9

Before you start this chapterPut your calculator away!1 Work out

a 24 4 (3 3 4) 1 5 b 4 3 6 2 32 c 12 2 (23 1 3)

2 Work outa 122 b 202 c 400 3 1.6 d 260 ____

13

Estimation and currency conversion

ObjectivesThis chapter will show you how to• check and estimate answers to problems D C

• estimate answers to problems involving decimals D C

• recall integer squares from 2 3 2 to 15 3 15 to make mental estimates of the answers to calculations D C

• select and use suitable strategies and techniques to solve problems and word problems D C

This chapter is about maths strategies and real-life applications of maths.

Currencies are bought and sold on the foreign exchange market. In 2001, an estimated $1.2 trillion was traded on the foreign exchange market each day!

150 Estimation and currency conversion150 Estimation and currency conversion

Number skills: multiplying and dividingP

1 Work out

a 36 3 24 b 108 3 72 c 486 4 27 d 1008 4 36

2 Prize money of £29 805 is shared equally between 15 people. How much does each person receive?

3 Two consecutive numbers have a product of 182 and a sum of 27. What are the two numbers?

4 You are told that 87 3 132 5 11 484.

Work out 11 484 ______ 870

.

5 What is the remainder when 258 is divided by 19?

6 475 football supporters are travelling to a match by coach. Each coach seats 45 people.

a How many coaches will be required?

b How many spare seats will there be?

1 Arrange each set of numbers in size order, with the smallest first.

a 2, 0, 24, 3, 26 b 211, 219, 23, 27, 29

2 The temperature in Istanbul is 3°C. The temperature in Moscow is 211°C. What is the temperature difference between these two cities?

3 Copy and complete these calculations.

a 4 1 5 27 b 28 1 5 2 c 6 1 5 22 d 2 24 5 7

4 Copy and complete these calculations.

a 6 3 5 218 b 24 4 5 23 c 3 27 5 21

d 240 4 5 210 e 4 25 5 29 f 22 3 23 3 2 5 g 3 4 3 23 5 236 h 22 3 3 23 5 230

5 What do you need to multiply 29 by to get 72?

6 Find two different pairs of numbers that have a difference of 7 and a product of 212.

FUNC

TIONALFUNC

TION

AL

Number skills: negative numbers

AO2

AO3

1519.1 Estimation

Exercise 9A1 Estimate the answer to each of these calculations.

a 436 1 394 _________ 109

b 27 3 105 ________ 55

c 40.26 3 8.49 ___________ 16.4

d 324 3 7.63 __________ 75.9

2 Estimate the answer to each of these calculations.

a 5.4 3 19.8 _________ 4.3 2 2.2

b 17.32 1 14.29 ____________ 4.08 2 1.79

c 584 1 829 _________ 749 2 485

d 294 1 149 _________ 842 2 385

9.1 Estimation

Skills check1 Work out

a 32 3 (11 2 9) b 39 3 100 c 30 4 0.12 Round each of these numbers to one significant figure.

a 324 b 2.8 c 0.0605

LWhy learn this?

You can use estimation to check that you have

enough materials to complete a DIY job.

ObjectivesD C Check and estimate answers to problems

D C Estimate answers to problems involving decimalsD C Make estimates and approximations of calculations

EstimatingEstimating the answer to a calculation gives you an approximate answer.

You can use estimation to check that an answer is about right.

To estimate

• round all the numbers to one significant figure• do the calculation using these approximations.

Keywordsestimate, approximate, round, significant figure

Use approximation to estimate the answer to each of these calculations.

a 119 3 5.4 _________ 46

b 5.3 3 19.8 _________ 6.2 2 1.7

c 560 3 5.45 __________ 0.534

Example 1

a 119 3 5.4 ___________ 46

100 3 5 _________ 50 5 500 _____ 50 5 10

b 5.3 3 19.8 ____________ 6.2 2 1.7 5 3 20 ________ 6 2 2 5 100 _____ 4 5 25

c 560 3 5.45 ____________ 0.534 600 3 5 _________ 0.5 5 3000 ______ 0.5 5 6000‘’ means ‘is approximately equal to’.

119 rounded to 1 s.f. is 100.5.4 rounded to 1 s.f. is 5.46 rounded to 1 s.f. is 50.

