Skip to main content
Core Mathematics
Katherine Yoshiwara
Contents
Search Book
close
Search Results:
No results.
Dark Mode
Prev
Up
Next
\(\require{cancel}\newcommand{\N}{\mathbb N} \newcommand{\Z}{\mathbb Z} \newcommand{\Q}{\mathbb Q} \newcommand{\R}{\mathbb R} \newcommand{\alert}[1]{\boldsymbol{\color{magenta}{#1}}} \newcommand{\blert}[1]{\boldsymbol{\color{blue}{#1}}} \newcommand{\bluetext}[1]{\color{skyblue}{#1}} \delimitershortfall-1sp \newcommand\abs[1]{\left|#1\right|} \newcommand\degree[0]{^{\circ}} \newcommand\Ccancel[2][black]{\renewcommand\CancelColor{\color{#1}}\cancel{#2}} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \newcommand{\fillinmath}[1]{\mathchoice{\underline{\displaystyle \phantom{\ \,#1\ \,}}}{\underline{\textstyle \phantom{\ \,#1\ \,}}}{\underline{\scriptstyle \phantom{\ \,#1\ \,}}}{\underline{\scriptscriptstyle\phantom{\ \,#1\ \,}}}} \)
Front Matter
Colophon
Preface
1
Preliminary Ideas
1.1
Halves and Quarters
1.1.1
One-Half
1.1.2
Other Ways to Write One-Half
1.1.3
Fourths
1.1.4
Other Ways to Write Fourths
1.1.5
Fractions on a Number Line
1.1.6
Benchmark Fractions
1.1.7
Vocabulary
1.1.8
Practice 1.1
1.2
Tenths and Hundredths
1.2.1
One-Tenth
1.2.2
Fractions in Tenths
1.2.3
Tenths and Fifths, Reducing Fractions
1.2.4
Hundredths
1.2.5
Decimal Form
1.2.6
Vocabulary
1.2.7
Practice 1.2
1.3
Whole Numbers
1.3.1
Factors
1.3.2
Primes and Composites
1.3.3
Greatest Common Factor
1.3.4
Lowest Common Multiple
1.3.5
Vocabulary
1.3.6
Practice 1.3
1.4
Angles and Triangles
1.4.1
Angles
1.4.2
Measuring Angles
1.4.3
Using a Protractor
1.4.4
Triangles
1.4.5
Sides and Angles
1.4.6
Vocabulary
1.4.7
Practice 1.4
1.5
Perimeter and Area
1.5.1
Perimeter
1.5.2
Area
1.5.3
Estimating Area
1.5.4
Vocabulary
1.5.5
Practice 1.5
2
Numbers and Variables
2.1
Decimal Numbers
2.1.1
The Metric System
2.1.2
Place Value
2.1.3
Comparing Decimal Fractions
2.1.4
Fractions to Decimals
2.1.5
Rounding and Estimating
2.1.6
Vocabulary
2.1.7
Practice 2.1
2.2
More Fractions and Percents
2.2.1
Percents
2.2.2
Calculating Percents
2.2.3
What Percent Is It?
2.2.4
Eighths
2.2.5
Thirds
2.2.6
Decimal Form of One-Third
2.2.7
Vocabulary
2.2.8
Practice 2.2
2.3
Variables
2.3.1
What is a Variable?
2.3.2
Bar Graphs
2.3.3
Using Letters for Variables
2.3.4
Vocabuary
2.3.5
Practice 2.3
2.4
Algebraic Expressions
2.4.1
What is an Algebraic Expression?
2.4.2
Sums and Products
2.4.3
Differences and Quotients
2.4.4
Using Algebraic Expressions
2.4.5
Evaluating Algebraic Expressions
2.4.6
Writing Algebraic Expressions
2.4.7
Vocabulary
2.4.8
Practice 2.4
2.5
Equations
2.5.1
What Is an Equation?
2.5.2
The Solution of an Equation
2.5.3
Finding Solutions: Opposite Operations
2.5.4
Isolating the Variable
2.5.5
Vocabulary
2.5.6
Practice 2.5
3
Measurement
3.1
Volume and Surface Area
3.1.1
Surface Area
3.1.2
Boxes and Cubes
3.1.3
Volume
3.1.4
Vocabulary
3.1.5
Practice 3.1
3.2
Exponents
3.2.1
A New Notation
3.2.2
Squares and Cubes
3.2.3
Products and Powers
3.2.4
Pythagorean Theorem
3.2.5
Vocabulary
3.2.6
Practice 3.2
3.3
Units of Measure
3.3.1
Length
3.3.2
Metric Units
3.3.3
Area and Volume
3.3.4
Liquid Measure
3.3.5
Vocabulary
3.3.6
Practice 3.3
3.4
Circles and Spheres
3.4.1
Perimeter
3.4.2
Circumference of a Circle
3.4.3
Area of a Circle
3.4.4
A Formula for the Area of a Circle
3.4.5
Volume of a Sphere
3.4.6
Vocabulary
3.4.7
Practice 3.4
3.5
Large Numbers
3.5.1
Millions and Billions
3.5.2
Multiplying by Powers of Ten
3.5.3
Using Powers of Ten
3.5.4
Scientific Notation
3.5.5
Using a Calculator
3.5.6
Vocabulary
3.5.7
Practice 3.5
4
Calculation
4.1
Adding and Subtracting Fractions
4.1.1
Like Fractions
4.1.2
Smaller Pieces
4.1.3
Adding Unlike Fractions
4.1.4
Lowest Common Denominator
4.1.5
Three Steps for Adding Fractions
4.1.6
Vocabulary
4.1.7
Practice 4.1
4.2
Multiplying and Dividing Fractions
4.2.1
Take Part
4.2.2
Multiplying by a Fraction
4.2.3
Dividing by a Fraction
4.2.4
More Dividing by Fractions
4.2.5
Vocabulary
4.2.6
Practice 4.2
4.3
Roots and Radicals
4.3.1
What Is a Square Root?
