# Worksheet on Changing the Subject in an Equation or Formula | Rearranging Formulae Worksheet

Worksheet on Changing the Subject in an Equation or Formula is given here. Get all different problems and practice every problem to test your knowledge. Changing the Subject in an Equation or Formula Worksheet should be the first priority for every student to get good marks in the exam. Don’t waste your time by searching for the best resource to learn the change the subject of an equation concept. Refer to our Rearranging Formula Worksheets and have the best practice now.

1. Given M = 1/2 × a × b, when M = 65 and a = 10, find b?

Solution:

Given that M = 1/2 × a × b
To find b, rewrite the given equation by changing the subject to b.
M = 1/2 × a × b
Move 1/2 × a to the left side and divide it with M
2M/a = b
b = 2M/a.
Substitute M = 65 and a = 10 in the above equation.
b = 2(65)/10 = 130/10
b = 13

The final answer is b = 13.

2. Given L = 1/5 n²r when L = 30 and n = 5, find r?

Solution:

Given that L = 1/5 n²r
To find r, rewrite the given equation by changing the subject to r.
L = 1/5 n²r
Move 1/5 to the left side and multiply it with L.
5L = n²r
Move n² to the left side and divide it with 5L
(5L)/n² = r
r = (5L)/n²
Substitute L = 30 and n = 5 in the above equation.
r = 5 (30)/(5)²
r = 30/5 = 6
r = 6

The final answer is r = 6.

3. Given A = 7b² when A = 700, find b?

Solution:

Given that A = 7b²
To find b, rewrite the given equation by changing the subject to b.
A = 7b²
Move 7 to the left side and divide it with A
A/7 = b²
Apply square root on both sides.
√(A/7) = √(b²)
√(A/7) = b
b = √(A/7)
Substitute A = 700 in the above equation.
b = √(700/7)
b = √100
b = 10

The final answer is b = 10.

4. Given R = 2 (m + n) when m = 15 and R = 100, find n?

Solution:

Given that R = 2 (m + n)
To find n, rewrite the given equation by changing the subject to n.
R = 2 (m + n)
Move 2 to the left side and divide it with R
R/2 = m + n
Move m to the left side and subtract it with R/2
R/2 – m = n
n = R/2 – m
Substitute m = 15 and R = 100 in the above equation.
n = R/2 – m
n = (100/2) – 15
n = 50 – 15 = 35
n = 35

The final answer is n = 35

5. Given C = (S × 100)/(100 × g) find S when C= 140 and G = 5?

Solution:

Given that C = (S × 100)/(100 × g)
To find S, rewrite the given equation by changing the subject to S.
C = (S × 100)/(100 × g)
Move (100 × g) to the left side and multiply it with C
C(100 × g) = S × 100
Move 100 to the left side and divide it with 100
C(100 × g)/100 = S
Cg = S
S = Cg
Substitute C= 140 and G = 5 in the above equation.
S = Cg
S = 140(5)
S = 700

The final answer is S = 700

6. P = Q + R find R if P = 5700 and Q = 2640?

Solution:

Given that P = Q + R
To find R, rewrite the given equation by changing the subject to R.
P = Q + R
Move Q to the left side and subtract it from the P.
P – Q = R
R = P – Q
Substitute P = 5700 and Q = 2640 in the above equation.
R = P – Q
R = 5700 – 2640
R = 3060

The final answer is R = 3060

7. In F = 5/2 (T – 32) find F if T = 64?

Solution:

Given that F = 5/2 (T – 32)
To find F, rewrite the given equation by changing the subject to F.
F = 5/2 (T – 32)
Substitute T = 64 in the above equation.
F = 5/2 (T – 32)
F = 5/2 (64 – 32)
F = 5/2 (32)
F = 5 × 16 = 80
F = 80

The final answer is F = 80.

8. In Q = a × b × c find a if Q = 4000, b = 10, c = 10?

Solution:

Given that Q = a × b × c
To find a, rewrite the given equation by changing the subject to a.
Q = a × b × c
Move bc to the left side and divide it from Q
Q/bc = a
a = Q/bc
Substitute Q = 4000, b = 10, c = 10 in the above equation.
a = 4000/(10 × 10)
a = 4000/100 = 40

The final answer is a = 40

9. If G = 2k find k if G = 70?

Solution:

Given that G = 2k
To find k, rewrite the given equation by changing the subject to k.
G = 2k
Move 2 to the left side and divide it from G
G/2 = k
k = G/2
Substitute G = 70 in the above equation.
k = 70/2
k = 35

The final answer is k = 35.

10. If n + o + p = 190 find o if n = 60 and p = 55?

Solution:

Given that n + o + p = 190
To find o, rewrite the given equation by changing the subject to o.
n + o + p = 190
Move n + p to the right side and subtract it from 190.
o = 190 – (n + p)
Substitute n = 60 and p = 55 in the above equation.
0 = 190 – (60 + 55)
o = 190 – 115
o = 75

The final answer is o = 75

11. In a = x + yz find z if a = 54, x = 12 and y = 3?

Solution:

Given that a = x + yz
To find z, rewrite the given equation by changing the subject to z.
a = x + yz
Move x to the left side and subtract it from a
a – x = yz
Move y to the left side and divide it from a – x
(a – x)/y = z
z = (a – x)/y
Substitute a = 54, x = 12 and y = 3 in the above equation.
z = (54 – 12)/3
z = 42/3
z = 14

The final answer is z = 14.

