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,  means l  w. (You should read this as “l over w”).

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

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.)