Multiple divisions I was confused a bit with a little arithmetic here. For instance $1÷1÷2$ and $2÷3÷7$. BODMAS isn't effective in this case. My question is this:
$2÷3÷7$
Am I to divide $2/3$ by $7$ or divide $2$ by $3/7$??
 A: I agree with Bill.  Mathematicians never write $2÷3÷7$.  
But you can have the same question with subtraction, where the same ambiguity could be imagined.  $7-3-2$, is it $7-(3-2) = 6$ NO, or $(7-3)-2=2$ YES.  Even that problem goes away once we reach negative numbers, and interpret subtraction as adding the negative.  $7-3-2$ means
$$
7 + {}^-3 + {}^-2
$$
and addition is assiciative, so both
$$
\big(7 + {}^-3\big) + {}^-2 = 2\qquad\text{and}\qquad
7 + \big({}^-3 + {}^-2\big) = 2
$$
are correct.
A: You need to carry on first division first.
$$\frac{\frac{2}{3}}{7}=\frac{\frac{2}{3}}{\frac{7}{1}}=\frac{2}{3}\cdot\frac{1}{7}=\frac{2}{21}$$
while
$$\frac{2}{\frac{3}{7}}=\frac{\frac{2}{1}}{\frac{3}{7}}=\frac{2}{3}\cdot\frac{7}{1}=\frac{14}{3}$$
BODMAS is an acronym and it stands for Bracket, Of, Division, Multiplication, Addition and Subtraction  .
It gives you the order of precedence of operations:
When there are similar operations, you can proceed with any one of them;
but when you have a mixture of operations:  


*

*Bracket gets the highest priority

*proceed with multiplication and division before addition and subtraction  

*For similar operations, you can proceed with the order in which they appear, or in any way you feel easier.  


E.g.  $$(4+2)-3=4+(2-3)$$
$$4\cdot \frac{9}{5} = \frac{4 \cdot 9}{5}$$
$$(4+2)\cdot3 \neq 4+(2\cdot3)$$
$$\frac{4-2}{3} \neq 4- \frac{2}{3}$$
E.g. $$4+(6-1)\cdot7-\frac{8}{2}$$
will be done like $$4+5\cdot7-4$$
$$=4+35-4$$
$$=35$$
And not like:
$$4+6-1\cdot7-\frac{8}{2}$$
$$=10-7-4$$
$$=-1$$
