Changing the Subject of a Formula is also similar to changing the equation by considering one variable as a subject. Perform required operation on both sides of the equation and find the Subject of a Formula. Get Worksheet on Changing the Subject of a Formula to learn the different techniques and apply them to Formula and Framing the Formula problems. Also, you can know the tricks to apply while writing the exams to get good marks.
How to Change the Subject of a Formula?
Practice all the questions given below and test your preparation level. Students can easily improve their knowledge of lagging concepts by practicing the problems given here. A clear explanation is also given for every problem on Formula Worksheets.
Changing the Subject of a Formula Solved Examples
1. Change the subject as indicated in the following formulas.
(a) A = l × b; make l as subject
(b) L = C.P. – S.P; make C.P. as subject
(c) V = u + ft; make f as subject
(d) S = D/T; make T as subject
(e) V = πrh²; make h as subject
(f) C = 2πt; make t as subject
(g) P = 2 (l + b); make b as subject
(h) S = n/2 (a + l); make n as subject
(i) A = P {1 + (Rn/100)}; make R as subject
(j) 1/x = y + z/y + 1; make z as subject
Solution:
(a) Given that A = l × b; make l as subject
A = l × b
Divde b on both sides
A/b = (l × b)/b
A/b = l
The final answer is l = A/b.
(b) Given that L = C.P. – S.P; make C.P. as subject
L = C.P. – S.P
Move S.P to the left side and add it to the L
C.P. = L + S.P
The final answer is C.P. = L + S.P
(c) Given that V = u + ft; make f as subject
V = u + ft
Subtract u on both sides
V – u = u – u + ft
V – u = ft
Move t to the left side and divide with (V – u)
(V – u)/t = f
The final answer is f = (V – u)/t
(d) Given that S = D/T; make T as subject
S = D/T
Move T to the left side and multiply it with S
ST = D
Now, S to the right side and divide it with D
S = D/T
The final answer is S = D/T
(e) Given that V = πrh²; make h as subject
V = πrh²
Divide πr on both sides
V/πr = πrh²/πr
V/πr = h²
h = √V/πr
The final answer is h = √V/πr
(f) Given that C = 2πt; make t as subject
C = 2πt
Move 2π to the left side and divide it with C
C/2π = t
The final answer is t = C/2π
(g) Given that P = 2 (l + b); make b as subject
P = 2 (l + b)
Move 2 to the left side and Divide it with P.
P/2 = l + b
Subtract l on both sides
P/2 – l = l – l + b
P/2 – l = b
The final answer is b = P/2 – l
(h) Given that S = n/2 (a + l); make n as subject
S = n/2 (a + l)
Move 2 to the left side and Multiply it with S.
2S = n (a + l)
Move (a + l) to the left side and divide it with 2S
n = 2S/(a + l)
The final answer is n = 2S/(a + l)
(i) Given that A = P {1 + (Rn/100)}; make R as subject
A = P {1 + (Rn/100)}
Move P to the left side and Divide it with A.
A/P = 1 + (Rn/100)
Move 1 to the left side and Subtract it with A/P.
A/P – 1 = Rn/100
Move 100 to the left side and Multiply it with A/P – 1.
100(A/P – 1) = Rn
Move n to the left side and Divide it with 100(A/P – 1).
{100(A/P – 1)}/n = R
The final answer is R = {100(A/P – 1)}/n
(j) Given that 1/x = y + z/y + 1; make z as subject
1/x = y + z/y + 1
Move 1 to the left side and Subtract it with 1/x.
1/x – 1 = y + z/y
Move y (addition) to the left side and Subtract it with 1/x – 1.
(1/x – 1) – y = z/y
Move y to the left side and Multiply it with (1/x – 1) – y.
y[(1/x – 1) – y] = z
The final answer is z = y[(1/x – 1) – y]
2. Change the subject of the below-given formulas.
(a) y = mx + c; make m as subject
(b) D = b² – 4ac; make b as subject
(c) T = 2π √(l/g); make l as subject
(d) S = ut + 1/2 gt²; make u as subject
(e) C = 2πr (h + x); make r as subject
(f) h² = p² + b²; make p as subject
(g) S.P. = {(100 + G%) C.P.}/100; make G% as subject
(h) HM = 2ab/(a + b); make M as subject
(i) I = (P × R × T)/100; make P as subject
(j) A = 1/2 (l₁ + l₂) h; make l₁ as subject
Solution:
(a) Given that y = mx + c; make m as subject
y = mx + c
Subtract con both sides
y – c = mx + c – c
y – c = mx
Move x to the left side and divide it with y – c
(y – c)/x = m
The final answer is m = (y – c)/x
(b) Given that D = b² – 4ac; make b as subject
D = b² – 4ac
Move 4ac to the left side and add it to the D
D + 4ac = b²
Apply square root on both sides
√(D + 4ac) = √b²
√(D + 4ac) = b
The final answer is b = √(D + 4ac)
(c) Given that T = 2π √(l/g); make l as subject
T = 2π √(l/g)
Move 2π to the left side and divide it with T
T/2π = √(l/g)
Apply square on both sides
(T/2π)² = (√(l/g))²
(T/2π)² = l/g
Move g to the left side and multiply it with (T/2π)²
g(T/2π)² = l
The final answer is l = g(T/2π)²
(d) Given that S = ut + 1/2 gt²; make u as subject
S = ut + 1/2 gt²
Move 1/2 gt² to the left side and subtract it from S
S – 1/2 gt² = ut
Divide t on both sides
(S – 1/2 gt²)/t = ut/t
(S – 1/2 gt²)/t = u
The final answer is u = (S – 1/2 gt²)/t
(e) Given that C = 2πr (h + x); make r as subject
C = 2πr (h + x)
Move (h + x) to the left side and divide it with C
C/(h + x) = 2πr
Move 2π to the left side and divide it with C/(h + x)
C/2π(h + x) = r
The final answer is r = C/2π(h + x)
(f) Given that h² = p² + b²; make p as subject
h² = p² + b²
Move b² to the left side and subtract it from h²
h² – b² = p²
Apply square root on both sides
√(h² – b²) = √(p²)
√(h² – b²) = p
The final answer is p = √(h² – b²)
(g) Given that S.P. = {(100 + G%) C.P.}/100; make G% as subject
S.P. = {(100 + G%) C.P.}/100
Move 100 to the left side and multiply it with S.P.
S.P. × 100 = (100 + G%) C.P.
Move C.P. to the left side and divide it with S.P. × 100
(S.P. × 100)/C.P. = 100 + G%
Move 100 to the left side and subtract it from (S.P. × 100)/C.P.
(S.P. × 100)/C.P. – 100 = G%
The final answer is G% = (S.P. × 100)/C.P. – 100
(h) Given that HM = 2ab/(a + b); make M as subject
HM = 2ab/(a + b)
Move H to the right side and divide it with 2ab/(a + b)
M = 2ab/H(a + b)
The final answer is M = 2ab/H(a + b)
(i) Given that I = (P × R × T)/100; make P as subject
I = (P × R × T)/100
Move 100 to the left side and multiply it with I
I × 100 = PRT
Move RT to the left side and divide it with 100I
100I/RT = P
The final answer is P = 100I/RT
(j) Given that A = 1/2 (l₁ + l₂) h; make l₁ as subject
A = 1/2 (l₁ + l₂) h
Move 1/2.h to the left side and divide it with A
2A/h = l₁ + l₂
Move l₂ to the left side and subtract it from 2A/h
2A/h – l₂ = l₁
The final answer is l₁ = 2A/h – l₂