DC

D

152 Estimation and currency conversion

3 A litre of matt emulsion paint will cover an area of about 15.5 m2.Rashid needs to paint a room with a total wall area of 645 m2.

a Which is the best approximate calculation to use for this problem?A 600 4 20 B 600 4 15 C 600 4 10

Give a full reason for your answer.

b Use estimation to decide how many litres of paint Rashid will need for two coats.

4 Pepe is on his way home. He has a further 84 miles to travel.His car has 14.8 litres of fuel remaining.Pepe’s car does 5.35 miles per litre of fuel.Use estimation to decide whether Pepe has enough fuel to get home.

5 Look at this calculation.

1.8 3 584.2 __________________ 7.43 1 84.89 1 7.68

Steven and Dirk use calculators to work it out.Steven gets an answer of 10.52. Dirk gets 7.04.Use approximation to decide who is more likely to be correct.

6 Estimate the value of each of these calculations.

a 394.25 3 22 ___________ 83.6 2 37.25

b 3 3 584.7 ___________________ (39.25 1 18.5) 3 10.4

c 75.5 3 32.6 ____________________ (527.5 1 149.25) 3 7.6

7 Use approximation to estimate the value of each of these calculations.

a 325 3 4.34 __________ 0.237

b 26.79 __________ 3.51 3 0.48

c 5.62 3 478 ___________ 64.5 3 0.527

8 Which is the better approximation for this calculation?

7.252 ___________

1.86 3 12.42

A 72 ______

2 3 12 B 72

______ 2 3 10

Give a reason for your answer.

9 Use approximation to estimate the value of 9.47 3 4.82 __________ 2.82

10 Estimate the answer to each of these calculations.

a 19.5 3 8.3 _________ 0.53

b 84.9 3 3.3 _________ 0.13

c 98.6 1 9.6 _________ 0.17

d 98.6 3 9.6 _________ 0.17

FUNC

TIONALFUNC

TION

AL

FUNC

TIONALFUNC

TION

AL

C

AO2

C

AO3

C

C

AO2

C

1539.2 Conversions

Exercise 9B1 The exchange rate from pounds to CAN$ is £1 5 CAN$2.

Convert each of these sums of money into CAN$.

a £300 b £930 c £8250 d £15.75

2 The currency exchange rate between Swedish kronor and pounds is £1 5 11 kronor. Convert each of these sums of money into pounds.

a 198 kronor b 253 kronor c 385 kronor d 814 kronor

3 Harry is going to Mexico.He wants to change £275 into pesos.The exchange rate is 19 pesos for £1.How many pesos will Harry get?

FUNC

TIONALFUNC

TION

AL

9.2 Conversions

Skills check1 Work out

a 480 4 10 b 326 3 20 c 30 3 1.52 Work out

a 23 3 19 b 40 3 1.6 c 384 4 16

Why learn this?The exchange rate

lets you work out how many euros you can

get for your pounds.

ObjectivesD C Convert between different currencies

Currency conversionMost countries in the world have their own currency. An exception is the eurozone, where the euro is the single currency. The eurozone covers most of Europe apart from the UK.

To convert one currency to another, you need to know the exchange rate.

The exchange rate tells you what one unit of currency is equal to in another country’s currency.

Every currency has an exchange rate with all other currencies.

You either multiply or divide by the exchange rate depending on whether you are converting to or from the given currency.

Keywordscurrency, exchange rate

Use the exchange rate £1 5 US$1.6 to convert

a £3 into US dollars b US$32 into pounds sterling.

Example 2

a £3 5 3 3 1.6 5 US$4.80

b US$32 5 32 4 1.6 5 £20

Each £1 is worth US$1.6 so you convert pounds to dollars by multiplying the number of pounds by 1.6.

To convert dollars into pounds you divide the number of dollars by 1.6.

US$ is an abbreviation for United States dollars.

Always give answers to an appropriate degree of accuracy.

D

D

154 Estimation and currency conversion

4 Steven went to Thailand on holiday.The exchange rate was £1 5 50 baht.Steven hired a bicycle for 875 baht.Find the price of the bicycle hire in pounds.

5 Yossi changed £1250 into Israeli shekels.He got 7500 shekels.What was the exchange rate?

6 An American tourist in Edinburgh wants to buy a tartan blanket.The blanket has a price tag of £200.The exchange rate is £1 5 US$1.6.a What is the price of the blanket in dollars?A week later the same blanket costs US$310.b What is the new exchange rate?

