New answers tagged fractions
3
votes
Reduction of fractions
I think the best defense against this sort of error (and explanation for students) is to know what the process of cancelling is actually doing and why it works.
If you think of cancelling as just ...
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7
votes
Accepted
Reduction of fractions
Your first example is equivalent to $(6\div2)\div2$. Writing it this way, the erroneous cancelation can be seen as treating division as associative, that is, as writing
$$
(6\div2)\div2=6\div(2\div2)=...
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5
votes
Reduction of fractions
Cancelling is a shorthand for:
The rule for multiplying fractions, used in reverse
Any number (except 0) divided by itself is 1
The rule for multiplying by 1
$$\frac{ac}{bc} = \frac{a}{b} \cdot \...
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