CHAPTER Ratios & Proportionsfjw.hct.ac.ae/student_info/foundations/bookm010/M010_textbook_unit... · a 40 = display 3 4 The ratio is ... The ratio is 5 : 3 Using a calculator to simplify

SUBTITLE | 151

Ratios &Proportions

CHAPTER

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MATHEMATICS FOUNDATION 1

Section 3.1Ratios and Proportions

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Order is important in ratios.

�EXAMPLE

Write the ratios.

(a) The ratio of teachers to students is 1 : 6 But the ratio of students to teachers is 6 : 1

(b) The ratio of cakes to candles is 1 : 8 The ratio of candles to cakes is 8 : 1

Ratios are used to compare the number of

objects in two or more groups.

The teacher has 3 students.

We write the ratio as

1 teacher to 3 students

1 teacher : 3 students

152 | CHAPTER 3 | RATIOS AND PROPORTIONS

RATIOS AND FRACTIONS | 153

Practice 1

Write the ratios.

The ratio of adults to children is _______.

The ratio of ___________ to ___________ is 3 : 2.

The ratio of ___________ to ___________ is 1 : 4 .

The ratio of people : keys is _______.

.

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Ratios are not the same as fractions but they do share some of their properties with fractions.

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Equivalent fractions are equal in value.

1 Unit

21

21

41

41

41

41

81

81

81

81

81

81

81

81

We can see 21

42

84

= =

We usually write fractions in their simplest form.

Which of the fractions is in simplest form? _______

To check if two fractions are

equivalent we cross multiply.

The fractions are equivalent if the

answers are equal.



�EXAMPLE

(a) Are the fractions equivalent?

21 and

63

21

63

1 × 6 = 6 The answers are equal.2 × 3 = 6

Yes, the fractions are equivalent.

Cross multiply

(b) Are the fractions equivalent?

41 and

103

14

103

1 × 10 = 10 The answers are not equal.3 × 4 = 12

No, the fractions are not equivalent.

Cross multiply

Practice 2

Are the fractions equivalent?

Circle the correct answer.NoYes(a)

32 and

96

Circle the correct answer.NoYes(b)

109 and

72

Circle the correct answer.NoYes(c)

85 and

2415

Circle the correct answer.NoYes(d)

47538 and

252

EQUIVALENT RATIOS | 155

Practice 3

Circle the correct answer.NoYes(e)

24

183 and 76

5795

Circle the correct answer.NoYes(f)

11521 and

14536

�� Like fractions, ratios can also be equivalent.When they are equivalent, we say the ratios are in proportion.

�EXAMPLE

Write two more equivalent ratios for the ratio given.

(a)

teachers to

students1 : 3 = 2 : 6 = 3 : 9

(b)

boysto girls

2 : 3 = 4 : 6 = 6 : 9



Practice 4

Write two more equivalent ratios for the ratio given.

(a)

_________=_________=1 : 2motorcycles

to passengers

(b)

_________=_________=1 : 5moons

to stars

(c)

_________=_________=1 : 10

supervisorsto

employees

EQUIVALENT RATIOS | 157

We sometimes write ratios in fraction form to help us with calculations.

�EXAMPLE

Are the ratios equivalent (in proportion)?

(a) 1 : 5 and 3 : 15

Write the ratios in fraction form. 5

1 and 153

Cross-multiply 1 × 15 = 15 and 5 × 3 = 15

The answers are equal.

Yes. The ratios are equivalent.

Practice 4

Are the ratios equivalent (in proportion)?

(a) 2 : 3 and 6 : 9 (b) 3 : 10 and 1 : 5

(c) 1 : 4 and 3 : 10 (d) 21 : 56 and 15: 40

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2 : 3 32

The second number becomes the denominator.



Section 3.1 Exercises Complete the following.1.

The ratio of printers to computers is ______ : ____(a)

The ratio of computers to printers is ______ : ____.(b)

The ratio of darts to dartboards is ______ : ____.(c)

The ratio of __________ to _________ is 1 : 3.(d)

The ratio of ______________________ is 4 to 3.(e)

The ratio of ______________________ is 3 to 4.(f)

The ratio of ______________________ is 3 : 1(g)

The ratio of ______________________ is 1 : 3(h)

dartboard

darts

EXERCISES | 159

2. Are the fractions equivalent?

(a) Yes No Circle the correct answer.

