ratio and proportion
DESCRIPTION
Ratio and Proportion. What Will You Learn ?. How exactly do you keep numbers in proportion ? What’s the difference between ratio , proportion and fractions ? If you work through this slideshow, you will find out that: Ratio and proportion are EASY! Fractions will make more sense too - PowerPoint PPT PresentationTRANSCRIPT
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What Will You Learn ?
How exactly do you keep numbers in proportion?
What’s the difference between ratio, proportion and fractions?
If you work through this slideshow, you will find out that:
• Ratio and proportion are EASY!• Fractions will make more sense too• You can work out most of the solutions in
your head!
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Getting in a ratio & proportion frame of mind...
There’s lots of differences among the classes in your school –
… Some have more boys than girls
… Fewer Senators fans than Leafs fans
… More cat-lovers than dog-lovers
… Fewer granola-gobblers than pizza-maniacs
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First Thoughts …CURR 383 C has 30 pupils:
10 Senators fans
20 Leafs fans
CURR 383 M has 18 pupils:
9 Senators fans
9 Leafs fansYou’re a Leafs fan.
Which class would you rather be in?Why?
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Did You Pick CURR 383C like Sam?
C : 10 + 20 = 30 M : 9 + 9 = 18
– Sam, a fanatical Senators fan, picked CURR 383C:
“10 is bigger than 9,
so there’s more Senators fans in “C” than “M”.
Yey!”
Do you agree with Sam?Why or why not?
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Did You Pick CURR 383M?
C : 10 + 20 = 30 M : 9 + 9 = 18
- But other Senator fans picked M:
MARTIN SAYS
“I’m not going to C - I’d be outnumbered 2 Leafs to every 1 Senators fan!”
BECKY SAYS:“Only one
third of C are Senators fans. It’s one half in
M.
HANNAH SAYS:“C only has 10 Senators has 10 Senators fans out of a total of 30 fans out of a total of 30
fans.
That’s 1 out of 3.”
Who is right?
2 to 1
is a ratiothird and half are
fractions
1 out of 3 is a
proportion
All answers are correct! But - 3 different sorts of answer.
Which do you prefer? Why?
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Recap – 3 Ways to Compare Numbers
Fraction?
Proportion?
Ratio?
Which question is a …“C only has 10 Senators
fans out of a total of 30 fans. That’s 1 out of 3.”
“Only one third of C are Senators fans.
It’s one half in M.”
“I’m not going to C.
I’d be outnumbered 2 to every 1.”
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What’s the Difference - Summing Up: .
“1 to every 2” is a Ratio“1 Senators fan to every 2 Leafs fans”“The ratio of Senators to Leafs fans is 1 to 2”“The ratio of Leafs to Senators fans is 2 to 1”
“1 out of 3” is a Proportion“1 out of every 3 fans is a Senators fan”“The proportion of Senator fans is 1 out of 3”
“One third” is a Fraction“One third of all fans are Senators fans“1/3 of all fans are Senators fans”
Ratios compare PART
WITH PART
Proportions compare PART WITH WHOLE
Fractions compare PART WITH WHOLE
using shorthand such as 1/3
3 different ways to say the same thing
3 different ways to compare numbers
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So comparing totals isn’t the only way to look at these numbers…
CURR 383 C has 30 pupils:
10 Senators fans
20 Leafs fans
CURR 383 M has 18 pupils:
9 Senators fans
9 Leafs fans…You can compare part with part using RATIO
…You can compare part with whole using
PROPORTIONS or FRACTIONS
Eg: 1/3 are Senators fansEg: 1 out of 3 are Senators fans
Eg: Senators : Leafs = 1 to every 2 = 1:2
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Ratio, Proportion or Fraction?two out of five
This is a … proportion
two fifths
This is a … fractionfour tenths
This is a … fractionfour to every ten
This is a … ratioten to every four
This is a … ratiofour out of ten
This is a … proportion4/10
This is a … fraction 4:10
This is a … ratio
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Ratio, Proportion or Fraction?3 Leafs fans to every 2 Senators fans
This is a …ratio
9 girls out of 10 use Facebook
This is a …proportion
3 boys out of 10 use Twitter
This is a …proportion
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Ratio, Proportion or Fraction?3 out of 4 pizza-maniacs love olives
This is a …proportion
Half of all 14-year old girls watchTwilight
This is a …fraction
One third of all road accidents involve drinking
This is a …fraction
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Ratio, Proportion or Fraction?3 out of 4 drivers speed at some time
This is a …proportion
Three quarters of drivers speed
This is a …fraction
3 drivers speed to every 1 who does not
This is a …ratio
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Ratio and ProportionRatio and Proportion: Different Words!
