# Rearrange Formulae

In this worksheet, students will learn how to rearrange formulae to find the given letter (subject) of the formula.

Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Simplify Algebraic Expressions to Maintain Equivalence

Difficulty level:

### QUESTION 1 of 10

Often you will be presented with a formula that will need to be manipulated in order to be useful to you.

You may have to rearrange the formula, making a different letter the subject.

Use the rules of equations (i.e. do the same to both sides) to achieve this.

Example:

The formula for finding a temperature in degrees centigrade from one in Fahrenheit is shown below.

Rearrange the formula to make F the subject.

Our aim is to get F on its own on the left-hand side.

Now it's over to you.

Rearrange the following formula to make w the subject.

v = lwh

(The current formula reads volume = length x width x height. We want to find out how to calculate width.)

l = vwh

w = vlh

w = v/lh

w = v/l/h

Rearrange the following formula to make u the subject.

v = u + at

u = v + at

u = v - at

u = v/at

u = vat

Rearrange the following formula to make a the subject.

v = u + at

a = v + ut

a = v - ut

a = (v - u)t

a = (v - u)/t

Rearrange the following formula to make c2 the subject.

a2 = b2 + c2

c² = a² + b²

c² = a² - b²

c² = b² - a²

c² = a² - b²

Rearrange the following formula to make c the subject.

a2 = b2 + c2

c² = a² + b²

c = √a² - b²

c = √(b² - a²)

c = √(a² - b²)

Rearrange the following formula to make h the subject.

A = ½bh

h = ½Ab

h = 2A/b

h = ½A/b

h = 2Ab

Rearrange the following formula to make h the subject.

P = 2(b + h)

h = ½Pb

h = 2P/b

h = ½P - b

h = 2P - b

Rearrange the following formula to make u the subject.

s = ut + ½at2

u = (s - ½at²)/t

u = v - at

u = st - 2at²

u = 2t² - ½at

Rearrange the following formula to make a the subject.

s = ut + ½at2

a = (s - ½at²)/t

a = sut²

a = st - 2ut²

a = 2(s - ut)/t²

Rearrange the following formula to make r the subject.

A = 4πr2

r = 4π/A

r = ½√π/A

r = √(A/4π)

r = √(4π/A)

• Question 1

Rearrange the following formula to make w the subject.

v = lwh

(The current formula reads volume = length x width x height. We want to find out how to calculate width.)

w = v/lh
EDDIE SAYS
v = lwh Divide both sides by lh: v/lh = w Then rearrange: w = v/lh How did you get on? As we're making width (w) the subject of the equation, we are rearrange the equation to find 'w'.
• Question 2

Rearrange the following formula to make u the subject.

v = u + at

u = v - at
EDDIE SAYS
v = u + at Subtract at from both sides: v - at = u Rearrange to get: u = v - at This is actually a physics equation which reads as: velocity - acceleration x time = initial velocity. The more you know!
• Question 3

Rearrange the following formula to make a the subject.

v = u + at

a = (v - u)/t
EDDIE SAYS
v = u + at Subtract u from both sides: v - u = at Divide by t: (v - u)/t = a Rearrange: a = (v - u)/t Remember, as we're making a the subject we must rearrange the equation so that the subject is at the beginning.
• Question 4

Rearrange the following formula to make c2 the subject.

a2 = b2 + c2

c² = a² - b²
EDDIE SAYS
a² = b² + c² Subtract b² from both sides: a² - b² = c² Rearrange: c² = a² - b² Are you beginning to feel more confident?
• Question 5

Rearrange the following formula to make c the subject.

a2 = b2 + c2

c = √(a² - b²)
EDDIE SAYS
a² + b² = c² Subtract b² from both sides: a² - b² = c² Square root both sides: √(a² - b²) = c Rearrange: c = √(a² - b²) When presented with x², we square root in order to find the value of x. You're making huge strides in progress maths-whiz and you're now halfway.
• Question 6

Rearrange the following formula to make h the subject.

A = ½bh

h = 2A/b
EDDIE SAYS
A = 1/2(bh) Double both sides: 2A = bh Divide by b: 2A/b = h Rearrange: h = 2A/b
• Question 7

Rearrange the following formula to make h the subject.

P = 2(b + h)

h = ½P - b
EDDIE SAYS
P = 2 (b+h) Halve both sides: P/2 = b + h Subtract b: h = ½P - b Rearrange: h = ½P - b
• Question 8

Rearrange the following formula to make u the subject.

s = ut + ½at2

u = (s - ½at²)/t
EDDIE SAYS
s = ut + 1/2 at² Subtract 1/2 at² from both sides: s - 1/2 at² = ut Divide by t: (s - 1/2 at²) / t = u Rearrange: u = (s - ½at²)/t This one was trickier so don't worry if you struggled the steps are the same, so take your time.
• Question 9

Rearrange the following formula to make a the subject.

s = ut + ½at2

a = 2(s - ut)/t²
EDDIE SAYS
s = ut + 1/2at² Subtract ut from both sides: s - ut = 1/2at² Double both sides: 2 (s - ut) = at² Divide by t²: 2 (s - ut)/t² = a Rearrange: a = 2(s - ut)/t² = a One more question to tackle! You've got this.
• Question 10

Rearrange the following formula to make r the subject.

A = 4πr2

r = √(A/4π)
EDDIE SAYS
A = 4πr² Divide both sides by 4π: A/4π = r² Square root: √(A/4π) = r Rearrange: r = √(A/4π) Great focus, that's another activity ticked off!
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