167 and

2611

(b) Yes No Circle the correct answer.

86 and

2015

3. Write two more equivalent ratios for the ratio given.

(a) nurses to babies 1 : 3 : :

(b) Carrots to rabbits 4 : 1 : :

4. Are the ratios equivalent?

(a) 4 : 6 and 10 : 15 (b) 8 : 12 and 14 : 21

(c) 21 : 30 and 2 : 3 (d) 9 : 32 and 2 : 7



Practice 1

Look at the ratio on the left.Circle the ratios on the right that are equivalent to the given ratio.

5.

6 : 95: 74 : 62 : 3(a)

3 : 62 : 42 : 31 : 2(b)

4 : 104 : 83 : 52 : 5(c)

10 : 303 : 82 : 61 : 3(d)

SIMPLIFY RATIOS | 161

Section 3.2Unit Ratios and Rates

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These ratios are all the same in proportion:

80 : 4040 : 2020 : 1010 : 5 2 : 1 (simplest form)

Always write the ratio as simply as possible. This is called the simplest form.

The simplest form of a ratio means that all the numbers in the ratio must be whole numbers and that all the numbers in the ratio cannot be divided by the same number (except 1).

�EXAMPLE

Write the following as ratios in their simplest form.

(a) 30 to 40 30 : 40 divide both terms by 10 = 3 : 4 (b) 18 to 6

18 : 6 divide both terms by 6 = 3 : 1


You can simplify ratios with two terms using the bca key on a calculator.

You cannot simplify ratios with more than two terms using the bca key.

(a) 30 : 40 = 4030

key: 30 bca 40 = display 3 � 4

The ratio is 43 or 3 : 4

b) 18 : 6 = 6

18

key: 18 bca 6 = display 3

The ratio is not 3. It is 3 to 1 or 13 or 3 : 1

(c) 25 : 15 = 1525

key: 25 bca 15 = display 1� 2� 3

Use the shift key to convert this to an improper fraction.

key: shift bca display 5 � 3

The ratio is 5 : 3

Using a calculator to simplify ratios only works when the ratio compares two numbers.

�� and then simplify them.

�EXAMPLE

Write the following as ratios in their simplest form.

(a) 2.4 to 10

2.4 has one digit after the decimal. Multiply it by 10 to change it to a whole number. You must also multiply all other terms of the ratio by the same number in order not to change the value of the ratio.

2.4 : 10 multiply by 1024 : 100 divide by 4 6 : 25

Most calculators can simplify a decimal ratio of two terms without having to multiply by 10.

key: 2.4 bca 10 = display 0.24

bca display: 6�25

SIMPLIFY RATIOS | 163

(b) 0.63 to 1.8 0.63 : 1.8 multiply by 100 63 : 180 divide by 9 7 : 20

Or, key: 0.63 bca 1.8 = display 0.35

display 7�20

bca

(c) 31 to 1

41

Multiply the denominators together: 3 × 4 = 12 Now, multiply both terms in the ratio by 12.

31 : 1

41 multiply by 12

= 4 : 15 the ratio cannot simplify any further

Or, key: 1 bca 3 ÷ 1 b

ca 1 bca 4 =

display: 4�15 You cannot simplify a ratio with three or more terms using the key.

(d) 24 to 40 to 16

24 : 40 : 16 divide by 8 = 3 : 5 : 2

(e) 1.25 to 3.75 to 7.5

1.25 : 3.75 : 7.5 multiply by 100

= 125 : 375 : 750 divide by 125

= 1 : 3 : 6

(f) Multiply the denominators together: 3 × 4 × 7 = 84

: :32

41

73 multiply by 84

= 56 : 21 : 36 the ratio cannot simply any further



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Another way to simplify a ratio is to write it in the form 1 : n or n : 1. This is called a unit ratio. It is often more useful because it is easier to read.The surface of the earth is made up of 356.9 million square kilometres of water and 147.1 million square kilometres of land.

