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?

RATIOWe 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 FansClass A has 30

students:

10 Giants fans20 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:MARTIN SAYS“I’m not going to class A - I’d be outnumbered 2 Patriots fans to every 1

Giants fan!”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 has 10 out of 30 Giants Giants fans.

That’s 1 out of 3.”

2 to 1

is a ratiothird and half are

fractions

1 out of 3 is a

proportion

All answers are correct! But - 3 different sorts of answer.

Which do you prefer? Why?

Recap – 3 Ways to Compare Numbers in written form.

Fraction?

Proportion?

Ratio?

Which question is a …

“Only one third of class A are Giants fans. It’s one half in B.”

“I’m not going to A.

I’d be outnumbered 2 to every 1.”

What’s the Difference - Summing Up: .

“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

3 different ways to say the same thing

3 different ways to compare numbers

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?

• 4 to 6

• 4 : 6

• 4 6

First quantity to Second quantity

First quantity : Second quantity

First quantity divided by the second quantity (as a fraction).

Ratio can be written in 3 ways in number form:

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 = 1 = 1 to 2

8 8 / 4 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

1 girl to every 2 boys

2 girls to every 4 boys

3 girls to every 6 boys

4 girls to every 8 boys

girls : boys = 4 : 8

girls : boys = 3 : 6

girls : boys = 2 : 4

girls : boys = 1 : 2

But the simplest ratio is still 1 : 2

But the simplest ratio is still 1 : 2

But the simplest ratio is still 1 : 2

This is the simplest ratio is 1 : 2

A Pizza Party

Ratio of girls to boys?

2 boys to every 1 girl

4 boys to every 2 girls

6 boys to every 3 girls

8 boys to every 4 girls

boys : girls = 8 : 4

boys : girls = 6 : 3

boys : girls = 4 : 2

boys : girls = 2 : 1

But the simplest ratio is still 2 : 1

But the simplest ratio is still 2 : 1

But the simplest ratio is still 2 : 1

This is the simplest ratio is 2 : 1

Ratio of boys to girls?

The Pizza Party

Simplest ratios2 : 1 is a simpler ratio than 4 : 2

but They both mean the same

2 : 1 = 4 : 2

Can you explain why2 : 1 = 6 : 3 ? 2 : 1 = 8 : 4 ? 2 : 1 =

100 : 50 ?

1 girl out of 3

2 girls out of 6

3 girls out of 9

4 girls out of 12

Simplest proportion of girls is still 1 out of 3

Simplest proportion of girls is still 1 out of 3

Simplest proportion of girls is still 1 out of 3

This is the simplest proportion of girls =

1 out of 3

The Pizza Party

What proportion is girls?

Proportion of boys?

Simplest proportion of boys?

Proportion of boys?

Simplest proportion of boys?

Proportion of boys?

Simplest proportion of boys?

Proportion of boys?

4 boys out of 6

6 boys out of 9

8 boys out of 12

Simplest proportion of boys is still 2 out of 3

Simplest proportion of boys is still 2 out of 3

Simplest proportion of boys is still 2 out of 3

Simplest proportion of boys?

This is the simplest proportion of boys

= 2 out of 3

2 boys out of 3

The Pizza Party

What proportion is boys?

Does order matter?

There are 20 boys and 10 girls in 6D.

Which of these are correct?b) girls : boys = 2 : 1a) boys : girls = 2 : 1 c) boys : girls = 1 : 2

ORDER MATTERS!Be careful what you write!

Click to check your answerboys : girls = 2 : 1 means 2 boys to every girl girls : boys = 2 : 1 means 2 girls to every boy

TRUE!

True or Not True?GUESS!

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 : 5You wish!

Ratio of porridge lovers to pizza guzzlers = 100 : 1

- Not until they invent Porridge Takeaways ..

TRUE!

TRUE!

TRUE!