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Prealgebra

Further your understanding of arithmetic and geometry, learn about variables, and solve linear equations, inequalities, and systems.

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Content

Arithmetic

Geometry

Algebra

Measurement and Statistics

1.
Ratios & Percentages
24 topics
1.1. Ratios
1.1.1. Introduction to Ratios
1.1.2. Equivalent Ratios
1.1.3. Writing Ratios Using Fractions
1.1.4. Working With Equivalent Ratios
1.1.5. More on Equivalent Ratios
1.1.6. Ratio Tables
1.1.7. Graphing Ratios
1.2. Unit Rates
1.2.1. Unit Rates
1.2.2. Solving Problems Using Unit Rates
1.2.3. Speed as a Unit Rate
1.2.4. Calculating Unit Rates Associated With Ratios of Fractions
1.2.5. Solving Unit Rate Problems Using Ratios of Fractions
1.3. Proportional Relationships
1.3.1. Understanding Proportional Relationships Using Tables
1.3.2. Understanding Proportional Relationships Using Graphs
1.3.3. Understanding Proportional Relationships From Descriptions
1.4. Percentages
1.4.1. Understanding Percentages Using Models
1.4.2. Converting Between Percentages and Fractions
1.4.3. Converting Between Percentages and Decimals
1.4.4. Finding Part of a Number Given a Whole and a Percentage
1.4.5. Finding Part of a Number Given a Whole and a Percentage: Word Problems
1.4.6. Finding a Percentage Given Two Numbers
1.4.7. Finding a Percentage Given Two Numbers: Word Problems
1.4.8. Finding a Total Given a Part and a Percentage
1.4.9. Percentage Increase, Decrease, and Error
2.
The Number System
24 topics
2.5. Addition and Subtraction of Rational Numbers
2.5.1. Subtracting a Positive Number From a Smaller Positive Number
2.5.2. Subtracting a Positive Number From a Negative Number
2.5.3. Subtracting a Positive Fraction From a Smaller Fraction
2.5.4. Subtracting a Positive Decimal From a Smaller Decimal
2.5.5. Adding a Positive Number to a Negative Number
2.5.6. Adding a Negative Number
2.5.7. Subtracting a Negative Number
2.5.8. Additive Inverses of Numbers
2.5.9. Solving Problems Using Addition and Subtraction of Rational Numbers
2.6. Multiplication and Division of Rational Numbers
2.6.1. Multiplying Positive Numbers With Negative Numbers
2.6.2. Multiplying Negative Numbers
2.6.3. Dividing With Negative Numbers
2.6.4. Dividing With Negative Decimals and Fractions
2.6.5. Reciprocals of Rational Numbers
2.6.6. Multiplying and Dividing With Zero
2.6.7. Fractions of Fractions
2.6.8. Solving Problems Using the Four Operations on Rational Numbers
2.7. Number Theory
2.7.1. The Multiples of a Number
2.7.2. Prime and Composite Numbers
2.7.3. Prime Factorization of Integers
2.7.4. The Greatest Common Factor of Two Integers
2.7.5. The Lowest Common Multiple of Two Integers
2.7.6. Divisibility of Integers
2.7.7. Divisibility of Integers by 3, 9 and 6
3.
Exponents & Radicals
32 topics
3.8. Exponents
3.8.1. Squaring Rational Numbers
3.8.2. Cubing Rational Numbers
3.8.3. Exponents With Rational Bases
3.8.4. The Zeroth Power
3.8.5. Powers of Negative One
3.8.6. Negative Exponents
3.9. The Rules of Exponents
3.9.1. The Product Rule for Exponents
3.9.2. The Quotient Rule for Exponents
3.9.3. The Power Rule for Exponents
3.9.4. The Power of Product Rule for Exponents
3.9.5. The Power of Quotient Rule for Exponents
3.9.6. Combining the Rules of Exponents
3.10. Scientific Notation
3.10.1. Writing Numbers in Scientific Notation
3.10.2. Converting a Number from Scientific Notation to Standard Notation
3.10.3. Adding and Subtracting Numbers Given in Scientific Notation
3.10.4. Adding Numbers in Scientific Notation With Different Powers of Ten
3.10.5. Multiplying Numbers Given in Scientific Notation
3.10.6. Dividing Numbers Given in Scientific Notation
3.11. Order of Operations
3.11.1. Evaluating Rational Number Expressions Without Exponents
3.11.2. Evaluating Rational Number Expressions With Positive Integer Exponents
3.11.3. Evaluating Rational Number Expressions With Integer Exponents
3.12. Radicals
3.12.1. The Square Root of a Perfect Square
3.12.2. Squaring a Square Root
3.12.3. The Cube Root of a Perfect Cube
3.12.4. Surds
3.12.5. Simplifying Expressions With Surds
3.12.6. Evaluating Numerical Expressions Containing Radicals
3.12.7. Adding and Subtracting Radicals
3.12.8. Rationalizing Denominators
3.13. The Rules of Radicals
3.13.1. Radicals as Fractional Exponents
3.13.2. The Product Rule for Radicals
3.13.3. The Quotient Rule for Radicals
4.
Algebraic Expressions
17 topics
4.14. Algebraic Expressions
4.14.1. Introduction to Algebraic Expressions
4.14.2. Constructing Algebraic Expressions
4.14.3. Evaluating Linear Expressions
4.14.4. Evaluating Rational Expressions
4.14.5. Identifying Terms in Linear Expressions
4.14.6. Identifying Coefficients and Constants in Linear Expressions
4.14.7. The Greatest Common Factor of Two Linear Expressions
