By Garrett P.

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This is reversing the process and so undoing the previous type of calculation. 69 gallons (rounded to 2 decimal places) Calculator constant and conversion table If you have to carry out a series of conversion calculations of the same kind, a good method is to use the constant facility on your calculator. This could be used to draw up a conversion table. You will see such tables for litres and gallons on petrol pumps; one converting gallons to litres is given in the margin. A disadvantage of the table is that conversions from whole numbers of litres to gallons are not easy.

Although the whole something is often given as a single cake or pizza, this can be very confusing. Fractions are often fractions of several objects (‘There were 40 people in the room; three-quarters of them were women’) or fractions of something smaller than 1 (‘As there are three of you, I’ll split this remaining piece of pie into thirds’). It is better not to rely on such diagrams. In dealing with multiplication and division of fractions you may have wondered about issues like these: ◗ Why does ‘of’ mean ‘multiply’ with fractions?

Mental methods can be shared; they do not need to be re-invented by every individual. Use the following task as a way of finding out some of the methods you use. Task 12 Buying stamps Mentally work out how much it would cost to buy the following postage stamps (do each part without using the solution to a previous one). Think about what method you use. (a) 50 at 28p each (b) 27 at 50p each (c) 25 at 75p (d) 28 at 75p Comment Did you always use the same method? If not, why not? 50 so 4 cost £3; 28 is 7 groups of 4, 7 × £3 = £21 Mental strategies With mental calculations there are no set methods – what you use depends on your personal strategies and the actual numbers.

### Compactness of certain integral operators (2005)(en)(3s) by Garrett P.

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