Learning Resources
Outcomes
By the end of this lesson you will be able to answer questions like the ones in the pre-test below.
If you prefer, you can proceed directly to the first page of the lesson without doing the pre-test. To do this simply click on the Lesson button above.
Alternately you can first answer the questions on the pre-test below in your Math 3103 binder. Then refer only to the pages of the lesson that contain instruction on the questions for which you get an incorrect answer or for which you would like some further explanation.
Pre-test
- Multiply or divide as indicated. You should be able to do these problems
mentally.
(a)
(b) 
(c) 
(d) 
(e)
(f) 
(g) 
- Try to do the following without using pencil and paper:
(a) How many one-sevenths are in
? How many one-fourteenths are in ?
(b) What is
of 
? of 
? - Perform the indicated operations:
(a)
(b) 
(c) 
- Start with the number 8 (call it step 0). Take of this number (call it step 1). Then take of the result in step 1 (call it step 2); then of the result in step 2 (call it step 3); etc.
(a) Plot the points on a graph using the step numbers as the x-coordinate and the results of your calculations as the y-coordinate.
(b) Describe the shape of the graph.
(c) Will the graph ever intersect or go below the x-axis? Explain.
By the end of this section you should be able to:
- Apply fraction concepts both mentally and with pencil and paper algorithms including:
- lowest common denominator (LCD)
- equivalent fractions
- reducing to simplest terms
- improper vs. mixed fractions
- factors
- prime factorization to find LCD
- ordering fractions by relative size
- Add, subtract, multiply and divide fractions (both mentally and using pencil and paper), and work with patterns and graphs based on operations with fractions.
- Simplify complex fractions containing rational numbers.
Prerequisites
To be successful in this lesson, it would be helpful to know the following:
- How to find the prime factors of a number.
- How to reduce fractions to simplest terms.
- How to write equivalent fractions.
- How to convert between improper fractions and mixed numbers.