x 1/3 = 1 so out of the ten 1/3’s, nine can be grouped into three whole units, leaving only 1/3 left over. Hence, 10/3 = 31/3 Similarly, 12/5 = 22/5 16/11 = 15/11 21/15 = 16/15 = 1 2/5 (by cancelling) We can also go from mixed numbers to improper fractions: 21/8 = (2 x 8) + 1 = 16 + 1 = 17 8 8 8 8 8 31/4 = (3 x 4) + 1 = 12 + 1 = 13 4 4 4 4 4 Addition of mixed numbers Eg. 2½ + 31/5 = 2 + 3 + ½ + 1/5 = 5 + 5/10 + 2/10 = 5 + 7/10 = 57/10 17/8 + 52/3 = 1 + 5 + 7/8 + 2/3 = 6 + 21/24 + 16/24 = 6 + 37/24 = 6 + 113/24 = 713/24 Multiplication and Division of mixed numbers Here, it is usually easiest to convert to improper fractions and multiply or divide as normal: Eg: 25/6 x 31/8 = 17/6 x 25/8 = 425/48 = 8 41/48 12/3 ¸ 2¾ = 5/3 ¸ 11/4 = 5/3 x 4/11 = 20/33 2½ x 41/3 ¸ 1¼ = 5/2 x 13/3 ¸ 5/4 = 5/2 x 13/3 x 4/5 = 260/30 = 26/3 = 8 2/3 Now try these examples: Note that in these questions 2/5 is the same as 2 5 1. 2/5 + 1/3 2. 7/8 – 1/5 3. 5/8 + 2/3 4. 2/9+4/11 5. 6/7 – 4/9 6. 7/8 – 1/3 7. 2 ½ - 1 5/8 8. 7 ¼ - 5 2/3 9. 2 4/5 + 6 7/8 10. 2/3 x 4/5 11. 8/9 x 1/3 12. 7/12 x 4/5 13. 8/9 ¸ 2/3 14. 2/11 ¸ 4/5 15. 6/7 ¸ 9/8 16. 2 ¼ x 3 ½ 17. 5 1/7 x 2 1/5 18. 3 2/3 x 4 4/9 19. 7 2/3 ¸ 3 4/5 20. 2 ½ ¸ 6 1/5 21. 3 1/3 ¸ 4 1/3 22. 2 ¼ ¸ 1/3 23. 5 2/7 x 11/3 24. 6 x 2 1/3 Answers on page 19 SECTION 3 - APPROXIMATING & ESTIMATING Estimates and approximations bring 2 major benefits: 1. They enable you to check that the final answer is near to the figure that your estimate led you to expect. This is particularly valuable if you are unsure in the use of the keys on the calculator. 2. They can provide you with a ‘short cut’, by showing plainly that you do not need to do all the calculations (eg. when comparing figures in tables). Example 1 Calculate 51/73 of 300 steps i. Approximate 51/73 to 50/75 (move to figures that make easily handled fractions) ii. simplify 50/ 75 to 2/3 (by dividing top and bottom by 25) iii. Approximate answer is 2/3 ´ 300 i.e 200 iv. Calculator answer 209.59 (in fairly close range to 200, your approx. answer) Example 2 The following table shows the number of items sold in one year by the Beans Co. in each of its operating districts. Column Y shows the number of salespeople employed in each （责任编辑：职场达人） |