The ratio of land to water is 147.1 : 356.9.

When you write this ratio you get land : water = 147.1 : 356.9 This is not easy to read.

If you divide both parts of the ratio by 147.1, you get land : water = 1 : 2.4 (to 1 d.p.) This is easy to read.

You can now see that:

The surface of the earth has almost 221 times as much water as land.

Similarly, the ratio of water to land is 2.4 : 1Unit ratios are very important in solving some applications.

�EXAMPLE

Write the following as unit ratios. Round your answers to 2 d.p. where necessary.

(a) 7 to 20

= 1 : 2.86 divide by 7

(b) 2.4 to 10

= 1 : 4.17 divide by 2.4

(c) 12 to 5

= 2.4 : 1 divide by the smaller number 5

(d) 0.68 to 2.73 to 1.97

= 1 : 4.01 : 2.90 divide by 0.68

To change a ratio to a unit ratio, you usually divide by the smallest number.

Note: (a) Write 4 : 10 in simplest terms.

4 : 10 in simplest terms is 2 : 5

(b) Write 4 : 10 as a unit ratio.

4 : 10 as a unit ratio is 1 : 2.5

Do not mix the two cases. A ratio in simplest terms is not necessarily the same as a unit ratio. A ratio in simplest terms consists of whole numbers only.

RATES | 165

� ��

When one amount is compared to one unit of another amount it is called a rate.

A speed of 80 km per hour is a rate of travelA salary of Dh 10,000 per month is a rate of payA typist typing 75 words per minute is a rate of typingAED 3.67852 per US dollar is a rate of exchange

You will often see the symbol ‘ / ’ used for ‘per’

So, when units in a ratio cannot be converted to the same units, the ratio is called a rate. In this case the ratio compares two different kinds of measurement.

A car travels 222 kilometres in 4 hours. This is a rate of 4h

222km .

The units cannot be made the same because they measure different things, but the numbers ��

4h

222km = 1h

55.5km

So, this can be written as 55.5 kilometres per hour or 55.5 km/h.The word “per” means “for each one.”

50 km/h is called a unit rate because it compares a quantity to one unit of another. The word unit in ‘unit rate’ means the number 1.

�EXAMPLE

Express the following as unit rates.

(a) 250 km to 3.5 h (to 2 d.p.) (b) Dh 55 : 20 kg = km/h = Dh/kg� ��!�"�#�� $�%��&�'�#"�

A ratio compares two numbers or quantities of the same kind.A rate compares two quantities of a different kind.

�EXAMPLE

I can type 45 words per minute. How many words can I type in 20 minutes?

To go from one minute to 20 minutes, you must multiply.20 × 45 = 900I can type 900 words in 20 minutes.

80 km/hDh 10,000/ month

75 words/minuteDh 3.67852/US$

80 km/hDh 10,000/ month

75 words/minuteDh 3.67852/US$



�EXAMPLE

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How many times can 780 go into 4680? You must divide.4680 ÷ 780 = 6The journey will take 6 hours.

�EXAMPLE

A car travels a distance of 415 km in 5 hours. What is the average speed of the car for the

journey?

You must go from 5 hours to one hour (unit rate). You must divide.

415 ÷ 5 = 83

The average speed is 83 km/h.

Section 3.2 Exercises

1 There are 20 teachers in Foundations. 12 of the teachers are men, the rest are women.

Write the answers in their simplest form.

(a) What is the ratio of men to women?

(b) What is the ratio of women to men?

%� +��F��m2 is enlarged to a new area of 13 m2. Find the � ��F��

3 A car can travel 200 km on 40 L of petrol. What is the rate of consumption in km per L?

�� P��Q�� "�Q��Q��V��Q��X��$�%>�Q��>�Q��>�Q�!>

Write your answers in simplest form.

(a) Write this ratio in its simplest form.

� Z [� ��"��X��J

(c) What is the ratio of tests to homework?

(d) What is the ratio of tests to the total?

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EXERCISES | 167

5 Measure the length and height of the images given below to the nearest cm.

(a) Record your measurements in the given table.

