Y9 Booster

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Y9 Booster

• Lesson 5

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Objectives what you should be able to do by the
end of the lesson

• Divide a quantity in a given ratio
• Solve simple problems using a unitary method

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Equivalent ratios
In the diagram below the ratio of blue beads to
green beads is 32. So for every five beads in
the chain, 3 are blue and 2 are green.
32
64
96
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If 32 64 96
Find 3 more equivalent ratios.
Complete this ratio 150?
Complete this ratio ?40
If the chain has 35 beads altogether how many are
green and how many are blue?
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Ratio spider diagram 1 M5.1
Find some equivalent ratios to 243660
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Unequal sharing
Example Share 20 in the ratio 32
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Working
32 is 5 parts
4
4
4
4
4
3 parts is 3 x 4 12 2 parts is 2 x 4 8
Answer 20 in the ratio 3 2 is 12 8
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Ratio spider diagram 2 M5.2
Complete the boxes
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Ratio problems 1 M5.3

• 1 The angles in a triangle are in the ratio
  9  5  4. Find
• the size of each angle.
• 2 Green paint is made by mixing 2 parts of blue
  paint
• with 5 parts of yellow. A
  girl has 5 litres of blue paint and 10 litres of
  yellow
• paint. What is the maximum amount of
  green paint
• she can make?
• 3 This recipe for fruit squash is for 6 people.
  300 g chopped oranges 1500 ml
  lemonade 750 ml orange juice
  How much lemonade do you need to
  make fruit squash for (a) 9
  people? (b) 10 people?

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1 The angles in a triangle are in the ratio
9  5  4. Find the size of each
angle.
Angles in a triangle total
180º
180º In the ratio 9 5 4
9 5 4 18 parts
180 18 10º per part
9 5 4 90º 50º 40º
The angles in the triangle are 90º, 50º and 40º.
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Ratio problems 1 M5.3

• 1 The angles in a triangle are in the ratio
  9  5  4. Find
• the size of each angle.
• 2 Green paint is made by mixing 2 parts of blue
  paint
• with 5 parts of yellow. A
  girl has 5 litres of blue paint and 10 litres of
  yellow
• paint. What is the maximum amount of
  green paint
• she can make?
• 3 This recipe for fruit squash is for 6 people.
  300 g chopped oranges 1500 ml
  lemonade 750 ml orange juice
  How much lemonade do you need to
  make fruit squash for (a) 9
  people? (b) 10 people?

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2 Green paint is made by mixing 2 parts of
blue paint with 5 parts of yellow.
A girl has 5 litres of blue paint and 10
litres of yellow paint. What is the
maximum amount of green paint she can
make?
Blue paint yellow paint 2 5
She has 5 litres of blue
And 10 litres of yellow
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2 Green paint is made by mixing 2 parts of
blue paint with 5 parts of yellow.
A girl has 5 litres of blue paint and 10
litres of yellow paint. What is the
maximum amount of green paint she can
make?
Blue paint yellow paint 2 5
She has 5 litres of blue
And 10 litres of yellow
7 litres
7 litres
7 litres 7 litres 14 litres of green
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Ratio problems 1 M5.3

• 1 The angles in a triangle are in the ratio
  9  5  4. Find
• the size of each angle.
• 2 Green paint is made by mixing 2 parts of blue
  paint
• with 5 parts of yellow. A
  girl has 5 litres of blue paint and 10 litres of
  yellow
• paint. What is the maximum amount of
  green paint
• she can make?
• 3 This recipe for fruit squash is for 6 people.
  300 g chopped oranges 1500 ml
  lemonade 750 ml orange juice
  How much lemonade do you need to
  make fruit squash for (a) 9
  people? (b) 10 people?

