How are fractions involving three numbers simplified.

Question

This is something thats been bugging me since my high school.

Is A/B/C = A/BC or AC/B

Answer 1

The expression $A/B/C$ is sufficiently ambiguous that it should not be written at all. Some people do follow the convention that it should be evaluated from left to right, making it $(A/B)/C$, but I would never count on a reader to interpret it that way with any confidence. For the same reason I would not write $A/BC$: depending on the reader’s conventions, it can be understood either as $(A/B)C$ or as $A/(BC)$, and these are not in general equal.

If you cannot write the three-storey fraction on multiple lines, you should use parentheses:

$$\frac{A}{\frac{B}C}=A\cdot\frac{C}B=\frac{AC}B\;,$$

on one line $A/(B/C)$, while

$$\frac{\frac{A}B}C=\frac{A}B\cdot\frac1C=\frac{A}{BC}\;,$$

on one line $(A/B)/C$.

Answer 2

Division is actually multiplying by the opposite, meaning:

$\frac{a}{\frac{b}{c}} = a * \frac{c}{b} = \frac{ac}{b}$

Answer 3

It depends if by $\frac{A}{\frac{B}{C}}$ you mean $$\frac{\quad A\quad}{\frac{B}{C}}\qquad\text{or}\qquad\frac{\frac{A}{B}}{\quad C\quad}.$$ (You meant the first one, according to the $\TeX$ you used, but it is rather hard to tell from the way that particular equation gets rendered!)