Subscribe to our YouTube channel for the latest videos, updates, and tips.


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










7th Grade Math Problems

8th Grade Math Practice

From Change the Subject of a Formula to HOME PAGE




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.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Conversion of Improper Fractions into Mixed Fractions |Solved Examples

    May 12, 25 04:52 AM

    Conversion of Improper Fractions into Mixed Fractions
    In conversion of improper fractions into mixed fractions, we follow the following steps: Step I: Obtain the improper fraction. Step II: Divide the numerator by the denominator and obtain the quotient…

    Read More

  2. Multiplication Table of 6 | Read and Write the Table of 6 | Six Table

    May 12, 25 02:23 AM

    Multiplication Table of Six
    Repeated addition by 6’s means the multiplication table of 6. (i) When 6 bunches each having six bananas each. By repeated addition we can show 6 + 6 + 6 + 6 + 6 + 6 = 36 Then, six 6 times or 6 sixes

    Read More

  3. Word Problems on Decimals | Decimal Word Problems | Decimal Home Work

    May 11, 25 01:22 PM

    Word problems on decimals are solved here step by step. The product of two numbers is 42.63. If one number is 2.1, find the other. Solution: Product of two numbers = 42.63 One number = 2.1

    Read More

  4. Worksheet on Dividing Decimals | Huge Number of Decimal Division Prob

    May 11, 25 11:52 AM

    Worksheet on Dividing Decimals
    Practice the math questions given in the worksheet on dividing decimals. Divide the decimals to find the quotient, same like dividing whole numbers. This worksheet would be really good for the student…

    Read More

  5. Worksheet on Multiplying Decimals | Product of the Two Decimal Numbers

    May 11, 25 11:18 AM

    Practice the math questions given in the worksheet on multiplying decimals. Multiply the decimals to find the product of the two decimal numbers, same like multiplying whole numbers.

    Read More