# How do I rearrange the equation to solve for 'M'?

• Dark_Dragon
In summary, you are trying to find M, the unknown factor in a equation T^2/R^3 = 4pi^2/GM. You can try transforming the equation one step at a time, or using the rules for moving fractions. After some experimentation, you find that M = (4pi^2)(R^3/T^2) / G.
Dark_Dragon
well i have my equation T^2/R^3 = 4pi^2/GM

and i want to find 'M' on its own, (i never have been good at this) but here is my attempt:

M = 4pi^2/G(T^2/R^3)

is this correct?

No (not as I read your notation). Note that when you "move" something like a/b to the other side of an equation it becomes b/a.

It may help to transform your equation only one step at a time. If you are in doubt about the transformation rules, then remember that you are transforming the two sides by doing the same thing on both sides, i.e. to "move" the term $a$ in $a+b$ you actually add $-a$ to both sides so that the original side becomes $a-a+b = 0+b = b$; to "move" the factor $a$ in $a \cdot b$ you actually multiply with $1/a$ on both sides that on the original side becomes $(a/a) \cdot b = 1 \cdot b = b$.

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after having a look at it for a while, i tried one step at a time and i came out with:

M = (4*pi^2)(T^2/R^3)/G

is this any better? please don't take offence if i didnt understand your post.

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This is the same result you got the first time, so its still not correct.

The problem is with $T^2/R^3$. Originally that factor is on one side of the equation and must at some transformation step be moved to the other side. You seem to move it verbatim to the other side so it ends up being the same $T^2/R^3$ which is not correct.

Note that the factor is in the form of a fraction (i.e. a/b) and you should carefully consider what happens when you move such a fractional factor to the other side of an equation. If you have a textbook you may want to look up reciprocal.

so you're saying that i need to turn the expression into R^3/T^2?

then would the equation be:

M = (4pi^2)(R^3/T^2) / G ?

am i any closer?

You were initially correct in your first post, just remember to bring R^3 to the numerator to simplify things.

Dark_Dragon said:
so you're saying that i need to turn the expression into R^3/T^2?

then would the equation be:

M = (4pi^2)(R^3/T^2) / G ?

am i any closer?

Now it looks right, yes.

ok thank you very much :)
i have a fair bit of trouble with rearrangements,

so thanks for the help! =)

## 1. How do you rearrange an equation?

Rearranging an equation involves isolating the variable you are solving for on one side of the equation and simplifying the remaining terms on the other side.

## 2. Why do we rearrange equations?

Rearranging equations allows us to solve for a specific variable and manipulate the equation to better understand the relationship between different variables.

## 3. What are some strategies for rearranging equations?

Some common strategies for rearranging equations include using the distributive property, combining like terms, and isolating the variable by performing inverse operations.

## 4. Can you rearrange an equation without changing its value?

Yes, as long as you perform the same operations on both sides of the equation, the value of the equation will not change.

## 5. How can rearranging equations help in problem solving?

Rearranging equations can help in problem solving by allowing us to solve for a specific variable and use that information to find other unknown values or to check the validity of a solution.

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