12. In rs²/4π² = m, find the value of s if m = 49, r = 4?

Solution:

Given that rs²/4π² = m
To find s, rewrite the given equation by changing the subject to s.
rs²/4π² = m
Move 4π² to the right side and multiply it with m
rs² = m(4π²)
Move r to the right side and divide it from m(4π²)
s² = m(4π²)/r
Substitute m = 49, r = 4 in the above equation. π² = 9.8
s² = 49(4 × 9.8)/4
s² = 480.2
s = √480.2
s = 21.91

The final answer is s = 21.91(approximately)

13. In Y = 2x (m + n), find x if Y = 50, m = 6, n = 4?

Solution:

Given that Y = 2x (m + n),
To find x, rewrite the given equation by changing the subject to x.
Y = 2x (m + n)
Move 2(m + n) to the left side and divide it by Y
Y/(2(m + n)) = x
x = Y/(2(m + n))
Substitute Y = 50, m = 6, n = 4 in the above equation.
x = 50/(2(6 + 4))
x = 50/2(10)
x = 50/20
x = 5/2

The final answer is x = 5/2

14. In L = m/2 {2b + (m – 1) d}, find d when L = 125, m = 10, b = 2?

Solution:

Given that L = m/2 {2b + (m – 1) d}
To find d, rewrite the given equation by changing the subject to d.
L = m/2 {2b + (m – 1) d}
Move 2 to the left side and multiply it with the 2.
2L = m{2b + (m – 1) d}
Move m to the left side and divide it with the 2L.
2L/m = 2b + (m – 1) d
Move 2b to the left side and subtract it from the 2L/m.
2L/m – 2b = (m – 1) d
Move m – 1 to the left side and divide it from the 2L/m – 2b.
(2L/m – 2b)/(m – 1) = d
d = (2L/m – 2b)/(m – 1)
Substitute L = 125, m = 10, b = 2 in the above equation.
d = (2(125)/10 – 2(4))/(10 – 1)
d = (250/10 – 8)/9
d = (25 – 8)/9
d = 17/9

The final answer is d = 17/9.

15. If T = 2 πr, find r if T = 88, π = 22/7?

Solution:

Given that T = 2 πr
To find r, rewrite the given equation by changing the subject to r.
T = 2 πr
Move 2 π to the left side and divide it from the T
T/2 π = r
r = T/2 π
Substitute T = 88, π = 22/7 in the above equation.
r = 88/2(22/7)
r = 88/(44/7) = 88 × 7/44 = 2 × 7 = 14
r = 14

The final answer is r = 14.

16. If S = H × R, find H when S = 450 and R = 15?

Solution:

Given that S = H × R
To find H, rewrite the given equation by changing the subject to H.
S = H × R
Move R to the left side and divide it from the S
S/R = H
H = S/R
Substitute S = 450 and R = 15 in the above equation.
H = 450/15
H = 30

The final answer is H = 30.

17. In c = (l – m)/(l + m), if c = 3/7 and l = 10, find m?

Solution:

Given that c = (l – m)/(l + m)
To find m, rewrite the given equation by changing the subject to m.
c = (l – m)/(l + m)
Move l + m to the left side and multiply it with the c.
c(l + m) = l – m
cl + cm = l – m
Move cl to the right side and m to the left side with proper opertaions.
cm + m = l – cl
m(c + 1) = l (1 – c)
Move (1 + c) to the right side and divide it by l (1 – c)
m = l (1 – c)/(1 + c)
Substitute c = 3/7 and l = 10 in the above equation.
m = 10 (1 – 3/7)/(1 + 3/7)
m = 10 (0.4)
m = 4

The final answer is m = 4

18. If R = (A × G × E)/100, find G if R = 80, A = 400, E = 10?

Solution:

Given that R = (A × G × E)/100
To find G, rewrite the given equation by changing the subject to G.
R = (A × G × E)/100
Move 100 to the left side and multiply it with the R.
100R = A × G × E
Move AE to the left side and divide it with the 100R.
100R/AE = G
G = 100R/AE
Substitute R = 80, A = 400, E = 10 in the above equation.
G = 100(80)/(400)(10)
G = 8000/4000
G = 2

The final answer is G = 2.

19. In A/B = 100, find B  if A = 200?

Solution:

Given that A/B = 100
To find B, rewrite the given equation by changing the subject to B.
A/B = 100
Move B to the right side and multiply it by 100.
A = 100B
Move 100 to the left side and divide it with the A.
A/100 = B
B = A/100.
Substitute A = 200 in the above equation.
B = 200/100
B = 2

The final answer is B = 2.

20. In PQR/T = AB, find B. if P = 2, Q = 3, R = 4, T = 4, A = 2?

Solution:

Given that PQR/T = AB.
To find B, rewrite the given equation by changing the subject to B.
PQR/T = AB
Move A to the left side and divide it from the PQR/T.
B = APQR/T
Substitute P = 2, Q = 3, R = 4, T = 4, A = 2 in the above equation.
B = (4 × 2 × 3 × 4)/4 = 24
B = 24.

The final answer is B = 24.