Example 1In 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 ProportionObjectives:

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

Example 2Find 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 3What happens when you take the ratios of

two successive Fibonacci numbers, larger over smaller? What number do you approach?

11

12

23

35

58

813

1321 ETC!

The Golden RatioWhat 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 ProportionWhat’s the relationship between the cross

products of a proportion?

14.2

150360 36012.4150

They’re equal!

Solving a ProportionCross Products PropertyIn a proportion, the product of the extremes

equals the product of the means.

Solving a ProportionTo 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 4Solve the proportion.

2650 75

x

50x = 1950x=39

Example 5Solve the proportion.

2 14 5

xx

Show your work in your notebook.

x= -6 or 1

More Proportion Properties

INTERESTING, huh?

Exercise 1If 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 2Solve for y:

yy 32

11

Show your work in your notebook

y=2

Exercise 3Which 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 4The 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.

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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 RectangleIf you make a rectangle with sides that have

the Golden Ratio, you’ve made a sparkly Golden Rectangle.

s

l

Extra Credit Opportunities1. Construct a Golden

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