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Division When dividing decimals, the first step is to write your numbers as a fraction. Note that the symbol / is used to denote division in these notes. Hence 2.14 / 1.2 = 2.14 1.2 Next, move the decimal point to the right until both numbers are no longer decimals. Do this the same number of places on the top and bottom, putting in zeros as required. Hence 2.14 becomes 214 1.2 120 This can then be calculated as a normal division. Always check your answer from the original to make sure that things haven’t gone wrong along the way. You would expect 2.14/1.2 to be somewhere between 1 and 2. In fact, the answer is 1.78. If this method seems strange, try using a calculator to calculate 2.14/1.2, 21.4/12, 214/120 and 2140 / 1200. The answer should always be the same. Example 6 4.36 / 0.14 = 4.36 = 436 = 31.14 0.14 14 Example 7 27.93 / 1.2 = 27.93 = 2793 = 23.28 1.2 120 Rounding Up Some decimal numbers go on for ever! To simplify their use, we decide on a cut off point and “round” them up or down. If we want to round 2.734216 to two decimal places, we look at the number in the third place after the decimal, in this case, 4. If the number is 0, 1, 2, 3 or 4, we leave the last figure before the cut off as it is. If the number is 5, 6, 7, 8 or 9 we “round up” the last figure before the cut off by one. 2.734216 therefore becomes 2.73 when rounded to 2 decimal places. If we are rounding to 2 decimal places, we leave 2 numbers to the right of the decimal. If we are rounding to 2 significant figures, we leave two numbers, whether they are decimals or not. Example 8 243.7684 = 243.77 (2 decimal places) = 240 (2 significant figures) 1973.285 = 1973.29 (2 decimal places) = 2000 (2 significant figures) 2.4689 = 2.47 (2 decimal places) = 2.5 (2 significant figures) 0.99879 = 1.00 (2 decimal places) = 1.0 (2 significant figures) Try these examples. Give all your answers to 2 decimal places and 2 significant figures 1. 2.45 + 7.68 2. 3.17 + 12.15 3. 2.421 + 13.1 4. 162.5 + 2.173 5. 12.5 – 3.7 6. 9.6 – 7.8 7. 163.5 – 2.173 8. 2.416 – 1.4 9. 26.95 – 1.273 10. 1.5 x 7.2 11. 2.73 x 8.14 12. 6.25 x 17 x 3 13. 2.96 x 17.3 14. 4.2 / 1.7 15. 53.9 / 2.76 16. 14.2 / 6.1 17. 2.5 / 0.03 18. 250/2.35 Answers on page 19 SECTION 2 - FRACTIONS Cancelling Down When we use a fraction, we usually give it in its simplest form. To do this we look at the top (the numerator) and the bottom (denominator) and see if there is a number by which both can be divided an exact number of times. Hence 2 = 1 x 2 = 1 since the twos “cancel out” 8 4 x 2 4 E.G. 6 = 3 x 2 = 3 8 4 x 2 4 15 = 3 x 5 = 3 35 7 x 5 7 16 = 8 x 2 = 2 OR 16 = 4 x 4 = 4 = 2 x 2 = 2 24 8 x 3 3 24 6 x 4 6 3 x 2 3 Use as many steps as you need to reach the answer. Adding Fractions When the denominators (the bottom lines) are all the same, you simply add the top line (numerators) Eg: 2 + 3 = 2 + 3 = 5 5 + 3 = 5 + 3 = 8 6 6 6 6 9 9 9 9 Remember to cancel down if necessary. When the denominators are different, we need to change the fractions so that the denominators are the same then we can add the top line as above. Suppose we wish to calculate 1 + 1 2 4 From the cancelling down process, we know that 1 = 1 x 2 = 2 2 2 x 2 4 The denominators of both fractions are now the same so we can calculate 1 + 1 = 2 + 1 = 2 + 1 = 3 2 4 4 4 4 4 Sometimes the denominators are not multiples of each other Eg: 1 + 2 4 3 In this case we can make 12 the common denominator using 1 = 1 x 3 = 3 2 = 2 x 4 = 8 4 4 x 3 12 3 3 x 4 12 We can then add these two fractions directly: 1 + 2 = 3 + 8 = 3 + 8 = 11 4 3 12 12 12 12 Eg: 2 + 1 = ? 5 6 2 = 2 x 6 = 12 1 = 1 x 5 = 5 5 5 x 6 30 6 6 x 5 30 2 + 1 = 12 + 5 = 12 + 5 = 17 5 6 30 30 30 30 Subtracting Fractions This works in the same way as addition. If the denominators are the same, simply subtract along the top line: 5 - 3 = 5 – 3 = 2 = 1 x 2 = 1 6 6 6 6 3 x 2 3 12 - 1 = 12 - 3 x 1 = 12 - 3 = 12 – 3 = 9 （责任编辑：职场达人） |
