© T Madas. What do we mean when we say two quantities are in proportion or directly proportional ?...

© T Madas

© T Madas

What do we mean when we say two quantities are in proportion or directly proportional ?It means that if:

one of them doubles,the other one also doubles.one of them trebles,the other one also trebles.one of them x4,the other one also x4.one of them halves,the other one also halves.one of them ÷4,the other one also ÷4.

Can you give examples of directly proportional quantities from every day life?

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Directly proportional quantities:They increase or decrease at the same rate

More formally:Two quantities are directly proportional if the ratio between them remains constant.

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© T Madas

Laps in Racing Cars

A racing car does 2 laps every 5 minutesHow long does it take to cover 17 laps?How many laps does it cover in 1 hour?

L T 2 : 5

17 laps in 42½ minutes In 1 hour it does 24 laps

1 : 2.5

÷2 ÷2

17 : 42.5

x17 x17

L T 2 : 5

0.4 : 1

÷5 ÷5

24 : 60

x60 x60

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© T Madas

Calculating Earnings

A plumber earns £51 in 6 hoursHow much does he earn in a 41 hour week?In many hours does he earn £1000?

H £ 6 : 51

£348.50 in 41 hours approximately 118 hours

1 : 8.5

÷6 ÷6

41 : 348.5

x41 x41

H £ 6 : 51

0.1176: 1

÷51 ÷51

117.6 : 1000

x1000 x1000

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© T Madas

Converting Currency

If £5 are worth €7 How many € are £8 worth?How many £ are €3 worth?

£ €5 : 7

£8 = € 11.20

1 : 1.4

÷5 ÷5

8 : 11.2

x8 x8

£ € 5 : 7

0.7143 : 1

÷7 ÷7

2.14 : 3

x3 x3

€ 3 ≈ £ 2.14

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© T Madas

In a chemical reaction solution A must be combined with solution B in the ratio of 5 : 8, to form a certain compound.

How many ml of solution B must be used, if 5.5 ml of solution A is to be used?

Chemistry Experiments

A B5 : 8 8.8 ml of solution B must be

mixed with 5.5 ml of solution A

1 : 1.6

÷5 ÷5

5.5: 8.8

X5.5 X5.5

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© T Madas

© T Madas

Laps in Racing Cars

A racing car does 2 laps every 5 minutesHow long does it take to cover 17 laps?How many laps does it cover in 1 hour?

L M

:2 5

:1 52

:17 ´ 1752 .= 42 5

17 laps in 42½ minutes

M L

:5 2

:1 25

:60 ´ 6025

=24

In 1 hour it does 24 laps

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© T Madas

Calculating Earnings

A plumber earns £51 in 6 hoursHow much does he earn in a 41 hour week?In many hours does he earn £1000?

h £

:6 51

:1 516

:41 ´ 41516 .= 348 5

He earns £348.50

£ h

:51 6

:1 651

:1000 ´ 1000651 » 118

He earns it in 118 hours

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© T Madas

Converting Currency

If €7 are worth £5How many £ are €3 worth?How many € are £8 worth?

€ £

:7 5

:1 57

:3 ´ 357 .» 2 14

€3 ≈ £2.14

£ €

:5 7

:1 75

:8 ´ 875 .=11 2

£8 = €11.20

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© T Madas

In a chemical reaction solution A must be combined with solution B in the ratio of 5 : 8, to form a certain compound.

How many ml of solution B must be used, if 5.5 ml of solution A is to be used?

Chemistry Experiments

A B

:5 8

:1 85

. :5 5 .´ 5 585

.= 8 88.8 ml of solution B must be used

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© T Madas

12 kg of flour cost £15.How much do 28 kg cost?

15´ 2812

5

4

7

= 35

12 kg of flour cost £15.How many Kg do £120 buy?

12´ 12015

4

5

24

= 96

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600 Mb require a 72 minute CD.How many minutes do 700 Mb need?

72´700600

12

6

7

= 84

600 Mb require a 72 minute CD.How many Mb correspond to 60 minutes?

600´6072

100

6

5

= 500

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In a pie chart 7200 voters are represented by 144°.How many voters do 120° represent?

7200´120144

1200

6

5

= 6000

In a pie chart 7200 voters are represented by 144°.By how many degrees are 1000 voters represented?

144´10007200

2= 20

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© T Madas

18 ´ 2045

40y

8024x

The variables in the table are directly proportional.Find the missing value.

