How do I rearrange an equation involving multiple variables and fractions?

[treacleybeak]

i have to rearrange and equation

without using the exact terms its along the lines of a = bcde and i have to make c the subject. have searched my study materiel and I am fine with multiplications etc and doing the same to both sides when doing the rearrangement ie
bcde = a
bcde divided by b = a cancel the b to get cde = a over b (as in a fraction) but how do i write the next divisions ie
cde/d = a over b cancel d to get ce = a over b but where do i put d? do i put a at the top and b and d below with a space between or do i have to write ce = a/b/d

just can't get my head round it and google brought me to you guys

help...

 

[CompuChip]

I will assume that none of b, d and e are zero, otherwise dividing by any of them would be a problem anyway.

If you go back to

bcde = a​

instead of first dividing by b and then by d, you can of course divide by bd. That gives you

bcde/(bd) = cde/d = bce/b = be = a/(bd).​

On the other hand, as you had reasoned already, you can first divide by b and then by d, giving be = (a/b)/d.
This shows that (a/b)/d = a / (b d).
Writing it in fractions: you can put whatever you divide by below the bar:
\frac{\frac{a}{b}}{d} = \frac{a}{b d}

Also note that (a / b) / d is something else than a / (b / d). When in doubt, you can plug in some numbers. Say a = 12, b = 6, d = 3. Then (a / b) / d = (12 / 6) / 3 = 2 / 3 while a / (b / d) = 12 / (6 / 3) = 12 / 2 = 6.

 

[treacleybeak]

\frac{\frac{a}{b}}{d} = \frac{a}{b d}


but does this not indicate a/bxd?

i struggled with fractions 22 years ago at school and never thought id need to bother with them again and while i get what to do with everything else its how to write the equation correctly that's the problem as its on a computer test and if i put a space or symbol in the wrong place i don't get another chance

 

[CompuChip]

bd means b multiplied by d. It's also written as b d or b*d.
Note that, when you type a/bxd into a computer, it will usually interpret it as (a/b)xd, i.e.
\frac{a}{b} \times d

If you mean
\frac{a}{b \times d}
you should write a/(bxd)