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This is wrong. h 1 . 50 t e same as 25 -;- T You have remembered the rule, to divide we invert and multiply. Obviously, you have inverted 51° so that the problem now looks like 2~ x 5~ . Your answer is wrong. Where you have gone wrong is in adding 25 and 50 instead of multiplying. Have another look at 29 and work out the answer again. Fractions From 30 A. 1. - = 16 10000 = 160000 16 ~· _1 10000 1 x 1 2. =80 x50=4000 50 1 7 7 . 9 3 1500 37 1500 = T x -9- = 500 3. This completes the section on multiplication and division of fractions.

3. 10 000 = 1O? 100 = 10? 10 = 10? 41 Indices A. 10 000 = 10 4 100 = 10 2 10 = 10 1 (we do not usually show an index of 1 but leave it as 10) Have you noticed anything about the number of noughts in relation to the index where the base is 10? 1 000000 = 10 6 10000 = 10 4 Q. What is the connection? 42 Indices A. The index is always the same as the number of noughts. You were quite right if you said something like this but note, this only appl ies when our base is 10. We can now see how to make this method save us a lot of time.

1000 = 103 So Q. If we also tell you that: 108 7 106 = 102 can you see the connection again between the indices involved in the division, and the index of the answer? 52 Indices A. You should have said something like 'When we divide two identical bases with different indices, we can subtract the indices from each other to get the index of the answer'. Th is means that We could also have written it as: Q. Work out the following: 106 104 = ? 103 102 ? 53 Indices A. We know that 10 5 -;- 10 3 = 10 5 - 3 Now if instead of dividing by 10 3 we were multiplying by 10- 3 {notice the minus sign in front of the index}, this would give us: 10 5 x 10-3 = 10 5 - 3 Therefore, 10 5 x 10- 3 means the same as 10 5 -;- 10 3 .

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