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 ..