is there any easy way to explain how to re-arrange equations?

Question

every question i'm doing (physics homework) has "re-arrange to solve for ___" and i'm struggling. i don't have any problems doing the equations once they've been re-arranged, but i was just wondering if there was any way of explaining the process so i had a better idea of how to do it.

Answer 1

It's called algebra

Examples:

a = b + c
you want b, so you subtract c from both sides
b = a - c

a * b / c = d / f
Say you want f. multiply both sides by cf and divide by ab
f = cd / ab

You have to do this about a million times in math class. Then it will be a snap when you need to do it in physics.

one last one you might recognize:

2 pi / T = sqrt (k/m)--you want m

square both sides
4 pi^2 / T^2 = k/m

multiply by mT^2 and divide by 4 pi^2
m = kT^2 / (4 pi^2)

Answer 2

Rearranging equations is the essence of algebra. It is based on the principle that, since the two sides of an equation are equal, then if you perform some operation identically on both sides, you'll get two new expressions that are still equal. For example, if this is true:

X = N+3

then this must also be true (after I put "10*" in front of each side):

10*X = 10*(N+3)

In algebra, you use this trick to apparently "move" symbols around from one place to another, and combine and separate them from other symbols. That's why they call it "rearranging"; but really it's just based on performing identical operations on both sides. Here's an example

3m + 9 = 11 - 4m

Look what happens if I add "4m" to both sides:

3m + 9 + 4m = 11 - 4m + 4m

Doesn't look too impressive until you realize that the "-4m+4m" is same as zero, and that you can combine the "3m" and the "4m" on the left to get "7m". Then it looks like this:

7m + 9 = 11

To "rearrange" further, subtract 9 from both sides:

7m + 9 - 9 = 11 - 9

which you can rewrite like this:

7m = 2

To rearrange one more time, divide both sides by 7:

7m/7 = 2/7

The two 7's cancel out on the left side, so:

m = 2/7

Usually, the object of "rearranging" is to get some certain variable or simple expression on the left side of the equation by itself. The technique is to wisely choose a sequence of operations that you can perform identically on both sides of the equation. And the strategy usually involves the following goals (let's say that some variable "X" is the thing you're trying to "move" to the left side):

* If there are multiple occurrences of "X" in the equation, try to get them all together so they can be combined into a single occurrence (like the way I combined 3m and 4m above, to make 7m).

* Try to "isolate" X by stripping away all the "non-X" stuff that's next to it. This is usually done by applying an operation (always on both sides!) that makes the non-X stuff "cancel out" (like the way I subtracted 9 from both sides to "get rid of" the 9 that was next to the 7m, above)

Typically, you have to apply both of the above techniques several times before you've "rearranged" the equation just the way you like it.

Answer 3

You can do things to both sides of the equation. So you can feel free to multiply, divide, add and subtract, as long as you do the same thing to both sides.