Change Subject of Formula: 10 Solved Examples Step by Step ( Simplemethd11)

 

Subject of the Formula: 10 Examples and Solution(SS1 ,SS2 and SS3) 

 Here in this post, we will see how to make an element subject of the formula to arrive at a particular point. This another high level mathematics that always featured in WAEC and NECO examination. Simplemethd11 Series is the key to enable you on how to solve this. To be able, you should know  some basic formula steps before you can solve subject of the formula.Here some examples and solution to subject of the formula with explanation and guides...

Example 1: Linear Equation with Fraction

Question:

Example 1: Linear Equation with Fraction

Question: Make x the subject of the formula: y = ½ax + b

Solution:

1. Subtract b from both sides:
   y - b = ½ax
2. Multiply both sides by 2 to clear the fraction:
   2(y - b) = ax
3. Divide both sides by a to isolate x:
   x = 2(y - b) / a

 Answer: x = 2(y - b) / a

That was a great operation to make x subject of the formula. The steps are your guides, in some cases, you may be asked to do the same thing, If you don't still understand after the first visit of the post, revisit the post like 4 to 7 times,  I promise you'll be good at last. Here is another one 

Example 2: Factoring Out the Target Variable

Question: Make p the subject of the formula:
T = ap + bp - c

Solution:

1. Add c to both sides to separate the p terms:
   T + c = ap + bp
2. Factor out p on the right side:
   T + c = p(a + b)
3. Divide both sides by (a + b):
   p =

   T + c

   a + b

✅ Answer: p = (T + c) / (a + b)

Yes, that amazing ap + bp , the variables in bold letters are to be factor out.First if you look the right hand side and the left side you can see there is a common factor for the two terms which is p, and its need to be factor out. Remember a multiply by p is ap  also, p multiply by b is bp. Make sure you know how to solve this. Study the method well..

Example 3: Variable speed on Both Sides of a Fraction

Question: Make w the subject of the formula:

G = 

w + 3

w - 2

Solution:

1. Multiply both sides by (w - 2) to remove the denominator as well as possible:
   G(w - 2) = w + 3
2. Open the bracket:
   Gw - 2G = w + 3
3. Rearrange the equation to get all w terms on one side:(note)
   Gw - w = 2G + 3
4. Factor out w:
   w(G - 1) = 2G + 3
5. Divide by (G - 1):
   w =

   2G + 3

   G - 1

✅ Answer: w = (2G + 3) / (G - 1)

This is so interesting, I hope you love this one. It is easy to do this, always remember to factor out any variable that paper 2 places. Simplemethd11 Series is the best for Mathematical explanation.

Example 4: Eliminating a Square Root

Question: Make g the subject of the formula:

t = 2π√(

L

g

)

Solution:

1. Divide both sides by 2π:
   

   t

   2π

   = √(L/g)
2. Square both sides to eliminate the radical:
   

   t2

   4π2

   =

   L

   g

3. Take the reciprocal of both sides:
   

   4π2

   t2

   =

   g

   L

4. Multiply both sides by L:
   g =

   4π2L

   t2

✅ Answer: g = 4π²L / t²

This is another common equation that is simple to solve. This mathematics is SS3 and  SS2 students.

Example 5: Formula Involving a Square Power

Question: Make v the subject of the formula:
E = ½mv² + mgh

Solution:

1. Subtract mgh from both sides:
   E - mgh = ½mv² 
2. Multiply both sides by 2 to clear the fraction :
   2(E - mgh) = mv²
3. Divide both sides by m:
   v² =

   2(E - mgh)

   m

4. Take the square root of both sides:
   v = √[

   2(E - mgh)

   m

   ]

✅ Answer: v = √[2(E - mgh) / m

That was amazing, just study the concept and you're good to go..

Example 6: Dealing with Negative Target Variables

Question: Make R the subject of the formula:
A = P(1 - R)

Solution:

1. Divide both sides by P:
   

   A

   P

   = 1 - R
2. Add R to both sides to make it positive element:
   R +

   A

   P

   = 1
3. Subtract (A/P) from both sides:
   R = 1 -

   A

   P

✅ Answer: R = 1 - (A / P)

You can see how to make R subject in the above equation. To do this, you only need to read your new concept mathematics and general mathematics.

Example 7: Cube Roots

Question: Make r the subject of the formula:

V =

4

3

πr³

Solution:

1. Multiply both sides by 3:
   3V = 4πr³
2. Divide both sides by 4π:
   r³ =

   3V

   4π

3. Take the cube root of both sides:
   r = ³√(

   3V

   4π

   )

✅ Answer: r = ³√(3V / 4π)

Example 8: Finding a Reciprocal Subject

Question: Make f the subject of the formula:
1f = 1u + 1v
Solution:

Find a common denominator for the right side:
1f = v + uuv
Invert both fractions to solve for f:
f = uvv + u

✅ Answer: f = uv / (v + u)

Example 9: Factoring with Square Roots
Question: Make k the subject of the formula:
m = √(k - xk + y)

Solution:
Square both sides:
m² = k - xk + y
Multiply by (k + y):
m²(k + y) = k - x
Open the  brackets:
m²k + m²y = k - x
Collect k terms on one side:
m²y + x = k - m²k
Factor out k:
m²y + x = k(1 - m²)
Divide to isolate k:
k = m²y + x1 - m²

✅ Answer: k = (m²y + x) / (1 - m²)

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The last example is what you must focus well because the variables are much, then look how we can solve this.

Example 10: Multi Variable Algebraic Restructuring
Question: Make a the subject of the formula:

S = n2[2a + (n - 1)d]

Solution:

Multiply both sides by 2:
2S = n[2a + (n - 1)d]
Divide both sides by n to open the first bracket:
2Sn = 2a + (n - 1)d
Subtract (n - 1)d from both sides:
2Sn - (n - 1)d = 2a
Divide the entire expression by 2:
a = Sn - (n - 1)d2

✅ Answer: a = (S / n) - [(n - 1)d / 2]

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Frequently Asked Questions (FAQ)

1. What does it mean to change the subject of a formula?

In this case changing the subject means rearranging an algebraic equation to separate one specific variable by itself on one side of the equal sign (usually the left side). This means, all the unwanted must be separated away from the appointed one.

2. What is the golden rule for rearranging formulas?

The golden rule is total balance for separation. Whatever mathematical operation you perform on one side of the equation (like adding, multiplying, or taking a root even dividing), you must perform the exact same operation on the other side.

3. How do you change the subject if the variable appears twice?

When the target variable is in two different places, collect all terms containing that variable on one side of the equals sign, move everything else to the other side, and then use factorization to separate it.

4. How do you remove a square root when rearranging equations?

To remove a square root, isolate the square root expression on its own side first, then square the entirety of both sides of the formula.

Class Work 

(1) Make p subject in the equation 

Qp + Rt = 3x - 7

(2) Make S subject in the equation 

  Pr - q.            Qw + S

--------------- =  -------------------

Sp + u.           Tu

  

I really hope this guide  believed you will be able to solve subject of the formula, this all about knowing different formulae and how to manipulate them well. I will advise you to make used of your mathematics text books all the time and revisit this Page. If you're missing some part put your comments in the comments box. Have a nice mathematics time.