Transcript Lesson 6-1 Proportions

Lesson 6-1
The Parthenon – represent Golden Ratio
Proportions
Lesson 5-1: Using Proportions
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Lesson 6-1 Proportions
Ratio: A ratio is a comparison of two numbers such as a : b.
When writing a ratio, always express it in simplest form.
Example:
What is the ratio of AB to CB ?
A
Now try to reduce the fraction.
8
10
D
4.8
 ratio of AB to CB 
Lesson 6-1 – Proportions
Lesson 5-1: Using Proportions
C
3.6
6
B
2
Golden Ratio ~ 1:1.618 ratio
 The Golden Rectangle is considered to be one of the most pleasing
and beautiful shapes to look at, which is why many artists have
used it in their work.
The two artists, who are perhaps the most famous for their use of
the golden ratio, are Leonardo Da Vinci and Piet Mondrian.
The Parthenon – represent Golden Ratio
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Example……….
A baseball player goes to bat 348 times and gets 107 hits.
What is the players batting average?
Solution:
Set up a ratio that compares the number of hits to the number
of times he goes to bat.
Convert this fraction to a decimal rounded to three decimal
places.
The baseball player’s batting average is
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Proportion
Proportion: An equation that states that two ratios are equal.
Terms
a c

b d
First Term
Second Term
Third Term
Fourth Term
To solve a proportion, cross multiply the proportion:
a(d) = b(c)
Extremes: a and d
Means : b and c
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Solve each proportion.
2
x

5
40
x 1
7

3
2
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Proportions- examples….
Example 1: Find the value of x.
x
2 ft
356 yards
84 yards
Example 2: Solve the proportion.
x 5

6 8
8x = 30
8•x = 6•5
x = 3.75
8x = 30
8
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Proportions- examples….
 Example 3: There are 76 boys in a sophomore class of 165
students. Find the ratio of boys to girls.
Example 4: A replica of The Thinker is 10 inches tall. The
replica and a statue of The Thinker, located in front of
Grawemeyer Hall on the Belnap Campus of the University
of Louisville have a ratio of 1:12. What is the height of the
UofL statue?
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Proportions- examples….
Example 5: The ratio of the measures of three sides of a triangle is
9:8:7, and its perimeter is 144 units. Find the measure of each side
of the triangle.
Example 6: The ratio of the measures of three angles of a triangle
5:7:8. Find the measure of each angle of the triangle.
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