What is division? 12 ones split up into 3 things is 4 ones (per thing.) 1 one split up into 100 things is 1/100 ones (per 1 thing.) Thus, "5 ones split up into 1/100 things is 500 ones (per 1 thing)" is probably better understood as "5 ones split up among hundredths of a thing is 500 hundredths, or 1 one per hundredth of a thing." On the other hand, for non-decimals, I would write that "5 ones split up among one-hundred things is 1/20 (0.05) ones per thing."(adsbygoogle = window.adsbygoogle || []).push({});

Fine. Logical.

Still, how is dividing something by a fraction (0 < x < 1) the same as multiplying something by the inverse of that fraction?

If X * Y = X / (1 / Y), and "X ones split up among 1/Y of a thing is X*Y "1/Y's," or 1 one per "1/Y" of a thing," then what would be the complement terminology in multiplication to the "split up among" terminology in division?

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# Multiplication and Division of Decimals

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