question about fractional division i.e., 1/(1/3)

Question

konradzuse · Answer

Originally I thought that when you get something over a fraction you want to make it into fraction * fraction i.e, in this case 1/1 * 1/3?

konradzuse · Answer

Apparently in this case the answer is 3, so it's goign to be 1 * 3/1 = 3?

phi · Answer

multiply top and bottom by 3
3/3

konradzuse · Answer

hmm?

phi · Answer

$$ \frac{3}{\frac{1}{3}}\cdot \frac{3}{3} $$

konradzuse · Answer

oh ok.

phi · Answer

oops make that a 1 up top in the first fraction

konradzuse · Answer

shouldn't it be 1/(1/3)

konradzuse · Answer

kk

konradzuse · Answer

Never have seen this method, like I said normally I just flip and multiply, but I always though the num/dom was one and the next ones were just multi, but flipped.

phi · Answer

flip and multiply is "short cut"  to doing it the way I showed.

konradzuse · Answer

I gues smaybe because they were in paren?  I feel like I've done it the other way before and it worked, so maybe I'm just thinking of that way, but continue on please.

anonymous · Answer

$\frac{1}{\frac{1}{3}}$ in english "the reciprocal of one third" or  think "how many thirds are in one?"

konradzuse · Answer

:O that  makes some sense there Satellite :).

konradzuse · Answer

but is that situational?  On wolfram if I do 1/1/3 I get 1/3 but if I do 1/(1/3) I get 3?

phi · Answer

thinking about is always a good option.  and stick to basic principles (multiply by 1 for example) rather than tricks, if you have any doubts

phi · Answer

On wolfram if I do 1/1/3  that is order of operations

konradzuse · Answer

but your method makes a lot of sense too, try to cancel out so in this case 1/3 * 3/3 = 3/(3/3) = 3/1 = 3 :)

konradzuse · Answer

oh okay.. stoopid wolfram :P.

anonymous · Answer

$$\frac{a}{b}/\frac{c}{d}=\frac{a }{b }*\frac{d}{c} $$

konradzuse · Answer

So no matter what it will always be 3 huh... grr...

phi · Answer

1/1/3  

is being interpreted as 
$$ \frac{\frac{1}{1}}{3} $$

konradzuse · Answer

yuh phi :)

konradzuse · Answer

I knew that robto.  in this case that would be 1/1/3/1 which would be 1/1 * 1/3 = 1/3...

amistre64 · Answer

unless there are grouping symbols, the math is read right to left.

1/1/3 is read as:  1/1 = 1,   1/3 = 1/3

1/(1/3)  tells us that (1/3) is evaluated first to get a different result

amistre64 · Answer

pfft  ... cant even get my directions correct lol;     read left to right

konradzuse · Answer

:)