Free Algebra
Tutorials!
 
Home
Point
Arithmetic Operations with Numerical Fractions
Multiplying a Polynomial by a Monomial
Solving Linear Equation
Solving Linear Equations
Solving Inequalities
Solving Compound Inequalities
Solving Systems of Equations Using Substitution
Simplifying Fractions 3
Factoring quadratics
Special Products
Writing Fractions as Percents
Using Patterns to Multiply Two Binomials
Adding and Subtracting Fractions
Solving Linear Inequalities
Adding Fractions
Solving Systems of Equations -
Exponential Functions
Integer Exponents
Example 6
Dividing Monomials
Multiplication can Increase or Decrease a Number
Graphing Horizontal Lines
Simplification of Expressions Containing only Monomials
Decimal Numbers
Negative Numbers
Factoring
Subtracting Polynomials
Adding and Subtracting Fractions
Powers of i
Multiplying and Dividing Fractions
Simplifying Complex Fractions
Finding the Coordinates of a Point
Fractions and Decimals
Rational Expressions
Solving Equations by Factoring
Slope of a Line
Percent Introduced
Reducing Rational Expressions to Lowest Terms
The Hyperbola
Standard Form for the Equation of a Line
Multiplication by 75
Solving Quadratic Equations Using the Quadratic Formula
Raising a Product to a Power
Solving Equations with Log Terms on Each Side
Monomial Factors
Solving Inequalities with Fractions and Parentheses
Division Property of Square and Cube Roots
Multiplying Two Numbers Close to but less than 100
Solving Absolute Value Inequalities
Equations of Circles
Percents and Decimals
Integral Exponents
Linear Equations - Positive and Negative Slopes
Multiplying Radicals
Factoring Special Quadratic Polynomials
Simplifying Rational Expressions
Adding and Subtracting Unlike Fractions
Graphuing Linear Inequalities
Linear Functions
Solving Quadratic Equations by Using the Quadratic Formula
Adding and Subtracting Polynomials
Adding and Subtracting Functions
Basic Algebraic Operations and Simplification
Simplifying Complex Fractions
Axis of Symmetry and Vertices
Factoring Polynomials with Four Terms
Evaluation of Simple Formulas
Graphing Systems of Equations
Scientific Notation
Lines and Equations
Horizontal and Vertical Lines
Solving Equations by Factoring
Solving Systems of Linear Inequalities
Adding and Subtracting Rational Expressions with Different Denominators
Adding and Subtracting Fractions
Solving Linear Equations
Simple Trinomials as Products of Binomials
Solving Nonlinear Equations by Factoring
Solving System of Equations
Exponential Functions
Computing the Area of Circles
The Standard Form of a Quadratic Equation
The Discriminant
Dividing Monomials Using the Quotient Rule
Squaring a Difference
Changing the Sign of an Exponent
Adding Fractions
Powers of Radical Expressions
Steps for Solving Linear Equations
Quadratic Expressions Complete Squares
Fractions 1
Properties of Negative Exponents
Factoring Perfect Square Trinomials
Algebra
Solving Quadratic Equations Using the Square Root Property
Dividing Rational Expressions
Quadratic Equations with Imaginary Solutions
Factoring Trinomials Using Patterns

Dividing a Whole Number by a Fraction Whose Numerator is 1

Dividing fractions is somewhat difficult conceptually. Therefore, it is a good idea to first see the process used to divide a whole number by a fraction whose numerator is 1, and then use that discussion to motivate the concept of reciprocal.

Begin by recalling how we think about the division of whole numbers. One approach is to ask ourselves how many collections of size equal to the divisor are contained in a group whose size is equal to the dividend. For example, we know 6 ÷ 2 = 3 because we know that a group of 6 items can be separated into 3 collections each containing 2 items. Now let’s apply the same thought process to the division . We can ask ourselves how many “collections” containing of an item are there in a group of 5 items. A model of this situation, showing five rectangles each divided into two equal parts, is shown below. ( Note: The rectangles must be the same size.)

If each of the five larger rectangles represents 1 unit, then each of the smaller rectangles represents unit. So, the number of smaller rectangles is the number of “collections” containing of an item that can be found in a group of 5 items. Since there are 10 smaller rectangles in the model, this shows that

 

Example 1

What is ?

Solution

Draw two rectangles, each divided into four equal parts.

If each larger rectangle represents 1 unit, then each smaller rectangle represents unit. Since there are 8 smaller rectangles in the model, this shows that

In each of the previous problems the answer can be obtained by multiplying the whole number by the denominator of the fraction.

We know that a fraction indicates the division of the numerator by the denominator. For example, and conversely . But we also know that . Try to see that if 7 ÷ 9 and are both equal to , then they must also be equal to each other. That is, .

All Right Reserved. Copyright 2005-2014