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Try reading this: http://psychassessment.com.au/PDF/Chapter%2001.pdf

ok so I have this formula \[v_{av}=\frac{\sum^n_{i=1}v_i\delta t_i}{\sum^n_{i=1}\delta t_i}\]

yeah I have looked it up. I would just like some clarification on a problem I am working on

I also have that \[\delta t_i=\frac{2z_i}{v_i}\]

now I am wondering if I can simplify this any further?

right that's what my thinking was.

\[\sum_i(v_i)\cdot(\frac{z_i}{v_i})=\sum_iz_i\]is valid

as long as it's under the same summation sign

or final answer I should say.

you are right, that rule wouldn't make sense mathematically either

this is valid...
\[\sum_i\left[(v_i)\cdot\left(\frac{z_i}{v_i}\right)\right]=\sum_iz_i\]

unless you have more info...you can't simplify it any more

thanks