What Does 'Changing the Subject' Mean?
In science, we use formulas constantly — from calculating speed to finding the energy stored in a spring. A formula is a mathematical relationship between two or more quantities. The subject of a formula is the variable that stands alone on one side of the equals sign.
The variable that is expressed in terms of all the other variables — it appears alone on one side of the equation, usually on the left.
For example, in the formula:
The subject is (velocity). But what if you already know , , and , and you want to find (time)? You need to rearrange the formula to make the subject.
Think of a formula like a balanced set of scales. Whatever you do to one side, you must do to the other — otherwise the balance is broken. Rearranging a formula is just about keeping that balance while moving things around to isolate what you want.
Being able to change the subject of a formula is an essential skill in MYP Sciences — it lets you use the same formula to solve for any variable, not just the one it was originally written for.
The Golden Rule: Inverse Operations
To rearrange a formula, we use inverse (opposite) operations to 'undo' what is being done to the variable we want to isolate.
Here is a summary of operations and their inverses:
| Operation | Inverse Operation |
|---|---|
| Add () | Subtract () |
| Subtract () | Add () |
| Multiply () | Divide () |
| Divide () | Multiply () |
| Square () | Square root () |
| Square root () | Square () |
Always perform the same operation on both sides of the equation. When isolating a variable, undo operations in reverse order to how they were applied to that variable. Think of it like this: if you added 3 and then multiplied by 2, to reverse the process you divide by 2 first, then subtract 3. In practice, this means undoing addition/subtraction before multiplication/division, and undoing multiplication/division before powers/roots — because those outer operations were applied last.
Quick numeric illustration of reverse order:
Suppose a variable has been transformed by: first multiplying by 4, then adding 6. So the expression is .
To undo this and isolate :
- Step 1: Undo the addition — subtract 6 from both sides.
- Step 2: Undo the multiplication — divide both sides by 4.
We undo the last thing done (adding 6) before the first thing done (multiplying by 4). This is reverse order!
This process is sometimes called 'balancing the equation' or 'performing inverse operations'. The goal is always the same: get the variable you want completely alone on one side.
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