Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
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 Page 1 of 3 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 Page 2 of 3 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