Linear Formula (SQA National 5 Maths): Revision Note

Changing the subject of a linear formula

What is a formula?

• A formula is a rule, definition or relationship between different quantities, written in shorthand using letters (variables)

  • A formula includes an equals sign

• Some examples you should be familiar with are:

  • The equation of a straight line

    • 

  • The area of a trapezium

    • 

  • Pythagoras' theorem

    • 

What is the subject of a formula?

• Usually a formula will have a single letter on its own on one side of the equals sign

  • That letter is known as the subject of the formula

    • For , the subject is

    • For , the subject is

  • You can use the formula to calculate the value of the subject, if you know all the other values

• By rearranging a formula, you can change the subject

  • This means rewriting the formula so a different letter is on its own on one side of the equals sign

How do I rearrange a formula to change the subject?  

• The method is as follows:

  • First, remove any fractions

    • Multiply both sides by the lowest common denominator

  • Then use inverse (opposite) operations to get the variable you want on its own

    • This is similar to solving equations

• For example, make  the subject of 

  • First remove fractions

    • Multiply both sides by 2
      

  • Then get  on its own

    • Subtract 6 from both sides
      

    • Divide both sides by 5
      

  • There may be more than one correct way to write an answer

    • The following are acceptable alternative forms 
      
      
      
      
      

Should I expand brackets?

• Expand brackets if it releases the variable you want from inside the brackets

  • If not, you can leave them in

• To make the subject of 

  • is inside the brackets, so expand

    • 

  • Rearrange

    • 
       

• To make  the subject of 

  • is not inside the brackets, so you do not need to expand

  • Instead, divide both sides by the bracket

    • 

What if I get fractions in fractions?

• Some rearrangements can lead to fractions in fractions 

  • 

• Either rewrite with a divide sign, , then use the method of dividing two fractions

  • 
    

• Or multiply top and bottom by the the lowest common denominator of the two fractions and cancel

  • becomes 

What if I end up dividing by a negative?

• Remember that  (minus below) is the same as (minus above) and the same as (minus outside)

  • Though be careful, as is 

• becomes  (minus below)

  • This is the same as  (minus above) or (minus outside)

    • brackets are required for minus above

    • brackets are assumed for minus outside

  • You can also expand the brackets