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# ONE MATHEMATICAL CAT, PLEASE! A First Course in Algebra

## Free Online Algebra I Course with Unlimited Randomly-Generated Practice Problems and Worksheets in Every Section

You're about to learn that  x  is to mathematics as "cat" is to English.
The hope is that the next time you find yourself faced with  x , you'll think:
 Section 1: The Language of Mathematics Back to the top! Web Exercise:   expressions versus sentences Read the text Solutions to text exercises FUN STUFF: WolframAlpha (Type in ANY math—incredible!!) Learn about your favorite number (type in your favorite number and click ENTER) Improve your vocabulary and feed the hungry at the same time Practice basic math skills and feed the hungry at the same time Section 2: Brushing Up On Basic Arithmetic Skills Back to the top! Web Exercises:   basic addition practice   multiplication   divisibility   basic properties of zero and one   mixed basic add/subtract/multiply/divide practice Read the text (solutions to text exercises are included) FUN STUFF: Addition Bingo     Multiplication Bingo     Division Bingo Circle 21 game Timed Flashcards—try to beat others in your age group Khan Academy Check out this collection of YouTube videos: it includes arithmetic, pre-algebra, algebra, geometry, and more. Practice multiplication tables and feed the hungry at the same time Section 3: The Real Numbers Back to the top! Web Exercises:   deciding if a number is a whole number, an integer, etc. Read the text Solutions to text exercises ThatQuiz offers fun number line practice. LOTS of other practice, too! Check it out!   Squares Ending in Five FUN STUFF: Use logical skills to locate the counterfeit coin Word game (try it yourself, before you click "generate") Section 4: Addition of Signed Numbers Back to the top! Web Exercises:   addition of signed numbers Read the text (solutions to text exercises are included)   Four Fours Problem FUN STUFF: Circle 0 game Classic Peg Puzzle (click "instructions" to see what you're trying to do; red can only move left-to-right; blue can only move right-to-left) Section 5: Subtraction of Signed Numbers Back to the top! Web Exercises:   subtraction of signed numbers   mixed addition and subtraction of signed numbers Read the text (solutions to text exercises are included) FUN STUFF: Color Chips to explore subtraction Diffy, a fun subtraction game (press "ENTER" after typing a difference in a square) Number Line Bounce Section 6: Average Back to the top! Web Exercises:   fractions with a denominator of 2 to decimal form   average of two signed numbers   average of signed numbers Read the text (solutions to text exercises are included)   Formula for Primes FUN STUFF: Wolf and Rabbit (in this game, ":" means "divided by") Towers of Hanoi (move a stack of disks from one peg to another in as few moves as possible) Section 7: The Base Ten Number System Back to the top! Web Exercises:   identifying place values   multiplying by powers of ten Read the text (solutions to text exercises are included) FUN STUFF: Base Blocks SET is a really fun game (click "Daily Puzzle" to play online; if you're never played before, click "How To Play") Section 8: Decimals Back to the top! Web Exercises:   changing decimals to fractions   multiplying and dividing decimals by powers of ten   changing decimals to percents   changing percents to decimals Read the text (solutions to text exercises are included)   Mind-Reading Number Trick FUN STUFF: Explore Percentages Circle 3 game Section 9: Mathematicians are Fond of Collections Back to the top! Web Exercises:   introduction to sets   interval and list notation Read the text Solutions to text exercises   Nine Point Circle FUN STUFF: Play with Pentominoes (click on "Activities" for some fun things to do) Cough in your sleeve and keep us all healthy! Section 10: Holding This, Holding That Back to the top! Web Exercises:   introduction to variables   reading set notation   going from a sequence of operations to an expression   going from an expression to a sequence of operations   solving simple sentences by inspection   using mathematical conventions Read the text Solutions to text exercises   Spherical Bands FUN STUFF: Number Puzzle    (math solution to a number puzzle) Section 10.5: Solving For A Particular Variable IMPORTANT FOR SCIENCE CLASSES! Back to the top! Web Exercises:   “undoing” a sequence of operations   solving for a particular variable   Getting bigger? Getting smaller? Divisibility By Seven FUN STUFF: Make a Tri-Hexa-Flexagon Make a Paper Tree (Don't use too many pieces, or you won't be able to make the cuts.) Section 10.7: Scientific Notation and