[Â HomeÂ ]

How to change the subject of a formula.

 This topic is part of the TCS FREE high school mathematics 'How-to Library', and will help you to change the subject of a formula. (See the index page for a list of all available topics in the library.)Â To make best use of this topic, you need to download the Algematics software. Click here for instructions.

### Theory:

A formula is an equation which specifies how a number of variables are related to one another. Formulas are written so that a single variable, the subject of the formula, is on the left hand side of the equation. Everything else goes on the right hand side of the equation.

For example, in the formula: v = u + at , v is the subject.

Formulas are used to calculate the value of the subject when values of all of the other variables are known.

To find ‘v’ in the example, you must substitute values for ‘u’, ‘a’, and ‘t’ in the right hand side of the equation, then evaluate. The answer will equal ‘v’.

To find unknown values of ‘u’, ‘a’, or ‘t’, you can make any of these other variables the subject, instead of ‘v’.

 To change the subject of a formula, begin with the variable to become the new subject, and apply inverse operations as for solving equations, in the opposite order to the order convention.

The following steps can be used to change the subject of this formula: v = u + at

#### (1) make ‘u’ the subject of the formula:

According to the order convention, beginning with ‘u’, you add ‘at’ to get ‘v’.

The inverse operation is then to subtract ‘at’:

·Â  Â Â Â Â  Subtractat’ from both sides:

v - at = u + at - at

· Â Â Â  Simplify:

v - at = u

·Â  Â Â Â  Swap sides so the subject is on the left hand side:

uÂ  =Â  v - at

#### (2) make ‘t’ the subject of the formula:

According to the order convention, beginning with ‘t’, you multiply by ‘a’ first, then add ‘u’ to get ‘v’.Â  The inverse operations are to subtract ‘u’ first, then divide by ‘a’.Â Â Â Â Â Â Â Â

·Â Â  Â Â Â  Subtract ‘u’ from both sides:

v - u = u + at - u

·Â  Â Â Â  Simplify:

v - u = at

·Â  Â Â Â  Divide both sides by 'a':

(v - u)¸a = at¸a

·Â  Â Â Â  Simplify:

(v - u)¸a = t

·Â  Â Â Â  Swap sides so the subject is on the left hand side:Â

t = (v - u)¸a

### Method:

IMPORTANT: This topic assumes that you know how to enter mathematical formulas into Algematics. Find out how by completing the three simple tutorials in the 'Getting Started' section of the Algematics program 'Help'.

We will use the example described in the ‘theory’ section above to demonstrate how to change the subject of a formula using Algematics.Â

We will use Algematics to make ‘u’ the subject of the formula: v = u + at

#### Step 1Â  Enter the data

Click Â and type the original formula into the maths box in the data entry dialog box. If the ‘EMPTY’ message is not displayed between the blue buttons, click the Â button until the message: ‘INSERT’ appears.Â  If necessary, use the ' * ' symbol for multiply and the ' / ' symbol for divide.

Â Â Â Â Â Â  Maths...

Â  Â v = u + at

Â

Â

Â

and then click

#### Step 2 Apply inverse operations to isolate the new subjectÂ

Repeat steps 'a', 'b' and 'c' below until all inverse operations have been performed...

 a. Type the inverse data into the input box ·Â Â Â Â Â Â Â Â  Click on the input box and type the inverse data: Â Â  Input For the example, type: ‘at’ b. Apply the required inverse operation ·Â Â Â Â Â Â Â Â  Click one of: , , ,Â  orÂ  For the example, click: Â to subtract ‘at’ from both sides. v - at = u + at - at c. Simplify the equation ·Â Â Â Â Â Â Â Â  Click v - at = u
Â

NOTE: Click the Â (swap) button if the subject has ended up
Â Â Â  on the right hand side of the equation:Â Â  u = Â v - at

Â