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Introducing Ratio

Introducing Ratio. First Thoughts …. There’s lots of differences between the classes in our school – … Some have more boys than girls … Less Patriots fans than Giants fans … More cat-lovers than dog-lovers … Less pizza-munchers than chicken-dippers. Ratios.

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Introducing Ratio

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  1. Introducing Ratio

  2. First Thoughts … There’s lots of differences between the classes in our school – … Some have more boys than girls … Less Patriots fans than Giants fans … More cat-lovers than dog-lovers … Less pizza-munchers than chicken-dippers

  3. Ratios • Compare the number of boys to girls in the class.

  4. The number of boys = • The number of girls = • If we compare boys to girls we get ___ boys to _____ girls.

  5. What do we call a comparison between two or more quantities? We just found the RATIO of boys to girls. RATIO Is the ratio of girls to boys the same ? No, when writing a ratio, ORDER matters.

  6. Equivalent Ratios

  7. Class A has 30 students: 10 Giants fans 20 Patriots fans Class B has 18 students: 9 Giants fans 9 Patriots fans Football Fans You’re a Giants fan. Which class would you rather be in? Discuss

  8. A: 10 +20 = 30 B: 9 +9 = 18 – Jamie, a Giants fan, picked class A: Did You Pick A? “10 is bigger than 9, so there’s more Giants fans in class A than class B. Yey!”

  9. A: 10 +20 = 30 B: 9 +9 = 18 - But other Giants fans picked class B: Did You Pick class B? 2 to 1 is a ratio 1 out of 3 is a proportion MARTIN SAYS “I’m not going to class A - I’d be outnumbered 2 Patriots fans to every 1 Giants fan!” third and half are fractions BECKY SAYS: “Only one third of class A is Giants fans. It’s one half in class B. HANNAH SAYS: “Class A only has 10 out of 30 Giants fans. That’s 1 out of 3.” All answers are correct! But - 3 different sorts of answer. Which do you prefer? Why?

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

  11. 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 Giants fan to every 2 Patriots” “The ratio of Giants to Patriots fans is 1 to 2” “The ratio of Patriots to Giants fans is 2 to 1” “1 out of 3” is a Proportion “1 out of every 3 fans is a Giants fan” “The proportion of Giants fans is 1 out of 3” “One third” is a Fraction “One third of all fans are Giants fans “1/3 of all fans are Giants fans” Ratios compare PART WITH PART Proportions compare PART WITH WHOLE Fractions compare PART WITH WHOLE using shorthand such as 1/3

  12. How many basketballs to footballs are there? • For every 4 basketballs there are 6 footballs. • The ratio is 4basketballs to 6 footballs.

  13. What are some other ways we can write the ratio of basketball to footballs? • 4 to 6 • 4 : 6 • 4 6 Ratio can be written in 3 ways in number form: First quantity to Second quantity Careful!! Order matters in a ratio. 4 to 6 Is NOT the same as 6 to 4 First quantity : Second quantity First quantity divided by the second quantity (as a fraction).

  14. Write the ratio of sandwiches to coke bottles 3 different ways. Since a fraction can be simplified, We can simplify the ratio 6/8 to 3/4. The ratio of sandwiches to coke bottles can also be expressed as 3 : 4 or 3 to 4. In other words, ratios can be simplified to form equivalent ratios.

  15. Equivalent Ratios • = 4 / 4 = 1 = 1 to 2 8 8 / 4 2 • Simplify the following ratios: • 4 to 8 • 10 to 8 • 8 to 10

  16. Equivalent Ratios can be formed by multiplying the ratio by any number. • For example, the ratio 2 : 3 can also be written as • 4 : 6 (multiply original ratio by by 2) • 6 : 9 (multiply original ratio by by 3) • 8 : 12 (multiply original ratio by by 4)

  17. A bag contains 18 marbles. There are 8 yellow marbles, 4 blue marbles, and 6 red marbles. • Write the following ratios all three ways… • Yellow to blue • Red to total • Total to blue

  18. More Review

  19. A Pizza Party 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

  20. The Pizza Party 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

  21. 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 ?

  22. The Pizza Party 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

  23. The Pizza Party 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

  24. Does order matter? There are 20 boys and 10 girls in 6D. 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!

  25. GUESS! True or Not True? TRUE! Ratio of pupils to teachers = 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 Takeaways .. TRUE! TRUE! TRUE!

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