7 A factory orders 5000 component parts from a company in Jamaica.The parts will be available in six months at a cost of J$192 000.At the time of the order the Jamaican dollar is trading at J$120 to £1.a How much does the company need to budget for, to cover the

cost of the order in pounds?Six months later the exchange rate goes up to J$125 to £1.b What is the new cost of the order?

8 Pepe is going to Barbados. Changing from £ £1 5 $2.5

Changing into £ £1 5 $3He needs to change some money into Barbadian dollars.The exchange rates are as shown.

Banks buy and sell currency at different rates in order to make a profit.

Pepe changes £50 into Barbadian dollars. a How much does he get?On his return Pepe has $12 left.b How much will he get if he changes

this to pounds sterling?

9 This table shows the exchange rates between pounds sterling and other currencies.

Japan (yen) Denmark (kroner) Australia (AUS$) Gambia (dalasi)

Changing from £ £1 5 142 yen £1 5 8 kroner £1 5 AUS$2 £1 5 35 dalasi

Changing into £ £1 5 154 yen £1 5 9 kroner £1 5 AUS$2.5 £1 5 40 dalasi

a Dirk goes to Denmark. He changes £800 into Danish kroner.

i How many kroner will Dirk get?During his holiday Dirk spends 4240 kroner.When he returns Dirk changes his remaining kroner into pounds sterling.

ii How much will Dirk get?

b Elin Haf has returned from Gambia. She changes her remaining dalasi and gets £23. How many dalasi did Elin Haf return with?

10 In London a pair of designer jeans is priced at £120.In New York the jeans can be bought for US$176.In Russia the jeans can be bought for 6750 roubles.Where are the jeans the cheapest?Use these exchange rates: £1 5 US$1.6 and £1 5 45 roubles.

FUNC

TIONALFUNC

TION

AL

FUNC

TIONALFUNC

TION

AL

FUNC

TIONALFUNC

TION

AL

FUNC

TIONALFUNC

TION

AL

FUNC

TIONALFUNC

TION

AL

FUNC

TIONALFUNC

TION

AL

D

C

AO2

C

C

AO2

C

155Chapter 9 Summary

Review exercise1 Estimate the value of 385 3 54 ________

1010 [2 marks]

2 Find an approximate value for 39 3 196 ________ 83

Show all your working. [2 marks]

3 The currency exchange rate between South African rands and pounds is £1 5 12 rand. Convert each of these sums of money into pounds.a 156 rand b 336 rand c 936 rand d 1506 rand [4 marks, 1 mark each]

4 Samuel is going on holiday to the Philippines.The currency of the Philippines is the peso.The exchange rate is £1 5 65 pesos.a Samuel changes £50 into pesos.

How many pesos does Samuel receive? [2 marks]

b After the holiday Samuel has 585 pesos remaining.Convert 585 pesos into pounds. [2 marks]

5 A jacket in Cardiff costs £80.The same jacket in Mexico costs 999 pesos.The exchange rate is £1 5 18 pesos.In which country is the jacket cheaper and by how much? [4 marks]

6 Look at this calculation. 34.96 __________ 3.61 3 0.54

Pepe, Daniel and Xabi use calculators to work it out.Pepe gets an answer of 179.3, Daniel gets 17.93 and Xabi gets 5.23.Use approximation to decide who is most likely to be correct. [3 marks]

7 Use approximation to estimate the value of 178 3 8.49 __________ 0.425

[3 marks]

8 Use approximation to estimate the value of 5.26 3 27.6 __________ 4.72 [3 marks]

9 In Bahrain a bottle of water costs 2.5 dinar when the exchange rate is 0.5 dinar to the pound.The same bottle of water costs £2.75 in Birmingham.In Mexico the bottle of water costs 27 pesos when the exchange rate is 18 pesos to the pound.In which country is the bottle of water cheapest? [3 marks]

FUNC

TIONALFUNC

TION

AL

FUNC

TIONALFUNC

TION

AL

FUNC

TIONALFUNC

TION

AL

C

AO2

C

In this chapter you have learned how to

• check and estimate answers to problems D C• estimate answers to problems involving

decimals D C

• make estimates and approximations of calculations D C

• convert between different currencies D C

Chapter summary

D

AO2

D