Example 1

In a survey of American families, 150 families had a total of 360 children. What is the ratio of children to families? On average, how many children are there per family?

Make sure you pay attention to the order of the wording

360/1502.4 children/family

What is a Ratio?

A ratio is a comparison of two quantities, usually by division.

• The ratio of a to b is a:b or• Order is important!

– Part: Part– Part: Whole– Whole: Part

– Units, sometimes important

ba

6.1 Ratio and Proportion

Objectives:

1. To recognize and use ratios and proportions to solve problems

Example 2

Find the first 13 terms in the following sequence:

1, 1, 2, 3, 5, 8, …

This is called the Fibonacci Sequence!

13,21,34,55,89,144,233

Foxtrot

Example 3

What happens when you take the ratios of two successive Fibonacci numbers, larger over smaller? What number do you approach?

1

1

1

2

2

3

3

5

5

8

8

13

13

21ETC!

The Golden Ratio

What happens when you take the ratios of two successive Fibonacci numbers, larger over smaller? What number do you approach?

It’s the Golden Ratio = 1.61803398…

What’s a Proportion?

When two ratios are equal, it’s called a proportion.

• What’s an example of a proportion? What ratio is equal to ½?

• Proportions are often used in solving problems involving similar objects.

Solving a Proportion

What’s the relationship between the cross products of a proportion?

14.2

150360

36012.4150

They’re equal!

Solving a Proportion

Cross Products Property

In a proportion, the product of the extremes equals the product of the means.

Solving a Proportion

To solve a proportion involving a variable, simply set the two cross products equal to each other. Then solve!

x25

15275

275x1525

x275375

x36.1

Example 4

Solve the proportion.

26

50 75

x

50x = 1950x=39

Example 5

Solve the proportion.

2 1

4 5

x

x

Show your work in your notebook.

x= -6 or 1

More Proportion Properties

INTERESTING, huh?

Exercise 1

If you work for 2 weeks and earn $380, what will you expect to earn in 15 weeks?

$2850

Show your work in your notebook

Exercise 2

Solve for y:

yy 3

2

1

1

Show your work in your notebook

y=2

Exercise 3

Which is longer: a yardstick or a meter stick? (Use the conversion factor 1 in. = 2.54 cm)

Show work in your notebook.

Meter stick

Remember: 1 m = 100 cm

Exercise 4

The sides of a rose garden in the shape of a right triangle are in the ratio of 8:15:17. If the perimeter is 60 ft, what is the length of the shortest side?

How are you going to do this one?

Think about what perimeter means

Work it out in your notebook.

12

The Greeks, Again!

The Greeks used the Golden Ratio to do everything from making a pentagram, to constructing a building, to combing their hair.

The Golden Rectangle

If you make a rectangle with sides that have the Golden Ratio, you’ve made a sparkly Golden Rectangle.

s

l

Extra Credit Opportunities

1. Construct a Golden Rectangle with a compass and straightedge and explain how it demonstrates the Golden Ratio