 # Changing The Subject Of The Formula │ Worked Examples

Are you always confused on how to change the subject of the formula? This article will give you a detailed guide on how to change the subject of the formula. We shall be solving different exercises in this article in order to help you gain mastery in solving equations involving changing subject of the formula.

## What is Subject Of The Formula?

Subject of the formula for any equation is the variable that you have to find or simply put, it is the particular unknown variable you need to find in order to solve the equation.

The formula is an equation consisting of letters of the alphabet or symbols which represent quantities. For instance the formula for area of a circle is:

A = ∏r2

Where A = Area of the circle

∏ = A value given as 3.142

r = radius of a circle

From this formula above, we can say that A is expressed in terms of ∏ and r. Sometimes, when solving mathematical exercises, the area could be given and you will be asked to solve for the radius. As such, you have to make the radius to become the subject of the formula. Therefore, it is important to learn the easy steps to get the subject of the formula easily.

### Example 1

Given the equation b = 3c + d, make d the subject of the formula.

### Solution

Before you begin to solve for d, you must understand the goal for making an unknown to become the subject of the formula. The major goal is to ensure that the unknown stands alone so that the value can be derived easily. The following steps will guide you on solving this equation.

Step 1: write out the full equation

b = 3c + d

Step 2: Move 3c to the LHS so that the unknown can stand on its own. Ensure that you change the sign to negative as it crosses the equality sign.

b – 3c = 2d

Step 3: Divide both sides with the coefficient of d

In this equation, the coefficient of d = 2

(b – 3c)/ 2 = 2d/2

(b – 3c)/ 2 = d

Therefore d = (b – 3c)/2

### Example 2:Make k the subject of the formula in f = g(1 + k)

#### Solution

We are going to solve this in two ways, each of them is correct and will arrive at the same answer. The first solution is given below:

Step 1: Write out the full equation

f = g(1 + k)

Step 2: Open the brackets

f = g + gk

Step 3: subtract g from both sides to make gk stand on its own

f – g = g + gk – g

It would now be:

f – g = gk

Step 4: Divide both sides with the coefficient of k

(f – g)/g = k

Simplifying,

f/g – 1 = k

Therefore, k = f/g – 1

Alternatively, we can use the second method to make k the subject of the formula

Step 1: Write out the full equation

f = g(1 + k)

Step 2: Divide both sides by g

f/g = {g(1 + k)}/g

f/g = 1 + k

Step 3: subtract 1 from both sides

f/g – 1 = 1 + k – 1

It would be given as;

f/g – 1 = k

Therefore k = f/g – 1

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### Example 3: Make a the subject of the formula in the equation v2 =  u2 + 2as

#### Solution

Step 1: Write out the full equation

v2 = u2 + 2as

Step 2: Subtract u2 from both sides of the equation

v2 –  u2 = u2 + 2as- u2

v2 – u2 = 2as

Step 3: divide both sides with the coefficient of a

In our equation, the coefficient of a = 2s

(v2 – u2) / 2s = 2as/2s

(v2 – u2) / 2s = a

Therefore, a = (v2 – u2) / 2s

Example 4: Given A = P + PTR/100, Make R the subject of the formula

Solution

Step 1: Write out the given equation

A = P + PTR/100

Step 2: Subtract P from both sides or more easily, move P across the left hand side while changing the sign

A – P = PTR/100

Step 3: Multiply both sides by 100

(A – P)100 = PTR/100 X 100

100(A – P) = PTR

Step 4: Divide both sides with the coefficient of R

100 (A – P) / PT = R

Therefore, R = 100 (A – P) / PT

You can now go ahead and apply these steps in any exercise involving changing the subject of the formula. This will help you to resolve an equation more easily and get the answer faster.

If you have further questions or comments regarding this article or other questions in mathematics, please use the comment section below. We shall respond to all as quickly as possible.