 Home
 INTERMEDIATE ALGEBRA
 Course Syllabus for Algebra I
 MidPlains Community College
 FRACTION OF A WHOLE NUMBER
 Systems of Linear Equations
 MATH FIELD DAY
 Course Outline for Finite Mathematics
 Calculus
 Algebra Final Examination
 Math 310 Exam #2
 Review of Trigonometric Functions
 Math 118 Practice test
 Precalculus Review
 Section 12
 Literal Equations
 Calculus Term Definitions
 Math 327A Exercise 2
 Public Key Algorithms II
 Maximizing Triangle Area
 Precalculus I Review for Midterm
 REVIEW OF A FIRST COURSE IN LINEAR ALGEBRA
 Math 6310 Homework 5
 Some Proofs of the Existence of Irrational Numbers
 ALGEBRAIC PROPERTIES OF MATRIX OPERATIONS
 Math 142  Chapter 2 Lecture Notes
 Math 112 syllabus
 Math 371 Problem Set
 Complex Numbers,Complex Functions and Contour Integrals
 APPLICATIONS OF LINEAR EQUATIONS
 Week 4 Math
 Fractions
 Investigating Liner Equations Using Graphing Calculator
 MATH 23 FINAL EXAM REVIEW
 Algebra 1
 PYTHAGOREAN THEOREM AND DISTANCE FORMULA
 Georgia Performance Standards Framework for Mathematics  Grade 6
 Intermediate Algebra
 Introduction to Fractions
 FACTORINGS OF QUADRATIC FUNCTIONS
 Elementary Algebra Syllabus
 Description of Mathematics
 Integration Review Solutions
 College Algebra  Applications
 A Tip Sheet on GREATEST COMMON FACTOR
 Syllabus for Elementary Algebra
 College Algebra II and Analytic Geometry
 Functions
 BASIC MATHEMATICS
 Quadratic Equations
 Language Arts, Math, Science, Social Studies, Char
 Fractions and Decimals
 ON SOLUTIONS OF LINEAR EQUATIONS
 Math 35 Practice Final
 Solving Equations
 Introduction to Symbolic Computation
 Course Syllabus for Math 935
 Fractions
 Fabulous Fractions
 Archimedean Property and Distribution of Q in R
 Algebra for Calculus
 Math112 Practice Test #2
 College Algebra and Trigonometry
 ALGEBRA 1A TASKS
 Description of Mathematics
 Simplifying Expressions
 Imaginary and Complex Numbers
 Building and Teaching a Math Enhancement
 Math Problems
 Algebra of Matrices Systems of Linear Equations
 Survey of Algebra
 Approximation of irrational numbers
 More about Quadratic Functions
 Long Division
 Algebraic Properties of Matrix Operation
 MATH 101 Intermediate Algebra
 Rational Number Project
 Departmental Syllabus for Finite Mathematics
 WRITTEN HOMEWORK ASSIGNMENT
 Description of Mathematics
 Rationalize Denominators
 Math Proficiency Placement Exam
 linear Equations
 Description of Mathematics & Statistics
 Systems of Linear Equations
 Algebraic Thinking
 Study Sheets  Decimals
 An Overview of Babylonian Mathematics
 Mathematics 115  College Algebra
 Complex Numbers,Complex Functions and Contour Integrals
 Growing Circles
 Algebra II Course Curriculum
 The Natural Logarithmic Function: Integration
 Rational Expressions
 QUANTITATIVE METHODS
 Basic Facts about Rational Funct
 Statistics
 MAT 1033 FINAL WORKSHOP REVIEW
 Measurements Significant figures
 PreCalculus 1
 Compositions and Inverses of Functions
Fractions
The thing that strikes me most about students and
fractions is the misuse of “shortcuts”
and the procedures required for each operation. I always begin with simplifying
fractions. Because of the future algebra class, particularly rational
expressions, heading
their way, I teach simplifying by factoring. It’s really difficult to simplify
polynomial
numerators and denominators without factoring.
Students really need to understand prime factorization to
accomplish simplification of
fractions. I hear students say that the twos will cancel out. This is actually
not true.
They really divide out for one.
The one topic of fractions that seems to try many students
is that of common
denominator. Students should be reminded of the procedures for each operation.
The
only operations requiring a common denominator are adding and subtracting.
Multiplication and division do not require common denominators.
Rule: To Add Two Fractions

Rule: To Subtract Two Fractions

Rule: To Multiply Two Fractions

Rule: To Divide Two Fractions

Before practicing with negative fractions, it might be
wise to check the basic fraction
understanding from the previous rules.
Combine and simplify the fractions.
answers:
After checking for the most basic use of the rules, the
idea of common denominator and
equivalent fractions must be addressed.
For equivalent fractions, I like to use a number line in
the following way. I have the
students draw three number lines. I then have them label from zero to one. On
the first
number line, I have them put one mark exactly between zero and one. On the
second
line, I have them put the one mark in the middle and then one mark in the middle
of the
two resulting segments. One the third line, they do the same, except they then
bisect each
of the four segments. Then I ask them how many segments they have traveled to
the
middle. We put this over the total number of segments. It becomes visually clear
to
them. This exercise suggests that a fraction can look different from another,
yet still have
the same numerical value on the number line.
When first working with equivalent fractions, I like to
start with a particular fraction and
then ask them to write the equivalent fraction with a given denominator.
For instance, find the equivalent fraction to 2/5 that has a denominator of 20.
To build fractions to “higher terms,” use multiplication
in the numerator and the
denominator.
Find the equivalent fraction to 20/30 that has a denominator of 15.
To reduce fractions to “lower terms,” use division in the numerator and the denominator.
The previous is different from reducing to “lowest terms.”
Lowest terms would leave no
common factors at all between the numerator and denominator.
After introducing the idea of equivalent fractions,
students are ready to find the LCD
(least common denominator). There are so many ways to do this, but I find that
factoring
works best when dealing with variable factors.
To add and we need a common denominator.
By rewriting with factored denominators, we can see
missing that need to be multiplied
into the denominator and numerator of each fraction.
From above, we can see that the first denominator needs
one factor of 2 and one factor of
5 to match with the second denominator. The second denominator needs one factor
of 3
to match up with the first denominator.
This works especially well with fractions containing variables.
The first denominator needs one factor of 3. The second
denominator needs one factor of
2, one factor of 5, and one factor of x.
Practice Problems: