SOLUTIONS
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Fraction Division
Fraction division is almost as easy as fraction multiplication. The rule for fraction
division is ab÷=⋅=dc ba cd adbc, that is, we invert (switch the numerator and deno-minator) the second fraction, and the fraction division problem becomes a fraction
multiplication problem. To see why this might be so, consider the computation
for^31 ÷^12. We can think of this division problem as asking the question, “HowEXAMPLES
÷=÷=⋅=
EXAMPLES
Perform the division.- chapter 1 Fractions How to Use This Book xi
- Fraction Multiplication
- Multiplying Fractions and Whole Numbers
- Fraction Division
- Simplifying Fractions
- The Greatest Common Divisor
- Denominators Adding and Subtracting Fractions with Like
- Denominators Adding and Subtracting Fractions with Unlike
- The Least Common Denominator (LCD)
- Finding the LCD
- Adding More than Two Fractions
- Whole Number–Fraction Arithmetic
- Compound Fractions
- Mixed Numbers and Improper Fractions
- Fractions and Division of Whole Numbers
- Mixed Number Arithmetic
- Multiplying Mixed Numbers
- Dividing Mixed Numbers
- Problems Recognizing Quantities and Relationships in Word
- Summary
- Quiz
- chapter 2 Introduction to Variables viii ALGEBRA DeMYSTiFieD
- Simplifying Fractions Containing Variables
- Operations on Fractions Containing Variables
- Fraction Division and Compound Fractions
- Adding and Subtracting Fractions Containing Variables
- Variables in Word Problems
- Summary
- Quiz
- chapter 3 Decimals
- Adding and Subtracting Decimal Numbers
- Multiplying Decimal Numbers
- Containing Decimals
- Division with Decimals
- Summary
- Quiz
- chapter 4 Negative Numbers
- The Sum of a Positive Number and a Negative Number
- Subtracting a Larger Number from a Smaller Number
- Number Subtracting a Positive Number from a Negative
- Double Negatives
- Problem Rewriting a Subtraction Problem as an Addition
- Multiplication and Division with Negative Numbers
- Negating Variables
- Fractions and Negative Signs
- Review
- Quiz
- chapter 5 Exponents and Roots
- Exponent Properties and Algebraic Expressions
- Adding/Subtracting Fractions
- Multiplying/Dividing with Exponents
- Roots
- Simplifying Roots
- Roots Expressed as Exponents
- Simplifying Multiple Roots
- Summary
- Quiz
- chapter 6 Factoring and the Distributive Property Contents ix
- Distributing Negative Numbers
- Combining Like Terms
- Adding/Subtracting Fractions
- Factoring
- Factoring with Negative Numbers
- More Factoring
- Factoring by Grouping
- Factoring to Simplify Fractions
- The FOIL Method
- Factoring Quadratic Polynomials
- Factoring the Difference of Two Squares
- More on Factoring Quadratic Polynomials
- Quadratic-Type Expressions
- Factoring to Simplify a Larger Family of Fractions
- Adding/Subtracting Fractions
- Summary
- Quiz
- chapter 7 Linear Equations
- Solving Linear Equations
- A Strategy for Solving Linear Equations
- Decimals
- Formulas
- Equations Leading to Linear Equations
- Summary
- Quiz
- chapter 8 Linear Applications
- Percents
- Increasing/Decreasing by a Percent
- Working with Formulas
- Number Sense
- Problems Involving Three Unknowns
- Grade Problems
- Coin Problems
- Investment Problems
- Mixture Problems
- Work Problems
- Distance Problems
- Geometric Figures x ALGEBRA DeMYSTiFieD
- Summary
- Quiz
- chapter 9 Linear Inequalities
- Inequalities and the Number Line
- Solving Linear Inequalities
- Interval Notation
- Applied Problems
- Bounded Intervals
- Solving Double Inequalities
- Applications of Double Inequalities
- Summary
- Quiz
- chapter 10 Quadratic Equations
- Solving Quadratic Equations by Factoring
- Extracting Roots
- Quadratic Formula Solving Quadratic Equations with the
- Rational Equations That Lead to Quadratic Equations
- Summary
- Quiz
- chapter 11 Quadratic Applications
- Number Sense Problems
- Revenue Problems
- More Work Problems
- The Height of a Falling Object
- Problems in Geometry
- Distance Problems
- Round-trip Problems
- Summary
- Quiz
- Final Exam
- Answers to Quizzes and Final Exam
- Appendix
- Index
- Chapter 1 FraCtions
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- formula: 13 ÷=⋅= many halves go into 3?” Of course, the answer is 6, which agrees with the
- Perform the division.
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