By Harold Ward (auth.)
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G. The last example could be wfltten3"-3"-4= -12(removmg the bracket). In the first case we are told to multiply ~ by ~ and then add ~ to the answer. In 3 1 2 the second case we add 4 to 3" and then multiply the answer by 3"' The order of working these complicated fractions is shown in the following example. Example 16 Simplify (~-~)~-(~+~) 12(~ x ~)-(~+~) 2 -t¥ ~ x 13 4 4 13 13 2~ 36-22 24 14 24 13 24 *7 48 '-c-::---,-=---=-=-x-=- 12 11 8 12 Step 1 Step 2 91 Simplify the contents of each bracket and remove brackets.
1 In such cases we multiply by 3 to get the time for one man, as it is bound to take longer. 2 It pays to carry out a rough check to see whether the answer required is larger or smaller than the original one. e. (constant) = 21 men. we can divide the constant by either one of the variables to find the other one. Compound Proportion In the previous section we had two variables (men and time taken), but we can extend the idea to cover three or more variables, in which case we have an example of compound proportion.
B pays£loo0 per annum plus 5 per cent on sales. If he can expect annual sales of about £100,000, which is the better paid? A gives£2oo0+2 per cent of£100,000 =£2000+£2000 =£4000 B gives£1000+5 per cent of£loo,OOO =£1000+£5000 =£6000 But ifhe had a bad year and sold only£30,000, then he would be better off with A. The student should check this. UNIT C USING THE BASE Students often have difficulty in deciding what is the base, and in changing it to the necessary figure of 100. If the principles of proportion are remembered, particularly the Rule of One (Chapter 5), there is no problem.