Melody

That is good MathsGod1

BUT

can you show me how you can cancel earlier please ?

Alan has given a proof for the 7* one here      

For seven:

Take the last digit, double it, and subtract it from the rest of the number. If the answer is divisible by 7 (including 0), then the number is also divisible by 7:

861:86-1x2=84

84/7=12

That is a good question MG  :)

There is no real difference.  You must always cancel ONE thing on the top with ONE thing on the bottom.

Eg. you might start by divided the 8 by two on the bottom and the 34 by two on the top.  

That would be one step  

Ok I am glad that it makes sense so far    

$$\\34\frac{1}{8}\times \frac{14}{51}\div 1\frac{15}{34}\\\\
\frac{(34*8+1)}{(8)} * \frac{14}{51} \div \frac{(1*34+15)}{(34)}\\\\
= \frac{273}{8} * \frac{14}{51} \div \frac{49}{34}\\\\
= \frac{273}{8} * \frac{14}{51} * \frac{34}{49}\\\\
$Done, it all makes sense now.$$$

Well I am glad it all makes sense, What are you going to do next?  (no multiplying!)     

I am sorry MG I know you tried really hard but you have messed up right from the beginning.  

I will start you off.

$$\\34\frac{1}{8}\times \frac{14}{51}\div 1\frac{15}{34}\\\\
$None of the fraction parts can be simplified so you firstly need to change all the mixed numerals to improper fractions.$\\\\
\frac{8*34+1}{8}\times \frac{14}{51}\div \frac{34*1+15}{34}\\\\
$now simplify what you have got$\\\\
*\\\\
$now invert the last fraction and change the divide to a time$\\\\
$Now you are up to cancelling BUT don't cancel yet$$$

Don't cancel yet.  Get it right up to here first!   Then tell me what you want to cancel.

Don't tell me in the LaTex.  Tell me underneath in normal text.

Good luck  

@@ End of Day Wrap   Sat 30/5/15   Sydney, Australia Time   11:36pm     ♪ ♫

Good evening/day/morning     

Today our great answers were supplied by DarkBlaze347, DragonLance, CPhill, Thejamesmachine, MathsGod1, Heureka, Alan, asinus, MathsGod1 Civonamzuk and Josh4444.  Thank you  

As Alan pointed out, you did not s***w it up!  If I was here I would not  have even attempted it.

I would have  been doing something more relevant to me like looking for your odd socks.  Do you think that they could have made it to Australia.  There have been some big tides lately :/

Yes you could have been designing the next genaration of Marsian rockets.  

OR

Cleaning out your sock drawer.     LOL

$$\frac{y^2*9}{5}=\frac{9y^2}{5}$$

There is nothing else that you can do with it  

YES absolutely  !!