Rearranging Formulas

Key Concepts in Rearranging Formulas

The Basics

  • Rearranging formulas involves manipulating the formula to make another variable the subject.
  • The end goal is to have the variable of interest on one side of the equals sign, and everything else on the other side.

Remember the Balance Principle

  • The same operations must be done to both sides of the equation to maintain the balance. If you add, subtract, multiply or divide anything on one side, you must do the same to the other.
  • For instance, in the formula d = rt where we want to make r the subject, we would divide both sides by t to get r = d/t.

Dealing with Addition and Subtraction

  • When the variable of interest is involved in addition or subtraction, rearrange by performing the opposite operation.
  • For example, in the formula x = y - z, to make y the subject, add z to both sides to get x + z = y.

Handling Multiplication and Division

  • To isolate a variable that is being multiplied or divided, apply the reciprocal operation to both sides of the equation.
  • In the formula A = πr², to make r the subject, we could divide both sides by π to get A/π = r², then square root both sides to get r = √(A/π).

Working with Powers and Roots

  • If the subject of the formula is involved in a square or square root, use the opposite operation to isolate it.
  • For instance, in the formula A = B², to make B the subject, apply the square root to both sides to get √A = B.

Remember to Factorise

  • Factorising can be very useful when trying to make a term the subject of a formula.
  • For example, with the formula x = ay + by, factoring the right side to x = y(a + b) makes it easier to make y the subject, by simply dividing both sides by (a + b) to get y = x / (a + b).

Strategies in Rearranging Formulas

Keep Practising

  • Regular practice of different types of formula rearrangements helps you to understand and apply concepts better.
  • Start with simple formulas and gradually work towards more complex ones.

Check Your Work

  • Always check your work by substituting values into your rearranged formula to verify it provides the same results as the original formula.

Being efficient in rearranging formulas not only benefits algebra, but it is also a central skill for science, technology, engineering, and maths-based tasks.