If you are finding an easy and simple procedure to change the subject of a formula or equation then this is the correct page. Here, we have given a detailed explanation about how to change the subject of an equation in a printable worksheet. This free downloadable activity sheet on the Change of Subject of an Expression helps kids to practice in a fun learning way.

So, make use of this provided Changing the Subject of a Formula Worksheet with Answers pdf & try to solve basic to complex problems about the subject of the formula.

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## Free & Printable Worksheet on Changing the Subject of the Formula Pdf

**I.** Change the subject as bolded in the following formulas:

(i) V = u + ft, make **u** as subject

(ii) L = 2 (a + b), make **b** as subject

(iii) X = my + c, make **c** as subject

**Solution:**

(i) Given that V = u + ft

Subtract ft on both sides

V – ft = u + ft – ft

V – ft = u

Hence, the subject of the formula **u = V – ft.**

(ii) Given that L = 2 (a + b)

Divide 2 on both sides

\(\frac { L }{ 2 } \) = \(\frac { 2(a+b) }{ 2 } \)

a + b = \(\frac { L }{ 2 } \)

Subtract a on both sides

a + b – a = \(\frac { L }{ 2 } \) – a

b = \(\frac { L }{ 2 } \) – a

Hence, the subject of the formula **b = \(\frac { L }{ 2 } \) – a.**

(iii) Given that X = my + c

Subtract my on both sides

x – my = my + c – my

x – my = c

Hence, the subject of the formula **c = x – my.**

**II.** What is the subject in each of the following formulas or equations? Make the subject as shown in the question.

(i) If 3ay + 2b² = 3by + 2a², write the formula for **‘y’** in terms of a, b in the simplest form.

(ii) In the expression S= 2(lb + bh + lh) what is the subject. Write the formula with** ‘h’** as the subject.

**Solution:**

(i) Given expression is 3ay + 2b² = 3by + 2a²

After rearranging the given expression, we get the formula for y in terms of a, b;

*y = \(\frac { 2 }{ 3 } \)(a + b)*

(ii) Given that S= 2(lb + bh + lh)

Here, S is the subject but now we have to change the subject of a formula with h;

*h = s−\(\frac { 2lb }{ 2(b+l) } \)*

**III.** Make h the subject of the formula r = h(a-b). Find h with the help of known values r = 100, a=5, and b=3.

**Solution:**

Given r = h(a-b)

Divide (a-b) on both sides

\(\frac { r }{ a-b } \) = \(\frac { h(a-b) }{ a-b } \)

h = \(\frac { r }{ a-b } \)

Now, substitute the given values r = 100, a=5 and b=3 in the rearranged formula;

h = \(\frac { 100 }{ 5-3 } \)

h = \(\frac { 100 }{ 2 } \)

h = 50.

**IV.** Change x as the subject of the formula \(\frac { x }{ a } \) + \(\frac { y }{ b } \) = 1. Find x, when a=3, b=6, and y=9.

**Solution:**

Given that \(\frac { x }{ a } \) + \(\frac { y }{ b } \) = 1

x/a = 1 – \(\frac { y }{ b } \)

x = a(1- \(\frac { y }{ b } \))

x = a – \(\frac { a }{ b } \) x y, Here is the x formula.

Now, find the x value by substituting a=6, b=3, and y=9 in the formula;

x = 6 – \(\frac { 6 }{ 3 } \) x 9 = 6 – 2 x 9 = 6 – 18 = -12

**V.** In the formula x = y(1+zt), x is the subject of the formula. But find z as the subject when x=150, y=100, and t=2.

**Solution:**

Given formula is x = y(1+zt)

x = y + yzt

subtract y on both sides

x – y = yzt

z = x – \(\frac { y }{ yt } \), hence z is the subject of a formula.

Now, substitute the given values in the rearrange formula;

z = 150 – \(\frac {100}{ 100 } \) x 2 = \(\frac { 50 }{ 200 } \)

= \(\frac { 1 }{ 4 } \)

z = \(\frac { 1 }{ 4 } \).

**VI.** The formula PV = C where p is pressure and v is the volume of a gas and c is constant. If p = 2 when v = \(\frac { 5 }{ 2 } \), find the value of p when v = 4.

**Solution:**

Given that when p=2, v=\(\frac { 5 }{ 2 } \)

PV = C

2 x \(\frac { 5 }{ 2 } \) = C

C= 5

If v = 4, then

PV = C

P(4) = 5

P = \(\frac { 5 }{ 4 } \)