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Because, depending how you want to do the multiplication, you might get wrong results.

A mixed number - for example 5 1/3 (five and one-third) should be considered, in this example, as 5 + 1/3 - that is, the whole number 5, plus 1/3. You can treat this as a polynomial and multiply it as such. For example, 2 x 5 1/3 = 2 x (5 + 1/3) = 2 x 5 + 2 x 1/3 = 10 + 2/3 = 10 2/3. If you need to multiply two mixed numbers, you need to multiply each part of one by each part of the other - as is common when multiplying polynomials. Usually it is simpler to convert the fraction to a mixed fraction first. Both methods give you the same answer. In any case, if you think up some method that looks great, but it gives you a DIFFERENT result, then such a method is wrong.

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Q: Why can't you multiply mixed numbers straight across?
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