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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 • Compare the number of boys to girls in the class. • The number of boys = • The number of girls = • If we compare boys to girls we get ___ boys to _____ girls. What do we call a comparison between two or more quantities? RATIO We just found the RATIO of boys to girls. Is the ratio of girls to boys the same ? No, when writing a ratio, ORDER matters. Football Fans Class A has 30 students: Class B has 18 students: 10 Giants fans 20 Patriots fans 9 Giants fans 9 Patriots fans You’re a Giants fan. Which class would you rather be in? Discuss Did You Pick A? A: 10 + 20 = 30 B: 9 + 9 = 18 – Jamie, a Giants fan, picked class A: “10 is bigger than 9, so there’s more Giants fans in class A than class B. Yey!” Did You Pick class B? A: 10 + 20 = 30 B: 9 + 9 = 18 to 1 - But other Giants 2fans picked class B: third and half are fractions BECKY SAYS: “Only one third of class A is Giants fans. It’s one half in class B. is a ratio 1 out of 3 MARTIN SAYS is a “I’m not going to class A I’d be outnumbered 2 proportion Patriots fans to every 1 Giants fan!” 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? Recap – 3 Ways to Compare Numbers in written form. “A only has 10 out of 30 Giants fans. That’s 1 out of 3.” “I’m not going to A. I’d be outnumbered 2 to every 1.” “Only one third of class A are Giants fans. It’s one half in B.” Which question is a … Fraction? Ratio? Proportion? What’s the Difference - Summing Up: . 3 different ways to 3 different ways to say the same thing 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 How many basketballs to footballs are there? • For every 4 basketballs there are 6 footballs. • The ratio is 4basketballs to 6 footballs. What are some other ways we can write the ratio of basketball to footballs? Ratio can be written in 3 ways in number form: 4 to 6 First quantity to Second quantity • 4:6 First quantity : Second quantity • 4 6 • First quantity divided by the second quantity (as a fraction). Careful!! Order matters in a ratio. 4 to 6 Is NOT the same as 6 to 4 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. Equivalent Ratios • Simplify the following ratios: – 4 to 8 – 10 to 8 – 8 to 10 4 = 4/4 8 8/4 =1 2 = 1 to 2 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) 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 More Review A Pizza Party Ratio of girls to boys? 4 girls to every 8 boys girls : boys = 4 : 8 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 8 boys to every 4 girls The Pizza Party boys : girls = 8 : 4 Ratio of But the simplest ratio is still 2 : 1 boys to girls? 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 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? 50 ? 2 : 1 = 100 : The Pizza Party What proportion is girls? 4 girls out of 12 Simplest proportion of girls is still 1 out of 3 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 The Pizza Party What proportion is boys? Proportion of of boys? 8 boys out 12 Simplestproportion proportionof of Simplest boys? boys is still 2 out of 3 6 boys out of 9 Proportion of boys? Simplest Simplestproportion proportionof of boys is still 2 out of 3 boys? 4 boys out of 6 Proportion of boys? Simplest Simplestproportion proportionofof boys is still 2 out of 3 boys? Proportion of boys? 2 boys out of 3 Simplest proportion of boys? This is the simplest proportion of boys = 2 out of 3 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 Click to check your answer girls : boys = 2 : 1 means 2 girls to every boy ORDER MATTERS! Be careful what you write! True or Not 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 ..