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Ratio and Proportion .

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

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Ratio and Proportion .

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  1. Ratio and Proportion .

  2. What Will You Learn ? How exactly do you keep numbersin 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!

  3. 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

  4. CURR 383 C has 30 pupils: 10 Senators fans 20 Leafs fans CURR 383 M has 18 pupils: 9 Senators fans 9 Leafs fans First Thoughts … You’re a Leafs fan. Which class would you rather be in? Why?

  5. C : 10 +20 = 30 M : 9 +9 = 18 – Sam, a fanatical Senators fan, picked CURR 383C: Did You Pick CURR 383C like Sam? “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?

  6. C : 10 +20 = 30 M : 9 +9 = 18 - But other Senator fans picked M: Did You Pick CURR 383M? 2 to 1 is a ratio 1 out of 3 is a proportion third and half are fractions 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 fans out of a total of 30 fans. That’s 1 out of 3.” Who is right? All answers are correct! But - 3 different sorts of answer. Which do you prefer? Why?

  7. Recap – 3 Ways to Compare Numbers Which question is a … “C only has 10 Senators fans out of a total of 30 fans. That’s 1 out of 3.” Fraction? “I’m not going to C. I’d be outnumbered 2 to every 1.” Ratio? Proportion? “Only one third of C are Senators fans. It’s one half in M.”

  8. What’s the Difference - Summing Up:. 3 different ways to say the same thing 3 different ways to compare numbers “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

  9. 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 Eg: Senators : Leafs = 1 to every 2 = 1:2 PROPORTIONS or FRACTIONS Eg: 1 out of 3 are Senators fans Eg: 1/3 are Senators fans

  10. Ratio, Proportion or Fraction? two out of five This is a … two fifths This is a … proportion fraction four tenths This is a … four to every ten This is a … fraction ratio ten to every four This is a … four out of ten This is a … ratio proportion 4/10 This is a … 4:10 This is a … fraction ratio

  11. 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

  12. 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

  13. 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

  14. Ratio and Proportion Ratio 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

  15. PART 2: Simplest Ratios and Proportions

  16. The dinner queue 4 girls to every 8 boys girls : boys = 4 : 8 Ratio of girls to boys? But the simplest ratio is still 1 : 2 3 girls to every 6 boys girls : boys =3 : 6 But the simplest ratio is still 1 : 2 2 girls to every 4 boys girls : boys =2 : 4 But the simplest ratio is still 1 : 2 1 girl to every 2 boys girls : boys =1 : 2 This is the simplest ratio is 1 : 2

  17. The dinner queue 8 boys to every 4 girls boys : girls = 8 : 4 Ratio of boys to girls? But the simplest ratio is still 2 : 1 6 boys to every 3 girls boys : girls = 6 : 3 But the simplest ratio is still 2 : 1 4 boys to every 2 girls boys : girls = 4 : 2 But the simplest ratio is still 2 : 1 2 boys to every 1 girl boys : girls = 2 : 1 This is the simplest ratio is 2 : 1

  18. Simplest ratios 2 : 1 is a simpler ratio than 4 : 2 but They both mean the same 2 : 1 = 4 : 2 Can you explain why 2 : 1 = 6 : 3 ? 2 : 1 = 8 : 4 ? 2 : 1 = 100 : 50 ?

  19. The dinner queue 4 girls out of 12 Simplest proportion of girls is still 1 out of 3 What proportion is girls? 3 girls out of 9 Simplest proportion of girls is still 1 out of 3 2 girls out of 6 Simplest proportion of girls is still 1 out of 3 1 girl out of 3 This is the simplest proportion of girls = 1 out of 3

  20. The dinner queue Proportion of boys? 8 boys out of 12 Simplest proportion of boys? Simplest proportion of boys is still 2 out of 3 What proportion is boys? 6 boys out of 9 Proportion of boys? Simplest proportion of boys is still 2 out of 3 Simplest proportion of boys? 4 boys out of 6 Proportion of boys? Simplest proportion of boys is still 2 out of 3 Simplest proportion of boys? Proportion of boys? 2 boys out of 3 Simplest proportion of boys? This is the simplest proportion of boys = 2 out of 3

  21. What fraction is girls? 4 / 12 The dinner queue Simplest fraction of girls is still 1 / 3 Simplest proportion of girls? What fraction is girls? 3 / 9 What fraction is girls? Simplest fraction of girls is still 1 / 3 Simplest fraction of girls? 2 / 6 What fraction is girls? Simplest fraction of girls is still 1 / 3 Simplest fraction of girls? 1 / 3 What fraction is girls? This is the simplest fraction of girls = 1 / 3 Simplest fraction of girls?

  22. The dinner queue What fraction is boys? 8 / 12 Simplest proportion of boys? Simplest fraction of boys is still 2 / 3 What fraction is boys? 6 / 9 What fraction is boys? Simplest fraction of boys is still 2 / 3 Simplest fraction of boys? 4 / 6 What fraction is boys? Simplest fraction of boys is still 2 / 3 Simplest fraction of boys? 2 / 3 What fraction is boys? This is the simplest fraction of boys = 2 / 3 Simplest fraction of boys?

