By George Boole
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Additional resources for A Treatise on Differential Equations
1500 . 10000 -;- 50000 = ? 5. 80710000= ? 1 35 Answers Give yourself 5 marks for each correct answer. Total scores of 20 and 25 show that you understand the programme. A score of 15 means that you need a further look at some of the frames. A score of 10 and under means that you really need to work through the programme again. The numbers in brackets after the answers are the frame numbers relating to the question. Read these frames first if your answer is wrong. You will most likely realise where your mistakes occurred.
Q. What is 94 x 93 ? Show the answer as a base and index. Indices 94 A. X 48 93 = 9 7 Which of the following two groups of examples contains a mistake? Work out each calculation in each group before deciding on your answer. Q. Group A. 92 x 9 6 10 5 7 7 = 10 X X 11 16 7 98 = 101 6 Go to 49. = 72 3 Group B. 101 7 102 82 X 10 1 6 = 103 3 52 = 154 X 82 X = 84 ) ) ) Go to 50. Indices 49 From 48 You say that Group A contains a mistake. Let us have a look at them again. 9 2 x 96 105 X 10 1 1 77 X 7 16 = 9 8 or another way to look at it 9 2 x 9 6 = 9 2 + 6 = 98 16 11 5 " " 10 X 10 = 10 = 10 5 X 10 11 = 105 + 11 = 10 16 = 723 another " "7 7 x 7 16 = 7 7 + 16 = 723 In each case the index figures (indices) of the multiplications were added together to give the index of the answer.
Let us have a look at them again. 9 2 x 96 105 X 10 1 1 77 X 7 16 = 9 8 or another way to look at it 9 2 x 9 6 = 9 2 + 6 = 98 16 11 5 " " 10 X 10 = 10 = 10 5 X 10 11 = 105 + 11 = 10 16 = 723 another " "7 7 x 7 16 = 7 7 + 16 = 723 In each case the index figures (indices) of the multiplications were added together to give the index of the answer. The bases preceding the indices (remember, both bases must be the same) are not added, the same base repeats in the answer. So! All the answers in Group A were correct and you were wrong.
A Treatise on Differential Equations by George Boole