What is a Formula?
A formula is essentially an equation which shows a relationship between variables.
For example, we have a formula to find the area of a rectangle. A = L x W. The area of a rectangle is dependent on the length of the rectangle and the width of the rectangle. As the length or width of the triangle changes, so does the area of the rectangle.
A formula always has more than one variable.
What is the subject of the formula?
The subject of a formula is the variable that is isolated (by itself) when compared to the other variables.
In this case, “v” is the subject of the formula because it is isolated from the rest of the variable.
In the second scenario, “m” is the current subject of the formula because it is isolated from the rest of the variables.
In many scenarios, you will need to rearrange the formula in order to make another variable the subject.
This question wants you to make “e” the subject rather than m.
Changing the Subject
When rearranging formulas, the key is to find the inverse operations to help isolate the subject.
So if we start with A = BC – 3D, we need to “move 3D” to the left hand side of the equation. If I add 3D to the right side, the 3D -3D cancels to become 0, but since I unbalanced the equation, I have to add 3D to the left hand side. The new equation now becomes A + 3D = BC (notice how the 3D is missing on the right hand side).
Now if I want to isolate C by itself, I know that BC means B multiplied by C, so the inverse of multiplying is dividing. So I have to divide the right hand side by B. By doing that I unbalanced the equation again, so I have to make sure that I divide the left hand side by B as well. The new equation now becomes (A + 3D)/B = C (notice how the B is missing from the right hand side).
That’s how you can isolate the subject by rearranging formulas.