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3 This recipe for fruit squash is for 6 people.
300 g chopped oranges 1500 ml
lemonade 750 ml orange juice
How much lemonade do you need to make fruit
squash for (a) 9 people? (b) 10 people?
a) For 6 people you need 1500 ml of lemonade
For 9 people (6 3) we need
1500 ml 750 ml
Answer 9 people would require 2250 ml of lemonade
b)
For 6 people we need 1500 ml of lemonade
For each person we require 1500 6 250 ml
10 people would require 250 ml x 10
Answer 10 people would require 2500 ml of
lemonade.
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Ratio problems 2 M5.4

• 1 In a game of rugby Robs ratio of successful to
  unsuccessful kicks was 5  3. Daves ratio was
  3  2. Who was the more successful?
• 2 The gears of a bicycle travelling along a flat
  road are such that for every 2 turns of the
  pedals the rear wheel makes 5 turns.If the
  pedals make 150 turns, how many turns will the
  rear wheel make?When travelling up a steep hill
  in a different gear, would you expect the rear
  wheel to make more or less than 5 turns for each
  2 turns of the pedals?Explain your answer.
• 3 The answers to a survey are shown in a pie
  chart. The angle representing Yes is 120, the
  angle for No is 150, and the angle for Dont
  know is 90.If 300 people took part in the
  survey, how many replied No?

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1. In a game of rugby Robs ratio of successful
to unsuccessful kicks was 5  3. Daves ratio
was 3  2. Who was the more successful?
Robs ratio of 5 3 means he is successful for 5
out of every 8 kicks
5 out of 8 0.625 or 62.5 successful
Daves ratio of 3 2 means he is successful for 3
out of every 5 kicks
3 out of 5 0.6 60 successful
Rob is the most successful with his ratio of 5 3
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Ratio problems 2 M5.4

• 1 In a game of rugby Robs ratio of successful to
  unsuccessful kicks was 5  3. Daves ratio was
  3  2. Who was the more successful?
• 2 The gears of a bicycle travelling along a flat
  road are such that for every 2 turns of the
  pedals the rear wheel makes 5 turns.If the
  pedals make 150 turns, how many turns will the
  rear wheel make?When travelling up a steep hill
  in a different gear, would you expect the rear
  wheel to make more or less than 5 turns for each
  2 turns of the pedals?Explain your answer.
• 3 The answers to a survey are shown in a pie
  chart. The angle representing Yes is 120, the
  angle for No is 150, and the angle for Dont
  know is 90.If 300 people took part in the
  survey, how many replied No?

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2 The gears of a bicycle travelling along a flat
road are such that for every 2 turns of the
pedals the rear wheel makes 5 turns.If the
pedals make 150 turns, how many turns will the
rear wheel make?When travelling up a steep hill
in a different gear, would you expect the rear
wheel to make more or less than 5 turns for each
2 turns of the pedals?Explain your answer.
Pedals
Wheels
x2
x5
Working 2
X 2.5
5
150
?
150
X 2.5
375
The rear wheel will turn 375 times
I would expect the rear wheel to make more/less
turns travelling up hill because
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Ratio problems 2 M5.4

• 1 In a game of rugby Robs ratio of successful to
  unsuccessful kicks was 5  3. Daves ratio was
  3  2. Who was the more successful?
• 2 The gears of a bicycle travelling along a flat
  road are such that for every 2 turns of the
  pedals the rear wheel makes 5 turns.If the
  pedals make 150 turns, how many turns will the
  rear wheel make?When travelling up a steep hill
  in a different gear, would you expect the rear
  wheel to make more or less than 5 turns for each
  2 turns of the pedals?Explain your answer.
• 3 The answers to a survey are shown in a pie
  chart. The angle representing Yes is 120, the
  angle for No is 150, and the angle for Dont
  know is 90.If 300 people took part in the
  survey, how many replied No?

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3 The answers to a survey are shown in a pie
chart. The angle representing Yes is 120, the
angle for No is 150, and the angle for Dont
know is 90.If 300 people took part in the
survey, how many replied No?
150º / 360º 15 / 36 5 / 12
We need 5/12 of 300
1/ 12 is 300 12 25
5 / 12 is 5 x 25 125
Answer 125 people in the survey said no.
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Objectives how have we done?

• Divide a quantity in a given ratio
• Solve simple problems using a unitary method

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Thank you for your attention