Functional Skills Maths
Using reverse calculations and
rearranging formulae
September 2012. Kindly contributed by Mrs Rajal Naik, the Manchester College.
Search for Rajal on www.skillsworkshop.org
Please refer to the download page for this resource on skillsworkshop.org for
detailed curriculum links and related resources. The formula cards mentioned in this
PPT are available separately.
Functional Maths - Coverage & range statements
L1 Use simple formulae expressed in words for one- or two-step operations
L2 Understand and use simple formulae and equations involving one- or two-step operations
Functional Maths - Process skills
L1[2] Use appropriate checking procedures [and evaluate their effectiveness ]at each stage
Adult Numeracy
N1/L2.4 Evaluate expressions and make substitutions in given formulae in words and symbols to produce results
N1/L2.2 Carry out calculations with numbers of any size using efficient written and mental methods (c) Know and use
strategies to check answers
References: Excellence Gateway (2009), Skills for Life, Core Curriculum http://www.excellencegateway.org.uk/sflcurriculum
Ofqual (2009), Functional Skills criteria for English, Mathematics and ICT
http://www.ofqual.gov.uk/qualification-and-assessment-framework/89-articles/238-functional-skills-criteria
Rearranging Formulas and
the use of Reverse
Calculations
by Mrs Rajal Naik
Introduction
In functional skills exams you may be asked to
 check your own answers using reverse
calculations
 make any part of the formula the subject
The following presentation will demonstrate
both of these topics.
Terminology
 What
is the subject of the
formula?
 This is the main term you are
trying to find the value for.
E.g. in area = length x width, area
is the subject.
Finding a Part of the Formula

When we want to find a part of the formula e.g.
in A=L x W, we need to rearrange it, to find the
length i.e. make the length the subject of the
formula , we do this in the following way.
AREA = LENGTH
X
WIDTH
Now use the cards to work out the Area or perimeter of the rectangles or
squares.
What is reverse calculation



Reverse calculations are used to check your
own answer, by reversing each step in the
calculation.
When you move a positive value to the other
side of the equals sign, the value becomes
negative and vice versa.
When you move a multiplication to the other
side of it, the value becomes a division and vice
versa.
Rules when rearranging the formula
( reverse calculation - easy method)
The following examples demonstrate this.
Remember both side of the equation must
balance at the end, If your answer is correct.
48
8
= 6×
35 - 9 = 26
=
+
Rules related to rearranging the formula
(the harder but correct method)

When we rearrange a formula, we can work out what
the reversed value of each bit of the sum will be, by
either adding, taking away, dividing or multiplying both
sides of the formula to preserve the equation. The
following formula for circumference demonstrates this,
when making the d, the diameter the subject.
C = πd
÷ both sides by π
C
÷ π
π
So
C =d
π
Cancel each other out
Now try these



Reverse the following equations to make 5 the
subject in both of the following equations.
1) a) 7 x 5 = 35, so 5 =?
b) 30 ÷ 5 = 6, so 5=?
2) Area = length x width. If area to be plastered
is 38m2 and length of plasterboard is 9.5 m
what is the width of the plasterboard?
Rearrange the formula to find the width.

Use the cards to help you rearrange the formula.