# Changing The Subject Of The Formula │ Worked Examples

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

**What is the Subject Of The Formula?**

The subject of the formula for any equation is the variable you must find, or simply put; it is the particular unknown variable you need to find to solve the equation.

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

A = ∏r^{2}

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, the area could be given when solving mathematical exercises, 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 vital to learn the easy steps to get the subject of the formula quickly.

**Example 1**

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

**Solution**

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

**Step 1: write out the full equation**

b = 3c + d

Step 2: Move 3c to the LHS so the unknown can stand independently. Ensure 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 will solve this in two ways; each 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

**See Also:**

**Quadratic Equation: How To Solve Using Factorization Method**

**Simultaneous Equation- Meaning, Methods and Examples**

**Example 3: Make a the subject of the formula in the equation v**^{2 }= u^{2 }+ 2as

^{2 }= u

^{2 }+ 2as

**Solution**

Step 1: Write out the full equation

v^{2 }= u^{2 }+ 2as

Step 2: Subtract u^{2} from both sides of the equation

v^{2 }– u^{2 }= u^{2 }+ 2as- u^{2}

v^{2 }– u^{2 }= 2as

**Step 3**: divide both sides with the coefficient of a

In our equation, the coefficient of a = 2s

(v^{2} – u^{2}) / 2s = 2as/2s

(v^{2} – u^{2}) / 2s = a

Therefore, a = (v^{2} – u^{2}) / 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 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.

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