Lesson 8: Lesson Eight--Applications and Final Test
This final lesson in "Cure Math Anxiety: Basic Skills--Fractions" provides more practical application problems and resources to take your final test.
Section One: Applications
You've probably been wondering, "where's the beef?" Where're the application problems I told you would be in this course? Where's all that "math-in-your-head" stuff?
In this section and the next one, then in the "Resources" section is your final test, which is on a website designed for this kind of thing, or you can take Cambridge GED, Lesson One Review and call it a test (but the thing is, since the answers are in the back of the book, it's not REALLY a test!).
In Cambridge GED are two practical application sections, Level Two and Level Three in the Fractions section of the book. I will take some problems from those pages.
One kind of application is very simple, finding what part a number is to another. Suppose an employer wants to know what fraction of all his employees are union members, or are on vacation?
An aside here: women taking this course, don't be offended if I use "his" for employer, okay? But the fact is, I don't abide by political correctness for one thing--it's a "divide and conquer" mechanism--and another fact is feminism generally doesn't impress me when the hero of NOW, Bill Clinton, is a well-known womanizer (read: sexist!).
So, anyway...
If an employer needs to know these things, he has someone who knows about fractions on hand, possibly a female, who can figure these things out. After all, if he takes funding from the government he is required to know these things!
Let's do p. 105, Lesson 9 exercise, number 2:
In the shop where Phil works there are 45 union members and 36 non-union members. a. What fraction of the workers are union members? b. What fraction do not belong to the union?
Solution:
As it says in the Lesson 9 introduction, you are simply taking part of a whole, or creating a fraction with the "part" as the numerator and the "whole" as the denominator, then reducing the fraction!
Now, if there are 45 union and 36 non-union, then there are 45 + 36 workers in all (the denominator), or 81 workers in all. The denominator will be 81.
For the part that is union: 45/81 = 5/9
For the part that is non-union: 36/81 = 4/9
Don't forget that both parts must equal one whole: 5/9 + 4/9 = 9/9 =1.
Supposing you must find the area of a triangle. Carpenters and architects, for instance, need to know this if they are using triangles in building projects and designing buildings or even pyramids!
The formula for finding the area of a triangle has a fraction in it, so this kind of problem is applicable. The formula for area of a triangle is:
A = 1/2 b x h where b = base of the triangle and h = height of the triangle (which in most triangles extends from the tip of the triangle to the base--the height is always perpendicular to the base and forms a square corner; in a right triangle [90 degree triangle], the height is the vertical side)
Look at the pictures on p. 110 of Cambridge GED for what the base and height look like in various kinds of triangles.
I cannot draw a triangle here, but supposing you need to know that area of a triangle that has a base of 12 feet and a height of 22 feet (see Lesson 13 exercise, problem 4 on p. 111).
Since b = 12 ft. and h = 22 ft., the area would be:
A = 1/2 b x h, so A = 1/2 x 12 x 22 = 132 sq. ft.
Don't forget that units (ft., in., yd., etc) are always square units in area problems (not only are you multiplying the numbers, you are also multiplying the units--ft. x ft. = square feet. You can also use exponents, but it's difficult on a keyboard).
Most of the practical problems you'll find with fractions are proportion problems.
A simple one is something like:
A scale on a map is 1/2 inch = 15 miles. How far apart are two towns that are two inches apart on a map?
Solution: If 1/2 inch = 15 miles, then how many miles would 2 inches be?
Remember to set up the proportion this way: inches/miles = inches/miles.
1/2/15 = 2/x, so that multiplying the two outside terms together then multiplying the two inside terms together gets you:
1/2 x = 30. Divide 30 by 1/2, which (remembering to invert 1/2 into 2/1) means multiplying 30/1 x 2/1 = 60/1 = 60.
So the two towns are 60 miles apart.
They must be two towns out here in West Texas!
By the way, all the problems here can be done in your head. Number two problem here requires, however, that you know the formula to find the area of the triangle and that you can take 1/2 of 22 (11) then multiply in your head 11 x 12.
