© t madas. what do we mean when we say two quantities are in proportion? it means that if: one of...
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© T Madas
© T Madas
What do we mean when we say two quantities are in proportion?
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.
© T Madas
3 pens cost £2
6 pens cost£49 pens cost£6
12 pens cost£8
etc15 pens cost£10
3 2
6 49 6
12 815 10
:::::
What do you notice?
Cost of pensPens £
© T Madas
3 pens cost £2
6 pens cost£49 pens cost£6
12 pens cost£8
etc15 pens cost£10
3 2
6 49 6
12 815 10
:::::
Cost of pensPens £
How much do 30 pens cost?
……
……
30 20
£20
x 10 x 10
© T Madas
3 pens cost £2
6 pens cost£49 pens cost£6
12 pens cost£8
etc15 pens cost£10
3 2
6 49 6
12 815 10
:::::
Cost of pensPens £
How much do 30 pens cost?
……
……
30 20
£20
x 2 x 2
© T Madas
3 pens cost £2
6 pens cost£49 pens cost£6
12 pens cost£8
etc15 pens cost£10
3 2
6 49 6
12 815 10
:::::
Cost of pensPens £
How much do 30 pens cost?
……
……
30 20
£20
x 5 x 5
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2 laps in 5 minutes4 laps in10 minutes
6 laps in 15 minutes8 laps in20 minutes
etc10 laps in25 minutes
2 54 10
6 158 20
10 25
:::::
What do you notice?
Laps in Racing CarsLaps Min
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2 laps in 5 minutes4 laps in10 minutes
6 laps in 15 minutes8 laps in20 minutes
etc10 laps in25 minutes
2 54 10
6 158 20
10 25
:::::
Laps in Racing CarsLaps Min
How many minutes does it take to cover 18 laps?
……
……
18 45
45
x 9x 9
© T Madas
2 laps in 5 minutes4 laps in10 minutes
6 laps in 15 minutes8 laps in20 minutes
etc10 laps in25 minutes
2 54 10
6 158 20
10 25
:::::
Laps in Racing CarsLaps Min
How many minutes does it take to cover 18 laps?
……
……
18 45
45
x 3x 3
© T Madas
2 laps in 5 minutes4 laps in10 minutes
6 laps in 15 minutes8 laps in20 minutes
etc10 laps in25 minutes
2 54 10
6 158 20
10 25
:::::
Laps in Racing CarsLaps Min
How many laps does it cover in 60 minutes?
……
……
24 60
24
x 6x 6
© T Madas
2 laps in 5 minutes4 laps in10 minutes
6 laps in 15 minutes8 laps in20 minutes
etc10 laps in25 minutes
2 54 10
6 158 20
10 25
:::::
Laps in Racing CarsLaps Min
How many laps does it cover in 60 minutes?
……
……
24 60
24
x 12x 12
© T Madas
2 laps in 5 minutes4 laps in10 minutes
6 laps in 15 minutes8 laps in20 minutes
etc10 laps in25 minutes
2 54 10
6 158 20
10 25
:::::
Laps in Racing CarsLaps Min
In how many minutes does it cover 5 laps?
12.5
5 12.5
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€ 7 = £5
€ 14 =£10
€ 21 =£15€ 28 =£20
etc
€ 35 =£25
7 5
14 1021 1528 2035 25
:::::
How many Euros are equal to £100?
140…
…
……
140 100
€ £
Money Conversions
x 10 x 10
© T Madas
€ 7 = £5
€ 14 =£10
€ 21 =£15€ 28 =£20
etc
€ 35 =£25
7 5
14 1021 1528 2035 25
:::::
How many £ are equal to €56?
40…
…
……
56 40
€ £
Money Conversions
x 8 x 8
© T Madas
© T Madas
= 10p3 : 10
6 : 209 : 3012 : 4015 : 50
What are thenext 4 ratios?
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= 10p3 : 10
6 : 209 : 3012 : 4015 : 50
How much do30 sweets cost?
……
……
30 : 100
x10 x10
© T Madas
= 40p
3 : 406 : 809 : 12012 : 16015 : 200
What are thenext 4 ratios?
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= 40p
3 : 406 : 809 : 12012 : 16015 : 200…
…
……
24 : 320
x2 x2
How much do 24lollipops cost?
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= £2
3 : 26 : 49 : 612 : 815 : 10
What are thenext 4 ratios?
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= £2
3 : 26 : 49 : 612 : 815 : 10
How much do24 boxes cost?
……
……
24 : 16
x8 x8
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= £2
3 : 26 : 49 : 612 : 815 : 10…
…
……
45 : 30
x3 x3
How many boxesdo I buy with £30?