80 ´ 4024

10

3

= 4003 . ...» 133 333

8

2045y

18x 2

5

= 84

4003

21.654y

3690x 36´ 5490

2

5

= 1085

.= 21 6

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12080y

9060x

The variables in the table are directly proportional.Find the missing value.

90´ 8060

=120

4060y

1218x 12´ 6018

2

3

= 4020

24

5075y

36x50´ 36

752

3

= 2412

15

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© T Madas

20 litres of petrol cost £16.

1. Work out the cost of 1 litre of petrol.

2. Work out the cost of 7 litres of petrol.

litres

20

10

1

7

cos

t

16

8

0.8

5.6

:

:

:

:

:

£0.80

£5.60

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© T Madas

Toca-Cola costs £1.24 for a 2 litre bottle.Sepsi-Cola costs £0.90 for a 1.5 litre bottle.Work out which brand is the cheapest.

2 lt£1.24

1.5 lt£0.90

lt £:2 1.24:

÷2 ÷2

1 0.62:

Toca-Cola

1 lt costs 62 pence,

lt £:1.5 0.90:

÷1.5 ÷1.5

1 0.60:

Sepsi-Cola

1 lt costs 60 pence,

Sepsi-Cola is the cheapest

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© T Madas

18 pens cost £2.16.

Calculate the cost of 24 pens.

pens £:18 2.16:

÷18 ÷18

1 unimportant:

x 24 x24

24 2.88:

pens £:18 2.16:

÷3 ÷3

6 0.72:

x 4 x 4

24 2.88:

£2.88

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© T Madas

Look at the nutritional information shown on the label opposite.

How many grams of carbohydrate do 100 grams of these beans provide?

Bono Baked BeansEach 150 g provides

108 kcal6.9 g19.5 g0.3 g0.5 g

EnergyProteinCarbohydrateFatSalt

beans carbs:150 19.5:

÷3 ÷3

50 6.5:x2 x2

100 13:

100 grams of beans provide 13 grams of carbohydrate

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© T Madas

Look at the nutritional information shown on the label opposite.

Calculate how many grams of carbohydrate do 100 grams of these beans provide, giving your answer correct to 3 significant figures.

Chilli Baked BeansEach 215 g provides

161 kcal10 g30.5 g0.2 g0.6 g

EnergyProteinCarbohydrateFatSalt

beans carbs:215 30.5:

÷215 ÷215

1 0.1419:x100 x100

100 14.19:

100 grams of beans provide 14.2 grams of carbohydrate

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© T Madas

Hojo Apple PieEach 175 g provides

434 kcal6.9 g79.5 g9.9 g0.5 g

EnergyProteinCarbohydrateFatSalt

Mojo Apple PieEach 150 g provides

375 kcal6.7 g70.5 g5.3 g0.5 g

EnergyProteinCarbohydrateFatSalt

Look at the nutritional information shown on the two labels.

Rohan eats the same amount from each apple pie.

Which apple pie provides Rohan with more energy.

grams energy:175 434:

÷175 ÷175

1 2.48:

grams energy:150 375:

÷150 ÷150

1 2.5:

each gram provides 2.48 kcaleach gram provides 2.5 kcal

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© T Madas

Mr Green sells a 2.4 kg bag of apples for £1.80 while Mr Red sells a 2.5 kg bag of apples for £2.

Who sells the cheaper apples?

kg £:2.4 1.80:

÷2.4 ÷2.4

1 0.75:

at Mr Green’s

1 kg costs 75 pence,

kg £:2.5 2:

÷2.5 ÷2.5

1 0.8:

at Mr Red’s

1 kg costs 80 pence,

Mr Green sells the cheaper apples

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© T Madas

The exchange rate between Sterling and Euros is:

£1 = €1.60

1. How many Euros do we get if we change £150?

2. How many Pounds do we get if we change €32.64?

£ €:

1 1.6:

x150 x150

150 240:

£150 = €240

£ €:

1 1.6:

÷1.6 ÷1.6

Whocares?

1:

€32.64= £20.40

x32.64 x32.64

20.4 32.64:

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© T Madas

The exchange rate between Sterling and Euros is:

£1 = €1.60

How many Pounds do we get if we change €32.64?

£

1

2

10

20

40

0.4

20.4

€

1.6

3.2

16

32

64

0.64

32.64

:

:

:

:

:

:

:

:

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