Ratio: “to every” 1 Senators fan to every 2 Leafs fans
Proportion: “out of”1 out of 3 hockey fans is a Senators fan
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PART 2: Simplest Ratios and Proportions
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1 girl to every 2 boys
2 girls to every 4 boys
3 girls to every 6 boys
4 girls to every 8 boys
girls : boys = 4 : 8
girls : boys = 3 : 6
girls : boys = 2 : 4
girls : boys = 1 : 2
But the simplest ratio is still 1 : 2
But the simplest ratio is still 1 : 2
But the simplest ratio is still 1 : 2
This is the simplest ratio is 1 : 2
The dinner queue
Ratio of girls to boys?
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2 boys to every 1 girl
4 boys to every 2 girls
6 boys to every 3 girls
8 boys to every 4 girls
boys : girls = 8 : 4
boys : girls = 6 : 3
boys : girls = 4 : 2
boys : girls = 2 : 1
But the simplest ratio is still 2 : 1
But the simplest ratio is still 2 : 1
But the simplest ratio is still 2 : 1
This is the simplest ratio is 2 : 1
Ratio of boys to girls?
The dinner queue
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Simplest ratios
2 : 1 is a simpler ratio than 4 : 2 but
They both mean the same2 : 1 = 4 : 2
Can you explain why2 : 1 = 6 : 3 ? 2 : 1 = 8 : 4 ? 2 : 1 = 100 : 50 ?
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1 girl out of 3
2 girls out of 6
3 girls out of 9
4 girls out of 12
Simplest proportion of girls is still 1 out of 3
Simplest proportion of girls is still 1 out of 3
Simplest proportion of girls is still 1 out of 3
This is the simplest proportion of girls =
1 out of 3
The dinner queue
What proportion is girls?
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Proportion of boys?
Simplest proportion of boys?
Proportion of boys?
Simplest proportion of boys?
Proportion of boys?
Simplest proportion of boys?
Proportion of boys?
4 boys out of 6
6 boys out of 9
8 boys out of 12
Simplest proportion of boys is still 2 out of 3
Simplest proportion of boys is still 2 out of 3
Simplest proportion of boys is still 2 out of 3
Simplest proportion of boys?
This is the simplest proportion of boys
= 2 out of 3
2 boys out of 3
The dinner queue
What proportion is boys?
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What fraction is girls?
Simplest proportion of girls?
What fraction is girls?
Simplest fraction of girls?
What fraction is girls?
Simplest fraction of girls?
What fraction is girls?
2 / 6
3 / 9
4 / 12
Simplest fraction of girls is still 1 / 3
Simplest fraction of girls is still 1 / 3
Simplest fraction of girls is still 1 / 3
Simplest fraction of girls? This is the simplest
fraction of girls = 1 / 3
1 / 3
The dinner queue
What fraction is girls?
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What fraction is boys?
Simplest proportion of boys?
What fraction is boys?
Simplest fraction of boys?
What fraction is boys?
Simplest fraction of boys?
4 / 6
6 / 9
8 / 12
Simplest fraction of boys is still 2 / 3
Simplest fraction of boys is still 2 / 3
Simplest fraction of boys is still 2 / 3
Simplest fraction of boys?
This is the simplest fraction of boys = 2 / 3
The dinner queue
What fraction is boys?
What fraction is boys?2 / 3
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Does order matter?
There are 20 boys and 10 girls in CURR 383T.
Which of these are correct?
b) girls : boys = 2 : 1
a) boys : girls = 2 : 1
c) boys : girls = 1 : 2
ORDER MATTERS!Be careful what you write!
Click to check your answerboys : girls = 2 : 1 means 2 boys to every girl girls : boys = 2 : 1 means 2 girls to every boy
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TRUE!
True or Not True? GUESS!
Ratio of teachers to pupils = 30 : 1
Ratio of fans to players = 1 : 1000 This would mean all the players would be sitting in the stadium!
Ratio of weekdays to weekend days = 2 : 5You wish!
Ratio of porridge lovers to pizza guzzlers = 100 : 1 - Not until they invent Porridge Pizza..
TRUE!
TRUE!
TRUE!
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PART 3: Recipes and Proportion
How to scale a recipe for 10 people down to 4 people without disaster!
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+ =
Your omelette tastes amazing! - So of course your friends start turning up.
Can you scale up your ingredients to feed them all?
It’s supper time! You make a simple omelette like this:
? eggs + ? tsp of butter = 2 omelettes
? eggs + ? tsp of butter = 3 omelettes
? eggs + ? tsp of butter = 4 omelettes
? eggs + ? tsp of butter = 5 omelettes
2 eggs + 5 ml of butter = 1 omelette
4 eggs + 10 ml of butter = 2 omelettes
6 eggs + 15 ml of butter = 3 omelettes
8 eggs + 20 ml of butter = 4 omelettes
10 eggs + 25 ml of butter = 5 omelettes
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Recipe for Shortbread Biscuits
Makes 20 shortbread biscuitsIngredients200g butter200g plain flour100g golden caster sugar100g fine semolina
Pre-heat the oven to gas mark 2, 300°F (150°C).
You will also need an 8 in (20 cm) diameter fluted flan tin, 1¼ in (3 cm) deep with a loose base.
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10 Mouth-watering Shortbread Biscuits!