Image Length (cm) Height (cm)

Small

Large

(b) Find the ratio of the lengths of the small image to the large image. (c) Find the ratio of the heights of the large image to the small image.

6 The cost for building a wall was Dh 250 for materials and Dh 150 for labour. What is the ratio, in simplest form, of the cost of materials to the total cost of labour and materials?

7 A car travels at a steady speed of 82 kilometres per hour. How long does the car take to travel 410 kilometres?

8 A lorry took 11 hours to travel 682 kilometres. What was the average speed of the lorry?

9 The distance by air from Abu Dhabi to Tokyo is 8075 km. An aeroplane can average � <&>�"�#��@��F��"�J

10 A top speed typist can type 325 words in 5 minutes. What is her maximum rate of typing in words per minute?

11 The petrol tank of a car holds 60 litres. The car can travel 12.6 km per litre. How far will the car travel on one full tank of petrol?

12 A petrol pump can deliver petrol at the rate of 0.5 L/s. How many seconds does it � �"��"��\>��J

13 An aircraft travelled 9152 kilmetres in 11 hours. What was the speed of the aircraft?

14 I take 3.5 hours to walk 19 km. What is my speed in km/h to 2 d.p.?

15 There are 114.808 yen to 1 euro. How many yen will I get for 50 euros?



Section 3.3Solving Proportions

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�EXAMPLE

Example 1Find the values of “n” that make the ratios equivalent

(a) Write the ratios as fractions.

Cross-multiply

Divide both sides by 8

n : 4 and 2 : 8

nX X

nX

8 4 2

8 8

=

=

nX

n

88

88

1

=

=

Sometimes one of the numbers in a proportion is not known. We want to �� "��]��;��

Use a letter to represent the unknown number. Look at the ratios.

n : 4 and 2 : 8

We want these ratios to be equivalent.

Write n4 8

2=

� � � ^��`��;��z{�

SOLVING PROPORTIONS | 169

�EXAMPLE

(b) 2 : 3 and n : 12

Write the ratios as fractions.and

n

32

12

Cross-multiply X Xn

Xn

2 12 3

24 3

=

=

Divide both sides by 8Xn

n

324

33

8

=

=

Practice 1

Find the values of “n” that make the ratios equivalent.

(a) 4 : 5 = n : 15 (b) 1 : 7 = n : 21

(c)1 : 7 = n : 16

(d)3 : n = 6 : 8

(e)2 : 5 = n : 13

(f)8 : n = 45 : 90

(g) 34 : 28 = 20 : n (h) 60 : n = 2 : 3


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We can use equivalent ratios to solve many types of word problems.

�EXAMPLE

Jamal walks 3 km in 1 hour. How far can he walk in 5 hours?

km h

3 1

n 5

n = 3 X 5

n = 15kmJamal can walk 15 km in 5 hours.

What are the units in the ratio?

You must keep the same order in all equivalent ratios. Put the information in a table and it helps you to keep the correct order.

��complete the table.Cross multiply.

(a)

Sami buys 5 grams of gold for Dh 210. Jassim buys 7 grams at the same price per gram. How much does 7 grams of gold cost?

g Dh

5 210

7 n

n X 5=7 X 210

7X210nX55

5=

Jamal can walk 15 km in 5 hours.

What are the units in the ratio?

��

Complete the table.

Cross multiply.

(b)

change GBP 300 to dirhams. 1 GBP = AED 6.07810(c)

GBP AED

1 6.07810

300 n

n × 1 = 300 × 6.07810

n = 1823.43

GBP 300 = AED __________________

Decide what are the units in the ratio. We want to change GBP to AED

From the Currency Table we see 1 GBP = AED 6.07810

Arrange the information in a table.


“n” is the number of kmhe can walk in 5 hours

“n” is the number of AED we get for GBP

300.

“n” is the cost of 7g of gold.

Practice 2

1. A 4-minute telephone call costs Dh 2.50. How much does a 30-minute callcost?

2. 10 grams of gold costs Dh 430. How many grams of gold can I buy for Dh 645?