  23. 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 boys : girls = 2 : 1 means 2 boys to every girl girls : boys = 2 : 1 means 2 girls to every boy Click to check your answer ORDER MATTERS! Be careful what you write!

  24. GUESS! True or Not True? TRUE! 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 : 5 You wish! Ratio of porridge lovers to pizza guzzlers = 100 : 1 - Not until they invent Porridge Pizza.. TRUE! TRUE! TRUE!

  25. PART 3: Recipes and Proportion How to scale a recipe for 10 people down to 4 people without disaster!

  26. It’s supper time! You make a simple omelette like this: + = 2 eggs + 5 ml of butter = 1 omelette Your omelette tastes amazing! - So of course your friends start turning up. Can you scale up your ingredients to feed them all? 4 eggs + 10 ml of butter = 2 omelettes ? eggs + ? tsp of butter = 2 omelettes ? eggs + ? tsp of butter = 3 omelettes 6 eggs + 15 ml of butter = 3 omelettes ? eggs + ? tsp of butter = 4 omelettes 8 eggs + 20 ml of butter = 4 omelettes ? eggs + ? tsp of butter = 5 omelettes 10 eggs + 25 ml of butter = 5 omelettes

  27. Recipe for Shortbread Biscuits Makes 20 shortbread biscuits Ingredients 200g butter 200g plain flour 100g golden caster sugar 100g 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.

  28. 10 Mouth-watering Shortbread Biscuits! 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! 20 biscuits 400g flour 200g sugar 200g semolina + + + = 400g butter ? ? ? ÷ 2 ÷ 2 ÷ 2 ? ? ÷ 2 ÷ 2 10 biscuits 200g flour 100g sugar 100g semolina + + + = 200g butter

  29. 20 biscuits 400g flour 200g sugar 200g semolina + + + = 400g butter Whoops ! … Jesse makes 2 shortbread biscuits 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? Check his calculations. Then click to see if you’re right 20 biscuits ÷ 10 ÷ 10 ÷ 10 ÷ 10 x 10 ? ? ? x10 x 10 x 10 ? ? x 10 ÷ 10 200 BISCUITS INSTEAD OF 2! WHAT DIFFERENCE DID THE MISTAKE MAKE? 2 biscuits 40 g flour 20 g sugar 4000 g flour 2000 g sugar 20 g semolina 2000 g semolina 40 g butter + + + = 4000 g butter

  30. 20 biscuits 400g flour 200g sugar 200g semolina + + + = 400g butter Whoops ! … Emma makes 5 shortbread biscuits 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? Check her calculations. Then click to see if you’re right ÷ 4 ÷ 2 ÷ 4 ÷ 4 ? ÷ 4 ÷ 4 THE BISCUITS WERE TOO SWEET! WHAT DIFFERENCE DID THE MISTAKE MAKE? 5 biscuits 100 g flour 50 g semolina 100 g butter 100 g sugar 50 g sugar + + + =

  31. Further Practical ExamplesRecipe No.1 Melon Merenga Serves 8 people Ingredients 300 g raspberries 200 g bananas 100 g melon Method Place ingredients in a blender and switch on power for 30 seconds. Pour and serve with ice or ice-cream.

  32. Can you work out the missing amounts? Melon Merenga for 8 + + = 600 g 400 g 200 g MelonMerenga for 4 + + = ? g ? g ? g 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) 300 g 200 g 100 g MelonMerenga for 2 + + = ? g ? g ? g 150 g 100 g 50 g You can work this out from the quantities for 1 person, BUT … Can you see a shortcut? MelonMerenga for 1 + + = ? g ? g ? g 75 g 50 g 25 g MelonMerenga for 6 + + = ? g ? g ? g 450 g 300 g 150 g

  33. Further Practical ExamplesRecipe No.2 Raspberry Fruitloop(Same ingredients. Different amounts) Serves 10 people Ingredients 500 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

  34. Can you work out the missing amounts? Raspberry Fruitloop for 10 + + = 500 g 250 g 150 g Raspberry Fruitloop for 5 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) + + = ? g ? g ? g 250g 125g 75g Raspberry Fruitloop for 1 + + = ? g ? g ? g 50g 25g 15g You can work this out from the quantities for 1 person, BUT … Can you see any shortcuts? Raspberry Fruitloop for 4 + + = ? g ? g ? g 200g 100g 60g Raspberry Fruitloop for 8 + + = ? g ? g ? g 400g 200g 120g

  35. Further Practical ExamplesRecipe No.3 Bombastic Banana Boat(Same ingredients. Different amounts) Serves 12 people Ingredients 120 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

  36. Can you work out the missing amounts? Banana Boat for 12 + + = 120 g 600 g 120 g Banana Boat for 6 + + = ? g ? g ? g 60 g 300 g 60 g 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) Banana Boat for 4 + + = ? g ? g ? g 40 g 200 g 40 g You can work this out from the quantities for 1 person, BUT … Can you see a shortcut? Banana Boat for 1 + + = ? g ? g ? g 10 g 50 g 10 g Banana Boat for 8 + + = ? g ? g ? g 80 g 400 g 80 g

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