+ + + = 400g flour
400g butter
200g sugar
200g semolina
This is the recipe for 20 biscuits. Can you scale down the recipe for 10?
Remember to keep your recipe in proportion – if you halve the sugar, remember to halve the rest as well or it won’t taste good!
?
+ + + = 10biscuits
200g flour
200g butter
100g sugar
100g
semolina
? ? ? ? ÷ 2 ÷ 2 ÷ 2 ÷ 2 ÷ 2
20biscuits
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… Jesse makes 2 shortbread biscuits
+ + + = 20biscuits
400g flour
400g butter
200g sugar
200g semolina
Jesse scaled down the recipe for 2 biscuits, but they don’t taste right!
Did he scale down correctly and keep the recipe in proportion?
?
+ + + = 2biscuits
4000 g flour
4000 g butter
2000 g sugar
2000 g
semolina
? ? ? ? x10 x 10 x 10 x 10 x 10 ÷ 10 ÷ 10 ÷ 10 ÷ 10
40 g butter
20 g sugar
20 g
semolina 40 g
flour
WHAT DIFFERENCE DID THE MISTAKE MAKE?
200 BISCUITS INSTEAD
OF 2!
Check his calculations.
Then click to see if you’re right
20biscuits
÷ 10
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… Emma makes 5 shortbread biscuits
+ + + = 20biscuits
400g flour
400g butter
200g sugar
200g semolina
Emma scaled down the recipe for 5 biscuits, but they don’t taste right!
Did she scale down correctly and keep the recipe in proportion?
+ + + = 5biscuits
100 g sugar
? ÷ 2
100 g butter
50 g sugar
50 g
semolina 100 g
flour
Check her calculations.
Then click to see if you’re right
WHAT DIFFERENCE DID THE MISTAKE MAKE?
THE BISCUITS
WERE TOO SWEET!
÷ 4 ÷ 4 ÷ 4
÷ 4 ÷ 4
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Serves 8 people
Ingredients300 g raspberries 200 g bananas 100 g melon
MethodPlace ingredients in a blender and switch on power for 30 seconds.
Pour and serve with ice or ice-cream.
Further Practical Examples Recipe No.1 Melon Merenga
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Can you work out the missing amounts?
+ + = 600 g 400 g 200 g Melon
Merenga for 8
+ + = ? g ? g ? g Melon Merenga for 4
+ + = ? g ? g ? g Melon Merenga for 2
+ + = ? g ? g ? g Melon Merenga for 6
300 g 200 g 100 g
150 g 100 g 50 g
+ + =
450 g 300 g 150 g
Melon Merenga for 1? g ? g ? g 75 g 50 g 25 g
You can work this out from the
quantities for 1 person, BUT …Can you see a
shortcut?
General Method:1) Work out the recipe for 1.2) Multiply by the number you need
Shortcut: 1) Work out from the quantities for 2 people. 2) X 3 (easier than X6)
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Further Practical Examples Recipe No.2 Raspberry Fruitloop
(Same ingredients. Different amounts)
Serves 10 people
Ingredients500 g raspberries 250 g bananas 150 g melon
Method Place ingredients in a blender and switch on power for 30 seconds.
Pour and serve with fresh raspberries
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Can you work out the missing amounts?
+ + = 500 g 250 g 150 g Raspberry
Fruitloop for 10
+ + = ? g ? g ? g Raspberry Fruitloop for 5
+ + = ? g ? g ? g Raspberry Fruitloop for 1
+ + = ? g ? g ? g Raspberry
Fruitloop for 8
250 g 125 g 75 g
50 g 25 g 15 g
+ + =
400 g 200 g 120 g
Raspberry Fruitloop for 4? g ? g ? g 200 g 100 g 60 g
You can work this out from the
quantities for 1 person, BUT …
Can you see any shortcuts?
General Method:1) Work out the recipe for 1.2) Multiply by the number you need
Shortcut: 1) Work out from the quantities for 4 people. 2) Just double it! (Easier than X8)
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Further Practical Examples Recipe No.3 Bombastic Banana Boat
(Same ingredients. Different amounts)
Serves 12 people
Ingredients120 g raspberries 600 g bananas 120 g melon
Method Place ingredients in a blender and switch on power for 30 seconds.
Pour into a scooped out melon half . Serve with fresh raspberries
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Can you work out the missing amounts?
+ + = 120 g 600 g 120 g Banana Boat
for 12
+ + = ? g ? g ? g Banana Boat for 6
+ + = ? g ? g ? g Banana Boat for 4
+ + = ? g ? g ? g Banana Boat for 8
60 g 300 g 60 g
40 g 200 g 40 g
+ + =
80 g 400 g 80 g
Banana Boat for 1? g ? g ? g 10 g 50 g 10 g
You can work this out from the
quantities for 1 person, BUT …Can you see a
shortcut?
General Method:1) Work out the recipe for 1.
2) Multiply by the number you need
Shortcut: 1) Work out from the quantities for 4 people. 2) Just double it!
(Easier than X8)