Download C10 - Understand and use given formulae

Tutor’s Toolkit: Application of Number
Carrying Out Calculations
C10 Understand and use given formulae
Useful Web Links:
Learn.co.uk: Maths: Using formulae
http://www.learn.co.uk/default.asp?WCI=Unit&WCU=36017
A small, but neat, introduction to using formulae.
The College Online: Mathematics
http://dspace.dial.pipex.com/town/way/po28/maths/formulae.htm
This article looks at famous mathematical formulae.
C10.1
Using percentages
Scope:
Students need to be able to:



calculate using a given formula,
make a reverse calculation using a given formula,
use negative numbers in formulae.
What students need to know:
Formulae
A formula is a rule which describes how to make a calculation for specific quantities. For
example, to work out the area of a rectangle, you multiply the length by the width.
A formula for this could look like:
A = lw. The l stands for the length and the w stands for the width.
In a formula, add (+) and subtract (–) are shown normally. However, if two things need to be
multiplied, they are written next to each other. This means that lw means l  w. Also, if two
things need to be divided, we write them like a fraction. So,
l
means l  w. (You should
w
read this as “l over w”).
NUMBER TOOLKIT
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CARRYING OUT CALCULATIONS: Understand and use given formulae
BBC Key Skills: http://www.bbc.co.uk/keyskills
© BBC 2004
Calculate using a given formula
Using a basic formula, you just replace the letters with the numbers given.
Example Question:
A painter is using a rule of thumb for working out the cost of painting a room. The formula
used is: C = 2.4(l + w) + 8.
C is the cost in £ and l and w are the length and width of the room in metres.
What would be the cost for a room 3.5m wide and 4.5m long?
Solution:
The information tells us that l = 4.5 and w = 3.5.
The formula is C = 2.4(l + w) + 8
Replace l with 4.5 and w with 3.5 in the formula.
We have:
C = 2.4(4.5 + 3.5) + 8
So,
C = 2.4  8 + 8
C = 19.2 + 8
C = 27.20
That is:
C = £27.20
NUMBER TOOLKIT
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CARRYING OUT CALCULATIONS: Understand and use given formulae
BBC Key Skills: http://www.bbc.co.uk/keyskills
© BBC 2004
Make a reverse calculation using a given formula
Sometimes the quantity at the beginning of the formula needs to be worked out. That means
reversing the calculation.
Example Question:
The same painter has told a client that a room that is 6m long will cost £30 to paint. How
wide would the room be?
The formula used is still: C = 2.4(l + w) + 8.
C is the cost in £ and l and w are the length and width of the room in metres.
Solution:
The information tells us that C = 30 and l = 6.
Using the formula, replace C with 30 and l with 6.
We have:
30 = 2.4(6 + w) + 8
So:
30 = 2.4  6 + 2.4w + 8
30 = 14.4 + 2.4w + 8
30 = 22.4 + 2.4w
30 – 22.4 = 2.4w
7.6 = 2.4w
w = 7.6  2.4
w = 3.17 (using a calculator)
That is:
w = 3.2m (to 1 decimal place)
Using negative numbers in formulae
Sometimes negative numbers are used in formulae. It is important to be clear with the
negative sign (smaller than a ‘minus’ and raised a little). Then the normal rules for arithmetic
using negative numbers should be used (For further information, refer to Interpreting
Information, Section I3.)
NUMBER TOOLKIT
Page 3 of 3
CARRYING OUT CALCULATIONS: Understand and use given formulae
BBC Key Skills: http://www.bbc.co.uk/keyskills
© BBC 2004