The top of a fraction means “how many”, the bottom of the fraction means “what sort of thing”. You cannot add two different things together. For example, what have you got if you add two oranges to three oranges? The answer is 5 oranges. You can add the numbers together because you’re adding the same sort of things. However, what do you have if you add two apples to three oranges? You have two apples and three oranges. You cannot add them together, because they’re different things.
Once pupils discover that the number at the bottom of a fraction represents what sort of thing the fraction is then they can understand why they cannot add a half to one fifth easily, why they have to convert both into something other, where the bottom of the fractions has the same number.
Friday, 9 July 2010
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