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Solution to the self assessment question about cakes

Solution to the self assessment question about cakes
4.9
Here you have to determine which piece of cake you have is the heaviest. So for Cake 1, you have 6/11 of a 1.35 kilogramme cake. And for Cake 2, you have 4/15 of a 2 pound 9 ounce cake. This is a difficult problem because you have different proportions of different cakes, and the cakes are also measured in different units. As in the question, you can calculate how much cake you have by multiplying the fraction by the mass. So for Cake 1, 6/11 multiplied by 1.35 kilogrammes gives you 0.7363 kilogrammes. In order to perform this calculation on Cake 2, you should convert the 2 pounds 9 ounce cake into kilogrammes.
60.2
2 pounds 9 ounces equals 41/16 pounds, because there are 16 pounds in an ounce. One pound equals 0.454 kilogrammes, and so 41/16 pounds multiplied by 0.454 gives 1.1634 kilogrammes. This is the mass of Cake 2 in kilogrammes.
91.5
Now, multiplying 4/15 by this mass in kilogrammes, 4/15 multiplied by 1.1634 kilogrammes gives 0.3102 kilogrammes. This is the mass of Cake 2 that you have in kilogrammes. And so clearly, Cake 1 is the heaviest.
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