Lesson Plan 0 - Quia
Algebra 1 Lesson Notes 3.5-3.6 ____________________
Objective: Find ratios, and write and solve proportions using cross-products.
ratio: a comparison of two quantities
Notation: for two quantities a and b, the ratio of a to b can be written:
a : b [pic]
Note: ratios should be written in simplest form
Example 1 (p162): Write a ratio
At a carwash fund raiser, 18 ninth graders and 14 tenth graders worked the first shift.
a. Find the ratio of ninth graders to tenth graders.
b. Find the ratio of ninth graders to all students working the first shift.
proportion: an equation that states that two ratios are equivalent.
Notation: the general form of a proportion is [pic] where b and d ( 0
Note: read as a is to b as c is to d
Example: Write a proportion.
15 is to 36 as w is to 108
6.5 is to p as 20 is to 65
Proportions can be set up multiple ways. But there MUST be a pattern.
Try it! A recipe for tomato salsa calls for 30 tomatoes to make 12 pints of salsa.
How many tomatoes are needed to make 4 pints.
Show four ways the proportion could be set up to solve this problem.
Proportions can be solved using inverse operations to isolate the variable. However, proportions are most often solved using cross products.
cross product: in a proportion, the product of the numerator of one ratio and the denominator
of the other ratio is called a cross product.
Every proportion has two cross products.
extremes [pic] means
ad = cb
the product of the means = the product of the extremes
To solve a proportion:
Cross Products Property (Means-Extremes Property):
The cross products of a proportion are equal.
If [pic], then ad = cb
Example 1 (p168): Use the cross products property to solve a proportion
a. Solve the proportion: [pic]
b. Solve the proportion: [pic]
Example 2 (p169): Solve a proportion
a. Solve: [pic] HINT: Remember grouping symbols.
( Check your answer!
b. Solve: [pic]
Example 3 (p 164): Solve a multi-step problem
a. The elevator that takes passengers from the lobby of the John Hancock center in Chicago
to the observation level travels 150 ft in 5 seconds. How long does it take the elevator to travel from the lobby to the observation level 1029 ft above the ground?
b. A backpacker in the Sierras hikes 5.5 miles in 2 hours. At that rate, how far will the
backpacker hike in 7 hours?
Example 3 (p 169): Write and solve a proportion
Georgia is making her own potting soil. For every 4 buckets of peat moss, she mixes in 3 buckets of perlite.
a. If she uses 10 buckets of peat moss, how many buckets of perlite should she use?
b. If she used 8 buckets of perlite, how much peat moss did she use?
An application of proportions: Architecture and design
scale drawing: a two-dimensional drawing of an object in which the dimensions of the
drawing are in proportion to the dimensions of the object.
scale model: a three-dimensional model of an object in which the dimensions of the model
are in proportion to the dimensions of the object.
scale factor: the ratio of the drawing’s or model’s dimensions to the actual dimensions.
Example 4 (p 170): Use the scale on a model
The ship model kits sold at a hobby store have a scale of 1 ft : 600 ft. A completed
model of the Queen Elizabeth II is 1.6 ft long. Estimate the actual length of the Queen Elizabeth II.
Example (p 173 #43):
At a typical National Football League game, the ratio of females to males in attendance
is 2:3. Estimate the number of male and female spectators at a game that has 75,000 spectators.
Example (p 173 PQ #16):
The ratio of the length to the width of a rectangle is 5:4. The length of the rectangle is 60 inches. What is its width?
( HW: A5-6a pp 165-167 #24-30 even, 45-51, 53
pp 171-173 #8-22 even, 35-36, 39, 41
A5-6b Lesson 3.5 Practice B / Lesson 3.6 Practice B
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