4.3.2
Approximating Square Roots
4.3.3
Squares and Square Roots
4.3.4
Pythagorean Theorem
4.3.5
Vocabulary
4.3.6
Practice 4.3
4.4
Negative Numbers
4.4.1
Opposites
4.4.2
Signed Numbers
4.4.3
The Integers
4.4.4
Graphing on a Number Line
4.4.5
Indicating Change with Signed Numbers
4.4.6
Vocabulary
4.4.7
Practice 4.4
4.5
Order of Operations
4.5.1
Which Operations Come First
4.5.2
Combined Operations
4.5.3
Parentheses
4.5.4
Fraction Bars
4.5.5
Using a Calculator
4.5.6
Exponents and Roots
4.5.7
Vocabulary
4.5.8
Practice 4.5
5
Using Variables
5.1
Working with Variables
5.1.1
Like Terms
5.1.2
Equivalent Expressions
5.1.3
Constant Multiples of Terms
5.1.4
Terms with Exponents
5.1.5
Multiplying Variable Expressions
5.1.6
Evaluating Algebraic Expressions
5.1.7
Vocabulary
5.1.8
Practice 5.1
5.2
More Algebraic Expressions
5.2.1
Writing Algebraic Expressions
5.2.2
Evaluating Algebraic Expressions
5.2.3
Formulas
5.2.4
Vocabulary
5.2.5
Practice 5.2
5.3
Problem Solving
5.3.1
Using Formulas
5.3.2
Writing an Equation
5.3.3
Modeling a Problem
5.3.4
Practice 5.3
5.4
More Equations
5.4.1
Equations with Two Operations
5.4.2
A Strategy for Solving Equations
5.4.3
Formulas
5.4.4
Problem Solving
5.4.5
Using Algebra to Solve Problems
5.4.6
Practice 5.4
5.5
Graphs
5.5.1
Line Graphs
5.5.2
Plotting Points
5.5.3
Graphing an Equation
5.5.4
Reading a Graph
5.5.5
Vocabulary
5.5.6
Practice 5.5
6
Core Concepts
6.1
Ratios
6.1.1
Comparing Quantities
6.1.2
Ratios
6.1.3
Decimal Form for Ratios
6.1.4
Rates
6.1.5
Vocabulary
6.1.6
Practice 6-1
6.2
Proportion
6.2.1
Proportional Variables
6.2.2
Proportional Reasoning
6.2.3
Using Proportions
6.2.4
Graphing Proportional Variables
6.2.5
Vocabulary
6.2.6
Practice 6-2
6.3
Slope
6.3.1
Equations Relating Proportional Variables
6.3.2
Steepness of the Graph
6.3.3
Rate of Increase
6.3.4
Visualizing Growth Rate on a Graph
6.3.5
Slope of a Line
6.3.6
Decreasing Graphs
6.3.7
Vocabulary
6.3.8
Practice 6-3
6.4
Similarity
6.4.1
Similar Figures
6.4.2
Scale Factors
6.4.3
Ratio and Proportion
6.4.4
Conditions for Similarity
6.4.5
Similar Triangles
6.4.6
Vocabulary
6.4.7
Practice 6-4
6.5
More About Similarity
6.5.1
Areas of Similar Figures
6.5.2
Volumes of Proportional Solids
6.5.3
Practice 6-5
7
Signed Numbers
7.1
Adding Signed Numbers
7.1.1
Adding Two Numbers with the Same Sign
7.1.2
Adding Two Numbers with Opposite Signs
7.1.3
Rules for Addition
7.1.4
Net Change
7.1.5
Vocabulary
7.1.6
Practice 7-1
7.2
Subtracting Signed Numbers
7.2.1
Subtracting a Positive Number
7.2.2
Subtracting a Negative Number
7.2.3
Rule for Subtraction
7.2.4
Notation
7.2.5
Vocabulary
7.2.6
Practice 7-2
7.3
Multiplying and Dividing Signed Numbers
7.3.1
Multiplication
7.3.2
Division
7.3.3
Powers of Negative Numbers
7.3.4
Vocabulary
7.3.5
Practice 7-3
7.4
Equations and Graphs
7.4.1
Solving Equations
7.4.2
The Cartesian Coordinate System
7.4.3
Plotting Points
7.4.4
Graphing Lines
7.4.5
Applications of Linear Equations
7.4.6
Vocabulary
7.4.7
Practice 7-4
Backmatter
A
Answers to Odd-Numbered Homework Problems
Glossary
Colophon
Colophon
Colophon
This book was authored in PreTeXt.
