Learning Resources

Home »  » Courses » Mathematics » Mathematics 3103 (delisted) » Unit 01 » Set 02 ILO 01 » Get Ready

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

Try to do the calculations for questions 1 to  5 mentally. The others may require pencil and paper.

  1. Reduce to lowest terms:
  2. Find the LCD of these fractions:   and 
  3. Convert to a mixed number: 
  4. Convert to an improper fraction:
  5. Put the following fractions in order from smallest to largest:     ,    , 
  6. Reduce to lowest terms:
  7. Find the LCD of these fractions:   ,    , 
  8. Convert to a mixed number:
  9. Convert to an improper fraction:
  10. Put the following fractions in order from smallest to largest:  , ,

Answers

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.

Introduction

This section consists of four lessons as follows:

Lesson 01 Basic Fractional Concepts 
This lesson deals with the topics of, lowest common denominator (LCD), equivalent fractions, reducing to simplest terms, improper vs. mixed fractions, factors, prime factorization to find LCD, and ordering fractions by relative size. Both mental calculations and pencil and paper algorithms are expected to be applied in this lesson.

Lesson 02 Adding and Subtracting Fractions 
This lesson is a review of the skills necessary to add and subtract fractions both mentally and using pencil and paper algorithms.

Lesson 03 Multiplying and Dividing Fractions
This lesson is a review of the skills necessary to multiply and divide fractions both mentally and using pencil and paper algorithms.

Lesson 04 Working with Complex Fractions

This lesson deals with simplifying complex fractions (that is fractions where the numerator and/or denominator also contain fractions) containing rational numbers. Working with complex fractions containing algebraic expressions is covered in another unit.

Prerequisites

To be successful in this lesson, it would be helpful to know the following:

  • Prime factorization of numbers.
  • How to reduce a fraction to lowest or simplest terms.
  • The concept of the LCD of two or more fractions.
  • How to change from an improper fraction to a mixed number and vice versa.