Geometry NOTES
Date: _________
Lesson 7-1: Ratios & Proportions
Word or
Word Phrase
Description
Picture or Example
ratio
A ratio is a comparison of two
quantities by division.
2 to 9, 2 : 9, or
2
9
The 2 numbers have to be in the same
unit of measure.
Write your answer in lowest terms.
proportion
Two equal ratios
extremes
The 1st and last numbers in the
proportion.
Means
The means are the middle two
numbers in a proportion.
3
2

21 14
Extended ratio
Compares 3 or more numbers
An isosceles right triangle
has angle measures that
are in the extended ratio
1: 1: 2 (45 : 45 : 90).
Cross Products
Propertry
In a proportion, the product of the
extremes equals the product of the
means.
3
2

21 14
3
2

21 14
3 14  2 21
42  42
Find the value of the variable in each proportion:
1.
3 12

7 x
2.
4.
x4 x

2
6
5.
4 x

3 2
3.
5 15

y 8
x 4

3 x
6. A pine tree is 18 inches wide and stands 2 feet tall. What is the ratio of the width of the pine tree
to its height?
Use a proportion to solve each problem.
7. About 45 of every 300 apples picked at the Newbury Apple Orchard are rotten. If 3560
apples were picked one week, about how many apples were rotten?
8. A grocer orders 800 gal of milk each week. He throws out about 64 gal of spoiled milk
each week. Of the 9600 gal of milk he ordered over three months, about how many gallons of
spoiled milk were thrown out?
9. About 56 of every 700 picture frames put together on an assembly line have broken
pieces of glass. If 60,000 picture frames are assembled each month, about how many will
have broken pieces of glass?
10.The ratio of width to length of a rectangle is 7 : 10. The width of the rectangle is 91 cm.
Write and solve a proportion to find the length.
Using Algebraic Equations to Solve Ratio Problems:
11. Members of the school band are buying pots of tulips and pots of daffodils to sell at their
fundraiser. They plan to buy 120 pots of flowers. The ratio, respectively, will be 2:3. How
many of each type of flower should they buy?
12.The measures of two complementary angles are in the ratio 1:3. What are the measures of
the angles?
13. The lengths of the sides of a triangle are in the extended ratio 3: 5 : 6. The perimeter of
the triangle is 98 inches. What is the length of the longest side?
HOMEWORK: pgs. 459-460 # 1-3, 7, 8-23, 37