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Absolute Values
Solving Two-Step Equations Algebraically
Multiplying Monomials
Factoring Trinomials
Solving Quadratic Equations
Power Functions and Transformations
Composition of Functions
Rational Inequalities
Equations of Lines
Graphing Logarithmic Functions
Elimination Using Multiplication
Multiplying Large Numbers
Multiplying by 11
Graphing Absolute Value Inequalities
The Discriminant
Reducing Numerical Fractions to Simplest Form
Addition of Algebraic Fractions
Graphing Inequalities in Two Variables
Adding and Subtracting Rational Expressions with Unlike Denominators
Multiplying Binomials
Graphing Linear Inequalities
Properties of Numbers and Definitions
Factoring Trinomials
Relatively Prime Numbers
Rotating a Hyperbola
Writing Algebraic Expressions
Quadratic and Power Inequalities
Solving Quadratic Equations by Completing the Square
BEDMAS & Fractions
Solving Absolute Value Equations
Writing Linear Equations in Slope-Intercept Form
Adding and Subtracting Rational Expressions with Different Denominators
Reducing Rational Expressions
Solving Absolute Value Equations
Equations of a Line - Slope-intercept form
Adding and Subtracting Rational Expressions with Unlike Denominators
Solving Equations with a Fractional Exponent
Simple Trinomials as Products of Binomials
Equivalent Fractions
Multiplying Polynomials
Graphing Equations in Three Variables
Properties of Exponents
Graphing Linear Inequalities
Solving Cubic Equations by Factoring
Adding and Subtracting Fractions
Multiplying Whole Numbers
Straight Lines
Solving Absolute Value Equations
Solving Nonlinear Equations
Factoring Polynomials by Finding the Greatest Common Factor
Algebraic Expressions Containing Radicals 1
Addition Property of Equality
Three special types of lines
Quadratic Inequalities That Cannot Be Factored
Adding and Subtracting Fractions
Coordinate System
Solving Equations
Factoring Polynomials
Solving Quadratic Equations
Multiplying Radical Expressions
Solving Quadratic Equations Using the Square Root Property
The Slope of a Line
Square Roots
Adding Polynomials
Arithmetic with Positive and Negative Numbers
Solving Equations
Powers and Roots of Complex Numbers
Adding, Subtracting and Finding Least Common Denominators
What the Factored Form of a Quadratic can tell you about the graph
Plotting a Point
Solving Equations with Variables on Each Side
Finding the GCF of a Set of Monomials
Completing the Square
Solving Equations with Radicals and Exponents
Solving Systems of Equations By Substitution
Adding and Subtracting Rational Expressions
Laws of Exponents and Dividing Monomials
Factoring Special Quadratic Polynomials
Solving Quadratic Equations by Completing the Square
Reducing Numerical Fractions to Simplest Form
Factoring Trinomials
Writing Decimals as Fractions
Using the Rules of Exponents
Evaluating the Quadratic Formula
Rationalizing the Denominator
Multiplication by 429
Writing Linear Equations in Point-Slope Form
Multiplying Radicals
Dividing Polynomials by Monomials
Factoring Trinomials
Introduction to Fractions
Square Roots
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Introduction to Fractions

What Fractions Are and Why They Are Important

A fraction can mean part of a whole. Just as a whole number answers the question, How many?, a fraction answers the question, What part of? Every day we use fractions in this sense. For example, we can speak of two-thirds of a class (meaning two of every three students) or three-fourths of a dollar (indicating that we have split a dollar into four equal parts and have taken three of these parts).

A fraction can also mean the quotient of two whole numbers. In this sense, the fraction tells us what we get when we divide the whole number 3 by the whole number 4.


A fraction is any number that can be written in the form , where a and b are whole numbers and b is not zero.

Explain why in this definition b cannot be 0.

From this definition, are all fractions.

When written as a fraction has three components.

  • The denominator (on the bottom) stands for the number of parts into which the whole is divided.
  • The numerator (on top) tells us how many parts of the whole the fraction contains.
  • The fraction line separates the numerator from the denominator, and stands for “out of ” or “divided by.”

Alternatively, a fraction can be represented as either a decimal or a percent.

Fraction Diagrams and Proper Fractions

Diagrams help us work with fractions. Each diagram represents the fraction three-fourths, or .

Note that in each diagram the whole has been divided into 4 equal parts, with 3 of the parts shaded.

The number is an example of a proper fraction because its numerator is smaller than its denominator. Let’s consider some other examples of proper fractions.

Explain why a fraction whose numerator is smaller than its denominator must have a value less than 1.


What fraction does the diagram represent?


In this diagram, the whole is divided into 9 equal parts, so the denominator of the illustrated fraction is 9. Four of these parts are shaded, so the numerator is 4. The diagram illustrates the fraction .


The diagram illustrates what fraction?



A manufacturing company plans to lay off 71 of its 230 workers. What fraction of its employees does the company plan to lay off?


There are 230 workers altogether, so the denominator of our fraction is 230. Because we are concerned with 71 of these workers, 71 is the numerator. The company plans to lay off of its employees.


The annual tuition at a college is $2,451. If a student paid $1,000 toward this tuition, what fraction of the tuition did the student pay?



The U.S. Senate approved a foreign aid spending bill by a vote of 83 to 17. What fraction of the senators voted against the bill?


First, we find the total number of senators. Because 83 senators voted for the bill and 17 voted against it, the total number of senators is 83 + 17, or 100. So of the senators voted against the bill.


You have read 125 pages of a novel assigned by your English instructor. If 39 pages remain, what fraction of the book have you read?


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