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. 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

8. 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!”

9. 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?

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
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

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?
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).

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 Simplify the following ratios: 4 to 8 10 to 8/

16. 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)

17. 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

18. More Review

19. 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

20. 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

21. 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 ?

22. 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

23. 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

24. 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!

25. 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!