Mathematics is one of the interesting & tricky subjects for students. But it can become simple & easy to solve by learning the fundamentals and important concepts of Maths. Today, we have come up with the most useful topic ie., Changing the Subject of a Formula. Here, we will find what is the subject of a formula? How do you change the subject of the formula? the process of rearranging formulae, changing the subject of an equation or formula questions and answers, etc.

## Changing the Subject of a Formula – Definition

The meaning of changing the subject of the formula is identified as the letter on its own on one side of the equation.

For instance, in the area of a rectangle formula A = bh (Area = base x height), the subject of the formula is ‘A’.

### How to Rearrange Formula with Explanation?

For changing the subject of a formula or rearrange a formula, variables or items in the formula should be rearranged thus a different variable is the subject. Having knowledge of solving equations and inverse operations is very important.

Suppose, in the formula A = bh, the area (A) is the subject of the formula thus it is the area that is being worked out.

In case, we have known the area and height of a rectangle and require the rectangle base, the formula A=bh will not help as it needs b to be calculated.

The formula A=bh should be rearranged to make b the subject of the formula.

A = bh means A = b x h

In order to do b the subject of a formula, b has to be isolated. In the above formula, the letter b is multiplied by h. The inverse of the product of ‘h’ is dividing by ‘h, hence divide both sides by h to isolate b.

A = bh

÷h = ÷h

$$\frac { A }{ h }$$ = b

Now, the b is the subject of the formula. To solve the base of a rectangle for any question the formula is b = $$\frac { A }{ h }$$ so divide the area (A) by the rectangle height (h).

### How do you change the Subject of the Formula or Equation?

The method of substitution to get the value of one variable is known as Changing the Subject in an Equation or Formula.

In order to change the subject of an equation or formula, following the below points is very important:

• For changing the subject, firstly, discover the needed variable as a subject.
• Apply the inverse operation for the variable to solve the equation.
• Lastly, calculate the expression or formula and find the subject of a formula or equation.

### Solved Examples on Changing the Subject of an Equation or Formula

Example 1:
In the formula, a = l + (n – 1)b make b as the subject. Find b when l = 5, a = 13, n = 3.

Solution:
Given formula is a = l + (n – 1)b
After applying the process of changing the subject of an equation, the formula for the subject b is;
b = $$\frac { a-l }{ n-1 }$$
Now, substitute the values of l, a, n in the formula and get the result of b
b = $$\frac { 13-5 }{ 3-1 }$$
= $$\frac { 8 }{ 2 }$$
= 4.

Example 2:
Rearrange the formula u = v + at to make t the subject of the formula.

Solution:
Given equation or formula is u = v + at
Now, subtract v on both sides (-v) ie.,
u-v = at
Now, divide a on both sides (÷a) ie.,
$$\frac { u-v }{ a }$$ = t
Hence, the letter t is separated, so t becomes the subject of the formula.

### FAQs on Rearranging Equations or Formulae

1. How to change the subject of a formula?

2. How can I change the subject of a formula with fractions?

3. How do you make L the subject by rearranging the given formula ie., s = mL + r?

Given s = mL + r
First, Subtract r on both sides
s – r = mL
Now, Divide m on both sides
(s – r)/m = L
Finally, the result is L = (s – r)/m