3. Four apples cost Dh 2. How much do ten apples cost?

4. 5 metres of material costs Dh 35. How much does 7 metres of material cost?

5. Ashley earns Dh 400 for 5 hours’ work. How much does he earn for 8 hours’ work?

WORD PROBLEMS | 171



6. 55 mL (millilitres) of water is mixed with 100 g of powder to make plaster. How many millilitres of water are needed to mix with 300 g of powder?

7. Seven tents cost Dh 5075. How many tents can I buy for Dh 18 125?

8. The scale on a map is 10 cm : 75 km. The distance between Abu Dhabi and Ras Al Khaimah is 345 km. What is the distance on the map?

9. Amna can type 63 words per minute. How many can she type in 20 seconds? (Hint: Both time periods must be in the same unit of measurement.)

10. Five trucks can carry 133 tonnes of sand. How many tonnes of sand can 8 trucks carry?

WORD PROBLEMS | 173

11. A photocopier makes 500 copies in 8 minutes. How many copies can it make in 1 hour?

12. A kilogram of gold costs costs AED 42 000. How much does 60 g of gold cost?

1 kg gold -AED 42 000

13. There are 30 teaspoons of sugar in a 1-L bottle of Coca-Cola. How many teaspoons of sugar are there in a 330 mL can of Coca-Cola?



�� "�It is called a ‘Currency Exchange Rate’ table. A Currency Exchange Rate table is like a price list in a restaurant.

Currency Exchange Rates

AEDCurrency CodeCurrency Name

2.46190AUDAustralian dollar

9.76280BHDBahraini dinar

2.75790CADCanadian dollar

4.24840EUREuropean Community euro

0.47630HKWDHong Kong dollar

0.08190INRIndian rupee

0.03266JPYJapanese yen

12.1129KWDKuwaiti dinar

2.17380NZDNew Zealand dollar

9.57090OMROmani riyal

6.07810GBPpound sterling

0.98450SARSaudi riyal

2.12080SGDSingapore dollar

3.67800USDUS dollar

WORD PROBLEMS | 175

Practice 3

Use the exchange rate table to change the currencies.

(a) AED 4000 = SAR ________

(b) AED 5500 = euro ________

(c) AED 1200 = HKD ________

(d) AED 9000 = JPY ________


Practice 4


(a) Singapore dollar 2000 = AED ________

(b) JPY 5500 = AED ________

(c) KWD 8000 = AED ________

(d) OMR 10 500 = AED ________


WORD PROBLEMS | 177

Practice 5


(a) Noura is going to Germany. She wants to take euro 5000. How many AED does she need to buy euro 5000?

(b) Badr is going to the UK. He will take AED 6500. How many pounds sterling (GBP) will he get for AED 6500?

(c) A car costs JPY 500 000 in Japan. What is the price of the car in AED?

(d) Mariam is shopping on the Internet. She orders some items which cost USD 800. What is their cost in AED?



(e) A barrel of oil costs AED 90. What is the cost of 150 barrels of oil in euros?

(f) A computer costs JPY 97 000. Mohammed wants to buy 25 computers for his company. What is the total cost in AED?

(g) Omar is on a business trip to New Zealand. His hotel costs NZD 150 per night. Omar stays for 5 nights. What is the total cost of his hotel stay in AED?

(h) Mariam is shopping on the internet. She orders some items which cost USD 800. She gets a 10% discount on her order. What is the cost after discount in AED?

Allocation According to a Given Ratio | 179

��%�� Sometimes you want to share or divide some amount or quantity according to a given ratio.For example you may want to: Share some money between two people so that one gets twice as much as the otherorShare a hundred computers among three companies so that one company has three times as many computers as the other two companies.

�Example

Salem has Dh 450. He gives his brother Ahmad Dh 250 and hisbrother Khalid Dh 200. Write a ratio for the money shared between Ahmad and Khalid.

Ahmed’s share : Khalid’s share = 250 : 200 = 5 : 4

Salem has divided Dh 450 between Ahmad and Khalid in the ratio 5 : 4

�Example

Divide Dh 400 between Fatima and Huda in the ratio 5 : 3Fatima gets 5 parts and Huda gets 3 parts. The total parts are: 5 + 3 = 8

METHOD 1 There are 8 parts altogether and the total to be shared is Dh 400.