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= £3
5 : 310 : 615 : 920 : 1225 : 15
What are thenext 4 ratios?
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= £3
5 : 310 : 615 : 920 : 1225 : 15
How much do 35ice creams cost?
……
……
35 : 21
x7 x7
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= £3
5 : 310 : 615 : 920 : 1225 : 15…
…
……
50 : 30
x10 x10
How many ice creamsdo I get with £30?
© T Madas
What are thenext 4 ratios?
3 : 46 : 89 : 1212 : 1615 : 20
3 laps in 4 minutes
L : M
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3 : 46 : 89 : 1212 : 1615 : 20
3 laps in 4 minutes
L : M
How long does hetake for 24 laps?
……
……
24 : 32
x8 x8
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3 : 46 : 89 : 1212 : 1615 : 20
3 laps in 4 minutes
L : M
How long does hetake for 39 laps?
……
……
39 : 52
x13 x13
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3 : 46 : 89 : 1212 : 1615 : 20
3 laps in 4 minutes
L : M
……
……
45 : 60
x3 x3
How many laps doeshe do in 60 min?
© T Madas
3 : 46 : 89 : 1212 : 1615 : 20
3 laps in 4 minutes
L : M
4.5 6
How many laps doeshe do in 6 min?
© T Madas
=
7 : 5€ : £
If I change €21, how many £s will I get?
……
……
21 :
x3 x3
15
© T Madas
=
7 : 5€ : £
If I change £25, how many €s will I get?
……
……
35
x5 x5
: 25
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5 : 8
5 laps in 8 minutes
L : M
How long does it take for 40 laps?
……
……
40 :
x8 x8
64
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5 : 8
5 laps in 8 minutes
L : M
How many laps does it cover in 32 min?
……
……
20
x4 x4
: 32
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5 : 8
5 laps in 8 minutes
L : M
How many laps does it cover in 20 min?
……
……
12.5
x2.5 x2.5
: 20
© T Madas
© T Madas
© T Madas
With every 30 pupil textbooks that are bought, 2 teacher books are supplied.
If we order 90 pupil textbooks how many teacher books do we get?
If another order contains 9 teacher books how many pupil textbooks should be there?
Pupil
30
60
90
120
150
180
Teacher
2
4
6
8
10
12
:
:
:
:
:
:
:
6 teacher books
© T Madas
With every 30 pupil textbooks that are bought, 2 teacher books are supplied.
If we order 90 pupil textbooks how many teacher books do we get?
If another order contains 9 teacher books how many pupil textbooks should be there?
Pupil
30
60
90
120
150
180
Teacher
2
4
6
8
10
12
:
:
:
:
:
:
:
6 teacher books
135 textbooks
Another Method30 textbooks
15 textbooks
135 textbooks
2 teacher books
1 teacher book
9 teacher books(9 x 15)
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© T Madas
3 : 4
1500
Yellow
……
…
……
…
Red
2000
2000 ml of yellow paint are needed
To make a certain shade of orange paint we must mix 3 parts red with 4 parts yellow.
If we use 1500 ml of red paint how many ml of yellow paint must we use?
x 500 x 500
© T Madas
© T Madas
Washing powder is sold in E3 and E10 sizes which are in the ratio of 3 : 10.
If the E3 size weighs 1.5 kg how much does the E10 size weigh?
3 : 10
1.5
E10
……
…
……
…
E3
5
The E10 size weighs 5 kg
÷ 2÷ 2
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© T Madas
An orange drink is made up of pure orange juice and water.
1000 ml of that drink contains 200 ml of pure orange juice.
How much water must we mix with 500 ml of orange juice in order to make this drink?
200
500
Water…
……
……
…
Orange
2000
2000 ml of water must be mixed
x 2.5 x 2.5
drink
1000 : 800
© T Madas
© T Madas
10
9
8
7
6
5
4
3
2
1
0
A water barrel with a scale next to it is shown below.When 75 litres of water are poured into the barrel, the water level rises from mark 5 to mark 8.1. How many litres of water were originally in the barrel?2. What is the total capacity of the water barrel?
3 marks =
1 mark =
5 marks =
10 marks =
75 litres
25 litres
125 litres
250 litres
÷3
x5
x2
© T Madas
© T Madas
30
80
mph
B
A C
The needle of the speedometer of a car turns through 90° when the speed increases from 30 mph to 80 mph.Write down the readings at the points A, B and C.By how many degrees does the needle turn when the speed increases from 20 mph to 60 mph?
0
130
160
50
90°
180°
18°
72°
50 mph =
100 mph =
10 mph =
40 mph =
The needle turns by 72° when the speed increases from 20 mph to 60 mph.
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