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 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? 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.

Equivalent Ratios

Which class would you rather be in? Football Fans Class A has 30 students: 10 Giants fans 20 Patriots fans Class B has 18 students: 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 - But other Giants fans picked class B: 2 to 1 is a ratio MARTIN SAYS “I’m not going to class A - I’d be outnumbered 2 Patriots fans to every 1 Giants fan!” 1 out of 3 is a proportion 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?

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.”

What’s the Difference - Summing Up: . 3 different ways to say the same thing 3 different ways to compare numbers Ratios compare PART WITH PART “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” 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 4 : 6 4 6 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).

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 8 / 4 2

For example, the ratio 2 : 3 can also be written as 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)

Write the following ratios all three ways… 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 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

The Pizza Party Ratio of boys to girls? 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

2 : 1 is a simpler ratio than 4 : 2 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 ?

What proportion is girls? 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

What proportion is boys? The Pizza Party 8 boys out of 12 Proportion of boys? Simplest proportion of boys is still 2 out of 3 Simplest proportion of boys? 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? 2 boys out of 3 Proportion of boys? Simplest proportion of boys? This is the simplest proportion of boys = 2 out of 3

Be careful what you write! 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!

True or Not True? TRUE! Ratio of pupils to teachers = 30 : 1 GUESS! 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!