Square numbers and division

why does dividing a squared number (say 4 squared) by a number (say 2) equal the same as dividing 4 by 2 then times by the remaining 4

So the first one is

\frac{n^2}{2}

\frac{n}{2} \times n = \frac{n}{2} \times \frac{n}{1}

when you multiply a fraction, you multiply through the top and bottom, so

(\frac{n}{2} \times \frac{n}{1}) = \frac{n \times n}{2 \times 1} = \frac{n^2}{2}

It doesn't matter which way round you multiply and divide, the result will be the same.

Original post by NotNotBatman

So the first one is

\frac{n^2}{2}

\frac{n}{2} \times n = \frac{n}{2} \times \frac{n}{1}

when you multiply a fraction, you multiply through the top and bottom, so

(\frac{n}{2} \times \frac{n}{1}) = \frac{n \times n}{2 \times 1} = \frac{n^2}{2}

It doesn't matter which way round you multiply and divide, the result will be the same.

Thank you so much this has been very helpful!

LaTex

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