400 ÷ 8 = 50 (each part is worth Dh 50) parts Dh8 400"

part Dh1 50"

Fatima gets 5 parts: 5 × Dh 50 = Dh 250Huda gets 3 parts: 3 × Dh 50 = Dh 150

Fatima gets Dh 250 and Huda gets Dh 150.

METHOD 2 There are 8 parts altogether and the total to be shared is Dh 400.

Fatima gets85 of the money and Huda gets

83 of the money.

Fatima gets: X Dh85 400 250=

Huda gets: X Dh83 400 150=

Fatima gets Dh 250 and Huda gets Dh 150.

Use the method you think is easier to follow.



�EXAMPLE

A net income of Dh 72,000 is to be shared among Laila, Nouria and Adel in the ratio 4 : 3 : 2. Find the share of each.

Laila’s share : Nouria’s share : Adel’s share = 4 : 3 : 2

Total parts = 4 + 3 + 2 = 9Each part is worth 72,000 ÷ 9 = 8000

9parts Dh72,000

1part Dh8,000

"

"

Laila’s share: 4 × Dh 8,000 = Dh 32,000Nouria’s share: 3 × Dh 8,000 = Dh 24,000Adel’s share: 2 × Dh 8,000 = Dh 16,000

�EXAMPLE

Faraj, Ahmad and Mohammad are partners in a company. Faraj invests Dh 36,000, Ahmad invests Dh 44,000 and Mohammad invests Dh 16,000. The three partners decide to share ��;��"��'��%��>>>��@��J

First, set up the ratio of their investments:

Faraj to Ahmad to MohammadDh 36,000 : Dh 44,000 : Dh 16,000 divide by 4000 = 9 : 11 : 4

Total number of shares = 9 + 11 + 4 = 24Value per share = 24,000 ÷ 24 = Dh 1000

Faraj gets 9 × 1000 = Dh 9000Ahmad gets 11 × 1000 = Dh 11,000Mohammad gets 4 × 1000 = Dh 4000

You can solve this problem without having to simplify the ratio.

The original ratio was 36,000 : 44,000 : 16,000

Total = 36,000 + 44,000 + 16,000 = 96,00024 000 ÷ 96 000 = 0.25

Faraj gets 0.25 × 36,000 = Dh 9000Ahmad gets 0.25 × 44,000 = Dh 11,000Mohammad gets 0.25 × 16,000 = Dh 4000

Allocation According to a Given Ratio | 181

Practice 3

1 Divide Dh 24,000 in the ratio of:

(a) 1 : 2

(b) 2 : 3

(c) 10 : 7 : 8

(d) 3 : 3 : 5 : 1

2 Ahmed and Salem plan a trip to Germany during the summer holidays. They agree to share the expenses for the trip in the ratio of 3 : 4 respectively. The trip costs Dh 4900. How much should each pay?

3 An inheritance of Dh 224,640 is to be divided among 3 heirs in the ratio 3 : 5 : 7. What is the amount that each of them will receive?

�� +�� F�� ;�� among the tenants in the ratio 6 : 8 : 9. The January bill is Dh1840. How much does each tenant pay?

&� +��'��\�G��@��@�� much does each receive?

G� +��'��!>G>�� ;�� shares held. If the three partners have nine shares, two shares and one share respectively, how much does each receive



Section 3.1 Exercises Find the value of ‘n’ that makes these fractions equivalent.1.

(b) n6

3 12=(a) n54

15=

(d) n12 8

10=(c) .n7

3 13 5=

Find the value of ‘n’ that makes these ratios equivalent.2.

(b) 20 : 30 and 2 : n(a) 8 : n and 4 : 9

(d) 4 : 11 and n : 99(c) 14 : n and 2 : 3

EXERCISES | 183

3. A car travels at a speed of 160 km/h. How long will it take the car to travel a distance of 450 km?

4. An engine uses 12 L (litres) of fuel every 100 hours. How much fuel is needed to run the engine for 750 hours?

5. On a map the scale is 5 mm : 15 m. A wall is 12 mm long on the map. What is the real length of the wall?

6. The scale of a map is 10 mm : 60 km. The distance between Abu Dhabi and Sharjah is 300 km. What is the distance on the map?


