[...]... of 2.00000 01 © 19 93, 2003 Mike Rosser To divide by a fraction one simply multiplies by its inverse Example 2 .16 3÷ 6 1 = 3 × = 18 6 1 Example 2 .17 44 49 11 7 77 44 8 1 = × = × = = 38 2 ÷ 49 7 8 1 2 2 7 Test Yourself, Exercise 2.4 1 2 3 4 5 6 7 8 9 10 2.5 1 1 1 + + = 6 7 8 3 2 1 + − = 7 9 4 2 60 21 × × = 5 7 15 4 24 ÷ = 5 19 2 2 4 1 = 7 3 1 4 1 2 +3 − = 6 4 5 1 1 3 +4 = 4 3 1 1 8 ÷2 = 2 6 1 1 3 20 −... section of its demand schedule Solution Price fall is 15 0 and quantity rise is 15 0 Therefore using the concept of arc elasticity 15 0 15 0 550 1 11 11 150 1, 350 e = 600 + 750 = × = × = = 15 0 15 0 1, 350 15 0 27 1 27 350 + 200 550 £ Price 18 15 12 9 6 3 D 0 20 40 Figure 2.2 © 19 93, 2003 Mike Rosser 60 80 10 0 12 0 Quantity Test Yourself, Exercise 2.5 1 2 3 With reference to the demand schedule in Figure 2.2... Figure 2.3 £ Price 15 10 5 D 0 40 80 12 0 Quantity Figure 2.3 4 The data below show the quantity demanded of a good at various prices Calculate the arc elasticity of demand for each £5 increment along the demand schedule Price £40 Quantity 0 2.6 £35 50 £30 10 0 £25 £20 15 0 200 15 10 250 300 Decimals Decimals are just another way of expressing fractions 0 .1 = 1/ 10 0. 01 = 1/ 100 0.0 01 = 1/ 1,000 etc Thus 0.234... the denominator of the fraction and then adding Example 2 .11 1 1×5 3 5 3 8 3 = + = + = 5 5 5 5 5 5 Example 2 .12 17 8 51 − 8 43 1 3 24 = − = = =2 2 − 7 63 7 21 21 21 21 Multiplication of fractions is carried out by multiplying the numerators of the different fractions and then multiplying the denominators © 19 93, 2003 Mike Rosser Example 2 .13 15 3 5 × = 8 7 56 The exercise can be simplified if one first... overdraft of £ 210 What is their total bank balance? Solution total balance = 8 × (− 210 ) = − 1, 680 Example 2.28 −32 24 10 3 2 6 3 24 ÷ = × = × = =− −5 10 −5 −32 1 −4 −4 2 Test Yourself, Exercise 2.7 1 2 3 4 5 6 7 8 Subtract−4 from−6 Multiply−4 by 6 −48 + 6 − 21 + 30 = −0.55 + 1. 0 = 1. 2 + (−0.65) − 0.2 = −26 × 4.5 = 30 × (4 − 15 ) = (−60) × (−60) = © 19 93, 2003 Mike Rosser 1 9 4 × − = 4 7 5 4 10 ( 1) 30 +... there are no physical analogies for powers other than 2 and 3, in mathematics one can encounter powers of any value Example 2.30 12 4 = 12 × 12 × 12 × 12 = 20,736 12 5 = 12 × 12 × 12 × 12 × 12 = 248,832 etc To multiply numbers which are expressed as powers of the same number one adds all the powers together Example 2. 31 33 × 35 = (3 × 3 × 3) × (3 × 3 × 3 × 3 × 3) = 38 = 6,5 61 To divide numbers in terms... of It therefore usually helps if any large numbers in a fraction are ‘factorized’, i.e broken down into the smaller numbers that they area multiple of © 19 93, 2003 Mike Rosser Example 2.8 21 × 8 21 168 = = 10 4 13 × 8 13 In this example it is obvious that the 8s cancel out top and bottom, i.e the numerator and denominator can both be divided by 8 Example 2.9 12 × 10 1 120 = = 8 960 12 × 8 × 10 Addition... necessary to get the required denominator For example, to convert 1/ 6 to a fraction with 12 as its denominator, one simply multiplies top and bottom by 2 Thus 1 2 1 2 = = 6 2×6 12 Example 2 .10 5 2 5 2+5 7 1 + = + = = 6 12 12 12 12 12 It is necessary to convert any numbers that have an integer (i.e a whole number) in them into fractions with the same denominator before carrying out addition or subtraction... 12 , (d) 12 and 15 , and (e) 15 and 18 A city bus service charges a uniform fare for every journey made When this fare is increased from 50p to 1 the number of journeys made drops from 80,000 a day to 40,000 Calculate the arc elasticity of demand over this section of the demand schedule for bus journeys Calculate the arc elasticity of demand between (a) £5 and 10 , and (b) between 10 and 15 , for. .. Example 2.23 Express 0.01p as a decimal fraction of 1 Solution 1p = £0. 01 Therefore 0.01p = £0.00 01 In mathematics a decimal format is often required for a value that is usually specified as a percentage in everyday usage For example, interest rates are usually specified as percentages A percentage format is really just another way of specifying a decimal fraction, e.g 62% = 62 = 0.62 10 0 and so percentages . variables 10 .5 Total differentials and total derivatives 11 Constrained optimization 11 .1 Constrained optimization and resource allocation 11 .2 Constrained optimization by substitution 11 .3 The. calculus 12 .1 Overview 12 .2 The chain rule 12 .3 The product rule 12 .4 The quotient rule © 19 93, 2003 Mike Rosser 12 .5 Individual labour supply 12 .6 Integration 12 .7 Definite integrals 13 Dynamics. (Adobe eReader Format) © 19 93, 2003 Mike Rosser Contents Preface Preface to Second Edition Acknowledgements 1 Introduction 1. 1 Why study mathematics? 1. 2 Calculators and computers 1. 3 Using the