This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses applications of proportions. By the end of the module students should be able to solve proportion problems using the five-step method.
Section overview
The Five-Step Method
Problem Solving
The five-step method
In
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The first and most important part of solving a proportion problem is to determine, by careful reading, what the unknown quantity is and to represent it with some letter.
The five-step method
The five-step method for solving proportion problems:
By careful reading, determine what the unknown quantity is and represent it with some letter. There will be only one unknown in a problem.
Identify the three specified numbers.
Determine which comparisons are to be made and set up the proportion.
Solve the proportion (using the methods of
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Interpret and write a conclusion in a sentence with the appropriate units of measure.
Step 1 is extremely important. Many problems go unsolved because time is not taken to establish what quantity is to be found.
When solving an applied problem,
always begin by determining the unknown quantity and representing it with a letter.
Problem solving
Sample set a
On a map, 2 inches represents 25 miles. How many miles are represented by 8 inches?
The unknown quantity is miles.
Let
number of miles represented by 8 inches
The three specified numbers are
2 inches
25 miles
8 inches
The comparisons are
2 inches to 25 miles →
8 inches to x miles →
Proportions involving ratios and rates are more readily solved by suspending the units while doing the computations.
In step 1, we let
represent the number of miles. So,
represents 100 miles.
If 2 inches represents 25 miles, then 8 inches represents 100 miles.
Try
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