By Semenov K.N.

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**Extra resources for A basis of identities of the Lie algebra s(2) over a finite field**

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4 5 5 Rewrite each of the following in the form 1 : n. a 5:8 b 4 : 13 c 8:9 d 25 : 36 e 5 : 27 f 12 : 18 g 5 hours : 1 day h 4 hours : 1 week i £4 : £5 Calculating a ratio when only part of the information is known EXAMPLE 4 Two business partners, John and Ben, divided their total profit in the ratio 3 : 5. John received £2100. How much did Ben get? John’s £2100 was –38 of the total profit. ) So, –81 of the total profit = £2100 ÷ 3 = £700 Therefore, Ben’s share, which was –85 of the total, amounted to £700 × 5 = £3500.

41 (rounded) If you calculate the differences, you can see that the actual increase gets bigger and bigger. 06)3 to find the amount after 3 years. That is, you could have used the following formula for calculating the total amount due at any time: total amount = P × multiplier raised to the power n = P × (1 + x)n where P is the original amount invested, x is the rate of interest expressed as a decimal, and n is the number of years for which the money is invested. qxd 16/03/06 08:20 Page 36 CHAPTER 2: FRACTIONS AND PERCENTAGES Using your calculator You may have noticed that you can do the above calculation on your calculator without having to write down all the intermediate steps.

How much pocket money did he have in the beginning? 20 is two-thirds of three-quarters of a sum of money, what is the total amount of money? 4 08:20 Page 28 Dividing by a fraction This section will show you how to: ● divide by fractions Key word reciprocal To divide by a fraction, we turn the fraction upside down (finding its reciprocal), and then multiply. EXAMPLE 5 Work out a –65 ÷ –34 b 2 –21 ÷ 3 –31 a Rewrite as –65 × –34 . 42 5 3 10 1 5 ÷ = × = =1 3 6 4 9 9 36 b First make the mixed numbers into top heavy fractions.

### A basis of identities of the Lie algebra s(2) over a finite field by Semenov K.N.

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