4.15. Simplifying Linear Expressions
4.15.1. Identifying Like Terms in a Linear Expression
4.15.2. Collecting Like Terms in a Linear Expression
4.15.3. Applying the Distributive Law With Linear Expressions
4.15.4. The Distributive Law With Three Terms
4.15.5. Distributing the Negative Sign in a Linear Expression
4.15.6. Simplifying Linear Expressions Using the Distributive Law
4.15.7. Simplifying Linear Expressions When a Group of Terms Is Subtracted
4.15.8. Simplifying Linear Expressions Containing Fractions
4.15.9. Factoring Numerical Expressions
4.15.10. Factoring Linear Expressions
5.
Equations & Inequalities
29 topics
5.16. Solving One-Step Linear Equations
5.16.1. Solving Linear Equations by Trial and Error
5.16.2. Solving One-Step Addition and Subtraction Equations
5.16.3. Solving One-Step Multiplication and Division Equations
5.17. Solving Multi-Step Linear Equations
5.17.1. Solving Two-Step Equations
5.17.2. Solving Linear Equations With Fractional Coefficients
5.17.3. Solving Linear Equations With Decimal Coefficients
5.17.4. Solving Linear Equations With Variables on Both Sides
5.17.5. Solving Linear Equations by Clearing a Rational Expression
5.17.6. Solving Linear Equations Using Cross-Multiplication
5.17.7. Solving Two-Variable Equations
5.17.8. Equations With Many Solutions and No Solutions
5.18. Solving Linear Inequalities
5.18.1. Representing Inequalities on Number Lines
5.18.2. Representing Compound Inequalities on Number Lines
5.18.3. Verifying Solutions of Linear Inequalities
5.18.4. Solving Linear Inequalities
5.19. Graphs of Linear Equations
5.19.1. The Cartesian Coordinate System
5.19.2. The Distance Between Two Points in the Coordinate Plane
5.19.3. Two-Variable Linear Equations and Their Solutions
5.19.4. Graphing Linear Equations
5.19.5. Horizontal and Vertical Lines
5.19.6. Calculating Slopes of Straight Lines
5.19.7. Equations of Lines in Slope-Intercept Form
5.19.8. Finding Properties of Lines Given in Slope-Intercept Form
5.20. Systems of Linear Equations
5.20.1. Introduction to Systems of Linear Equations
5.20.2. Approximating Solutions to Systems of Linear Equations
5.20.3. Solving Systems of Two Linear Equations Using Substitution
5.20.4. Solving Systems of Two Linear Equations Using Elimination
5.20.5. Systems of Equations With No Solutions and Infinitely Many Solutions
5.20.6. Calculating the Intersection of Two Lines
6.
Geometry
43 topics
6.21. Introduction to Geometry
6.21.1. Points, Lines, Rays, and Parallel Lines
6.21.2. Units
6.21.3. Units of Area and Volume
6.21.4. Segments and Measures of Segments
6.21.5. Congruent Segments
6.21.6. Midpoints
6.21.7. Collinear Points
6.21.8. The Segment Addition Postulate
6.22. Angles
6.22.1. Angles and Measures of Angles
6.22.2. Congruent Angles
6.22.3. Sums of Angles
6.22.4. Null, Right, Straight, and Full Angles
6.22.5. Vertical Angles
6.22.6. Acute, Obtuse, and Reflex Angles
6.22.7. Solving Problems With Angles
6.23. Advanced Angles
6.23.1. Complementary Angles
6.23.2. Supplementary Angles
6.23.3. Parallel Lines and Transversals
6.23.4. Angle Criteria for Parallel Lines
6.23.5. Angle Bisectors
6.23.6. Perpendicular Lines and Bisectors
6.24. Triangles
6.24.1. Interior Angles of Triangles
6.24.2. Exterior Angles of Triangles
6.24.3. Problem Solving With Angles of Triangles
6.24.4. Classifying Triangles
6.24.5. The Triangle Inequality
6.24.6. The Isosceles Triangle Theorem
6.24.7. Heights of Triangles
6.25. Polygons
6.25.1. Polygons
6.25.2. Interior Angles of Polygons
6.25.3. Exterior Angles of Polygons
6.25.4. Congruent Polygons
6.25.5. Regular Polygons
6.25.6. The Perimeter of a Polygon
6.26. Quadrilaterals
6.26.1. Classifying Quadrilaterals
6.26.2. Properties of Rectangles and Squares
6.26.3. Properties of Trapezoids
6.27. Area and Perimeter
6.27.1. Areas of Rectangles and Squares
6.27.2. Areas of Parallelograms
6.27.3. Areas of Triangles
6.27.4. Areas of Trapezoids
6.27.5. Areas and Perimeters of Composite Shapes
6.27.6. The Area Between Two Shapes
7.
Statistics
20 topics
7.28. Summarizing Data
7.28.1. Introduction to Statistics
7.28.2. The Mean of a Data Set
7.28.3. The Median of a Data Set
7.28.4. The Mode of a Data Set
7.28.5. Range, Quartiles and Interquartile Range
7.28.6. Mean Absolute Deviation
7.28.7. Comparing Data Sets Using Measures of Centrality
7.28.8. Comparing Data Sets Using Measures of Spread
7.28.9. Outliers
7.28.10. Removing Outliers
7.29. Representing Data
7.29.1. Frequency Tables
7.29.2. Dot Plots
7.29.3. Measuring Centrality Using Dot Plots
7.29.4. Measuring Range and MAD From Dot Plots
7.29.5. Measuring Quartiles and IQR From Dot Plots
7.29.6. Interpreting Shapes of Distributions Using Dot Plots
7.29.7. Box Plots
7.29.8. Histograms
7.29.9. Comparing Measures of Center
7.29.10. Comparing Measures of Spread