Algebraic Manipulation – Changing the Subject of a Formula
Algebraic manipulation means rearranging a formula so that a different letter becomes the subject – the letter that's alone on one side of the equals sign. The formula y = mx + c has y as its subject; rearranged to make x the subject, it becomes x = (y − c) ÷ m. The rearranging steps are exactly the same inverse-operation moves you already use to solve an equation – you're just solving for a letter instead of a number.
This skill is essential whenever a formula is written with the “wrong” variable as the subject for the problem you're trying to solve – rather than starting from scratch, you rearrange the formula once, and then it becomes reusable for that new purpose.
Rearranging a Formula
To change the subject, undo each operation acting on the target variable, in reverse order – exactly like solving an equation.
Subtract c from both sides: y − c = mx. Divide both sides by m: x = (y − c) ÷ m.
w = 48 ÷ 6 = 8.
Real-Life Application
- Physics formulas: rearranging speed = distance ÷ time to solve for time instead.
- Finance: rearranging an interest formula to solve for the principal amount.
- Cooking: rearranging a recipe's ratio formula to solve for a different ingredient amount.
Key Takeaways
- Changing the subject means rearranging a formula to isolate a different variable.
- Undo operations in reverse order, exactly as when solving an equation.
- A rearranged formula can be reused directly for a new type of problem.
Practice: Algebraic Manipulation
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