7. Use the Currency Exchange Rate table on Page 174 to change the currencies.

(a) AED 4000 = euro __________

(b) GBP 3000 = AED __________

(c) AED 5500 = GBP __________

(d) AED 1200 = USD __________

EXERCISES | 185

(e) SAR 5500 = AED __________

(f) HKD 4000 = AED __________

(g) AED 18 000 = USD __________

(h) KWD 3500 = AED __________



(i) OMR 5600 = AED __________

(j) AED 900 = JPY __________

8. Convert AED 500 into Singapore dollars.

9. Mohammed is going to France. He will take AED 10 000 to spend there. How many euros will Mohammed receive for AED 10 000?

EXERCISES | 187

10. Omar is going to Hong Kong. He has AED 2000. How many Hong Kong dollars (HKD) will he get for AED 2000?

11. Amna is on holiday in the USA. She buys a dress for USD 150. What is the cost of the Dress in dirhams (AED)?

12. John has to send Canadian dollar 15 000 to Canada. How many dirhams (AED) is this?

13. Ali is on a business trip in the UK. His hotel costs GBP 79 per night. Ali stays for 3 nights. What is the total cost of his hotel stay in dirhams (AED)?



14. A box of dates costs AED 48. What is the cost of 50 boxes in US dollars?

15. A barrel of oil costs AED 90. The price increases by 20%. What is the new price of a barrel of oil in US dollers?

16. Hamad and his family are on holiday in Australia. The hotel room costs Australian dollar 120 per night. Hamad stays for 1 week. What is the total cost of the hotel room in dirhams (AED)?

17. A barrel of oil costs AED 90. What is the price of 100 barrels of oil in Canadian dollars?

EXERCISES | 189

18. Maryam is shopping on the Internet. She buys a book and 3 CDs. The book costs USD 22. The CDs cost USD 35 each. What is the total cost in dirhams (AED)?

19. Hessa is going to India. She has AED 4000. How many Indian rupees does she receive?

20 My friend is going to Hong Kong. I give my friend AED150. I ask her to buy 15 metres of silk. The price of the silk is HKD 350. Does my friend have enough money?

21. Aisha is going to New Zealand on holiday. She changes 12 500 dirhams (AED) to New Zealand dollars (NZD). How many New Zealand dollars (NZD) does she get?



22. Mariam is on holidays in Toyko. She buys a digital camera. It costs 35 000 Japanese yen (JPY). She gets a 10% discount. What is the cost after discount in dirhams (AED)?

23. a) Paul is going to New York. He will take Dh 5400. How many US dollars (USD) will he get for his Dh 5400?

b) When he returns he still has USD 75.00. How many dirhams (AED) will he get?

24. Laila orders a dress from Hong Kong. The cost of the dress is 6500.00 Hong Kong dollars (HKD). She gets a discount of 7%. What is the cost of the dress after discount in dirhams (AED)?

25. Khaled went to Saudi Arabia to buy camels. The price of a camel was 960 Saudi riyals (SAR). He bought 58 camels. What was the total cost in dirhams (AED)?

26. The cost of a camera in Britain is 650 pounds sterling (GBP). The same camera costs 3000 dirhams (AED) in Dubai. Which camera costs more, and by how much? (Show your work.)

27. Zeyad, Nasser, Eissa and Jalal are the shareholders of a company. Their shares are in � ��&�Q�\�Q��Q��&��;��"��'��\&>�>>>�� ;��@�� much does each one receive?

28. 704 students are allocated to three campuses A, B and C in the ratio 5 : 3 : 8 respectively. How many students are there in each campus?

EXERCISES | 191

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CHAPTER Ratios & Proportionsfjw.hct.ac.ae/student_info/foundations/bookm010/M010_textbook_unit... · a 40 = display 3 4 The ratio is ... The ratio is 5 : 3 Using a calculator to simplify