Rearranging formulas

Rearranging Formulas

Definition and Basics

  • Rearranging formulas is the process of making one variable the subject of a formula.
  • This is a common requirement in mathematics, where a formula given might be useful, but needs to be reorganized to solve for a different variable.

Consider the Operations

  • Each operation (addition, subtraction, multiplication, division) has an opposite, or inverse operation, that can be used to rearrange the formula.
  • Addition pairs with subtraction, multiplication pairs with division, square operation pairs with square root, and vice versa.
  • For example, if x = y + 2 is your formula, and you need to solve for y, subtract 2 from both sides to get y = x - 2.

Dealing with Fractions

  • Fractions are made of two parts: the numerator (top number) and the denominator (bottom number). If a number is in the form of a fraction, you can ‘clear’ the fraction by multiplying every term by the denominator.

Reverse Order of Operations

  • Apply BIDMAS/BODMAS rule in reverse order when rearranging formulas because you usually ‘do’ the operation you come to last, first.
  • BODMAS stands for brackets, orders (powers and roots), division and multiplication (from left to right), addition and subtraction (from left to right).

Rearrange Step-by-Step

  • Rearrange the formula step-by-step. Remember that whatever operation you perform on one side of the equation must also be performed on the other side.

Rearranging More Than One Recipe

  • When rearranging formulas to change the subject of the formula, you may have more than one way to do it. For example, in the equation s = ut + 0.5at², either u or a could be made the subject.

Points to Remember

  • Always reverse the order of operations when rearranging formulas.
  • Multiply by the denominator to clear fractions, and remember to do so for every term.
  • Keep equations balanced. What you do to one side, you must do to the other.
  • Remain flexible in your thought process. Different parts of the equation can be rearranged to solve for different variables.

Rearranging formulas expands your ability to solve more complex problems by enabling you to manipulate given formulas to solve for desired variables. Regular practice will adapt you to this necessary algebraic skill.