# Change the Subject of a Formula

In mathematics we will learn how to change the subject of a formula and find the value of the variable.

Change the Subject of a Formula

### Subject of the formula:

It is a variable which is expressed in terms of other variables involved in the formula.

Formulas are written so that a single variable, the subject of the formula is on the L.H.S. of the equation. Everything else goes on the right side of the equation. We evaluate the formula by substituting for the literal numbers on the right hand side.

For example:

In the formula v = u + at, v is the subject.

To find v in the example, we substitute the values u, a and t in the R.H.S. of the equation.

### Changing the subject of the formula:

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

1. To make ‘u’ the subject of the formula in v = u + at

v - at = u + a̶t̶ - a̶t̶   [subtract at from both sides]

v - at = u

or, u = v - at

2. To make ‘t’ the subject of the formula, v = u + at,

v - u = u̶ + at - u̶   [subtract u from both sides]

v - u = at

On dividing both sides by a we get;

(v - u)/a = a̶t/a̶

or, (v - u )/a = t

or, t = (v - u)/a

Change the Subject of a Formula

### Solved examples to change the subject of a formula

1. The volume of a cuboid is the product of length and breadth of the cuboid.

Solution:

If l, b, h are length, breadth and height of the cuboid.

Also, if the volume is denoted by v then

V = l × b × h

or, l = V/(b × h)   Here, the subject is l.

or, b = V/(l × h)   Here, the subject is b.

or, h = V/(l × b)   Here, the subject is h.

2. In the relation C/5 = make (F - 32)/9 make F as the subject.

Solution:

C/5 = (F - 32)/9

⇒ 9C/5 = F - 32

⇒ 9C/5 + 32 = F

⇒ F = 9C/5 + 32

3. Make y the subject of the formula x = (y + z)/(y - z)

Solution:

x = (y + z)/(y - z)

x (y - z) = y + z   [multiply both sides by (y - z)]

xy – xz = y + z

xy - y = z + zx

y (x - 1) = z (x + 1)

y = z(x + 1)/(x - 1)

### More worked-out problems to change the subject of a formula

4. Write the formula for finding the area of the rectangle and indicate the subject in this formula. Also, make l as the subject. If A = 42 cm² and b = 6 cm, then find l.

Solution:

If area is denoted by A, length by l and breadth by b,
then area of the rectangle is given by A = l × b

In this formula, A is the subject.

When we change the subject, i.e., make l as the subject then the formula becomes l = A/b

In order to find the value of l, substituting the value of A and b,

we get l = 4̶2̶/6̶ cm

Therefore, length (l) = 7 cm.

5. For a right angled triangle, square of the hypotenuse (h) is equal to the sum of squares of its other two sides (p, b).

Frame the formula for the above statement and find out h if p = 4 and
b = 3.

Also, make ‘p’ the subject of the formula and find p if h = 10 and
b = 8.

Solution:

From the above statement,

h² = p² + b²

When p = 4 and b = 3

h² = 4² + 3²

= 16 + 9

h² = 25

h² = 5²

Therefore, h = 5

Changing the subject,

p² = h² - b²

p = √(h² - b²)

= √(10² - 8²)

= √(100 - 64)

= √36

= 6   [when h = 10 and b = 8]

6. In the formula, l = a + (n - 1)d make d as the subject. Find d when
l = 10, a = 2, n = 5.

Solution:

d = (l - a)/(n - 1) where d is the required subject

Now, substituting the values of l, a, n in the formula;
we get, d = (10 - 2)/(5 - 1)

= 8/4

= 2.

Formula

Formula and Framing the Formula

Change the Subject of a Formula

Changing the Subject in an Equation or Formula

Practice Test on Framing the Formula

Formula - Worksheets

Worksheet on Framing the Formula

Worksheet on Changing the Subject of a Formula

Worksheet on Changing the Subject in an Equation or Formula

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

## Recent Articles

1. ### Adding 1-Digit Number | Understand the Concept one Digit Number

Sep 17, 24 02:25 AM

Understand the concept of adding 1-digit number with the help of objects as well as numbers.

2. ### Counting Before, After and Between Numbers up to 10 | Number Counting

Sep 17, 24 01:47 AM

Counting before, after and between numbers up to 10 improves the child’s counting skills.

3. ### Worksheet on Three-digit Numbers | Write the Missing Numbers | Pattern

Sep 17, 24 12:10 AM

Practice the questions given in worksheet on three-digit numbers. The questions are based on writing the missing number in the correct order, patterns, 3-digit number in words, number names in figures…

4. ### Arranging Numbers | Ascending Order | Descending Order |Compare Digits

Sep 16, 24 11:24 PM

We know, while arranging numbers from the smallest number to the largest number, then the numbers are arranged in ascending order. Vice-versa while arranging numbers from the largest number to the sma…

5. ### Worksheet on Tens and Ones | Math Place Value |Tens and Ones Questions

Sep 16, 24 02:40 PM

In math place value the worksheet on tens and ones questions are given below so that students can do enough practice which will help the kids to learn further numbers.