1. PROPORTIONS Write ratios Use properties of proportions
“Circle Limit IV (Heaven and Hell)”
M. C. Escher, 1960

2. Example 1 – Write a Ratio
In 17 seasons as a major-league baseball player, Chipper Jones of the Atlanta Braves made 2490 hits in 8142 times at bat. What is his overall major-league batting average?
number of hits
number of times at bat
Batting average =
or about 0.306

3. Example 2 – Extended Ratios in Triangles
In a triangle, the ratios of the measures of the three sides is 4:6:9, and its perimeter is 190 inches.
Find the lengths of the sides of the triangle.

4. Example 2 – Extended Ratios in Triangles cont.
Recall that equivalent fractions can be found by multiplying the numerator and denominator by the same number. Thus:
We can rewrite 4:6:9 as 4x:6x:9x and use those measures for the sides of the triangle. 9x 4x 6x

5. Example 2 – Extended Ratios in Triangles cont.
Write an equation to represent the perimeter of the triangle as the sum of the measures of its sides. 9x 4x 6x

6. Example 2 – Extended Ratios in Triangles cont.
Use the value of x to find the measures of the sides of the triangle.
4x = 4(10) or 40 inches
6x = 6(10) or 60 inches
9x = 9(10) or 90 inches

7. USE PROPERTIES OF PROPORTIONS
An equation stating that two ratios are equal is called a proportion.
Every proportion has two cross products.

8. Example 3 – Solve Proportions by Using Cross Products
Solve the proportion
Original problem
Cross products
Simplify
Divide each side by 35

9. Example 4 – Solve Proportions by Using Cross Products
Original problem
Cross products
Simplify
Add 10 to each side
Divide each side by 6

10. Example 5 – Solve Problems Using Proportions
The Gulfstream V business jet has a length of 96 feet and a wingspan of 94 feet.
A toy model is made in proportion to the real airplane.
If the wingspan of the toy is 36 cm, find the length of the toy.

11. Example 5 – Solve Problems Using Proportions cont.