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

  • Thread starter treacleybeak
  • Start date
In summary, the individual is trying to rearrange an equation to make c the subject. They are struggling with how to write the equation correctly and are seeking help to understand the process. They have searched through their study material and understand how to do the rearrangement by dividing both sides, but are unsure of where to place the variables in the fraction. They have also realized that order of operations matters when dealing with fractions.
  • #1
treacleybeak
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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...
 
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  • #2
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:
[tex]\frac{\frac{a}{b}}{d} = \frac{a}{b d}[/tex]

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.
 
  • #3
[tex]\frac{\frac{a}{b}}{d} = \frac{a}{b d}[/tex]


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
 
  • #4
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.
[tex]\frac{a}{b} \times d[/tex]

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

1. How do I rearrange an equation?

Rearranging an equation involves manipulating the given equation to isolate the desired variable on one side of the equation.

2. What are the steps to rearrange an equation?

The basic steps to rearrange an equation are: identify the desired variable, use inverse operations to move all other terms to the other side of the equation, and simplify the equation to its final form.

3. How do I know if I rearranged the equation correctly?

You can check your rearranged equation by plugging in values for the variables and ensuring that both sides of the equation are equal.

4. Can I rearrange an equation with more than one variable?

Yes, you can rearrange an equation with multiple variables as long as you follow the same steps and ensure that the desired variable is isolated on one side of the equation.

5. What are some common mistakes to avoid when rearranging an equation?

Some common mistakes to avoid when rearranging an equation include forgetting to perform the same operation on both sides of the equation, not properly distributing a negative sign, and making calculation errors.

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