Rearranging equations

  2. Basics
  3. Mathematics
  4. Rearranging equations
    5. 10'

In maths, adding, subtracting, multiplying and dividing are all examples of operators. 

Algebra is the process by which an equation can be manipulated to make another quantity the subject of the equation. 

The videos below demonstrate how to rearrange simple equations. 

Key Concepts

The order in which you would use an equation can be remembered as BODMAS:

  1. Brackets
  2. Other operator (e.g. power of, sin)
  3. Division/Multiplication (order doesn't matter)
  4. Addition/Subtraction (order doesn't matter)

If you want to rearrange an equation to make another physical quantity the subject, the BODMAS order above is reversed. 

 

Summary

Try these questions for yourself and then watch the video to check your answer.

\(y = x + 4\)

Rearrange the equation \(y = x + 4\) to make \(x\) the subject by subtracting \(4\) from both sides.

\(y = 4x\)

Rearrange \(y = 4x\) to make \(x \) the subject by dividing each side by \(4\) (HINT: any number divided by itself is equal to \(1\)).

\(y = {3x\over 4}\)

Rearrange \(y = {3x\over 4}\) to make \(x\) the subject by cross-multiplying.

\(y = x^2\)

Reaarange \(y = x^2\) to make \(x\) the subject by square rooting both sides. This is the same as raising each side to the power of \(1\over 2\).

 

Test Yourself

Use quizzes to practise application of theory.


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