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
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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
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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.
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Extra Credit Opportunities1. Construct a Golden
Rectangle with a compass and straightedge and explain how it demonstrates the Golden Ratio