Significant Figures IMPORTANT FOR SCIENCE CLASSES! Back to the top! Web Exercises:   scientific notation   significant figures and related concepts FUN STUFF: Fill and Pour SUDOKU: a new game every day (play online or print it out) Section 11: Introduction to Fractions Back to the top! Web Exercises:   rewriting fractions as a whole number plus a fraction   locating fractions on a number line   fractions involving zero Read the text (solutions to text exercises are included) FUN STUFF: Play with Pattern blocks to visualize fractions (hover your mouse over any corner to rotate pieces) Renaming Fractions Soda Constructor Bored? Click on one of the images, and have fun! Section 12: Multiplying Fractions Back to the top! Web Exercises:   finding reciprocals   determining if a product is positive or negative   multiplying and dividing fractions   practice with the form $\,a\cdot\frac{b}{c}\,$   more practice with the form $\,a\cdot\frac{b}{c}\,$   renaming fractional expressions Read the text (solutions to text exercises are included) FUN STUFF: Multiplying Fractions Dividing Fractions Fighter Pilot Training  (test your reflexes) Section 13: Adding Fractions Back to the top! Web Exercises:   practice with multiples   finding least common multiples   renaming fractions with a specified denominator   practice with factors   adding and subtracting fractions   adding and subtracting simple fractions with variables   divisibility equivalences Read the text (solutions to text exercises are included) FUN STUFF: Renaming fractions Have fun adding fractions Sieve of Eratosthenes (a classic method for determining prime numbers) Section 13.5: Prime Numbers and Related Concepts Back to the top! Short on time? Section 13.5 can be skipped without any loss of continuity. Web Exercises:   prime numbers   the Prime Factorization Theorem   relatively prime numbers and related concepts Section 14: I Live Two Blocks West Of You Back to the top! Web Exercises:   identifying inequalities as true or false   bigger, smaller, greater, lesser   practice with the phrases “at least” and “at most”   identifying inequalities with variables as true or false   solving equations of the form $\,xy = 0\,$ Read the text Solutions to text exercises FUN STUFF: ExploreLearning You can only use each "gizmo" for five minutes each day unless you subscribe (and pay), but these are really cool! Section 15: Numbers Have Lots of Different names! Back to the top! Web Exercises:   recognizing zero and one Read the text Solutions to text exercises FUN STUFF: Have fun with some CHOCOLATE MATH! How does "Chocolate Math" work? Section 16: Exact versus Approximate Back to the top! Web Exercises:   writing fractions in simplest form   deciding if a fraction is a finite or infinite repeating decimal   deciding if numbers are equal or approximately equal Read the text (solutions to text exercises are included)   Area of an Ellipse   Buffon Needle Problem (estimate pi!) FUN STUFF: Daily Word Search Section 17: Rounding Back to the top! Web Exercises:   rounding decimals to a specified number of places Read the text (solutions to text exercises are included) FUN STUFF: Rounding Flash Cards Math Words (fascinating origins and information on a wide variety of mathematical words) Section 18: Unit Conversion Back to the top! Web Exercises:   Tables of Unit Conversion Information   classifying units as length, time, volume, weight/mass   practice with unit abbreviations   practice with unit names   practice with unit conversion information   one-step conversions Read the text (solutions to text exercises are included)   Wilson's Theorem FUN STUFF: Practice with Unit Conversion Improve your memory by playing CONCENTRATION Section 19: More Unit Conversion Back to the top! Web Exercises:   multi-step conversions   rate problems   work problems (This web exercise is an experiment with a very different style. Enjoy!) Read the text (solutions to text exercises are included)   Fermat's Little Theorem FUN STUFF: Optical Illusions Snowflakes (practice paying attention to details) Section 20: Exponent Notation Back to the top! Web Exercises:   exponents   practice with order of operations   taking PEMDAS too literally: don't make this mistake!   basic exponent practice with fractions Read the text (solutions to text exercises are included) FUN STUFF: Play HANGMAN online Section 21: Exponent Laws Back to the top! Web Exercises:   practice with $\,x^mx^n = x^{m+n}\,$   practice with $\,(x^m)^n = x^{mn}\,$   practice with $\,x^m/x^n = x^{m-n}$   practice with $\,x^{-p} = 1/x^p$   one-step exponent law practice   multi-step exponent law practice Read the text (solutions to text exercises are included)   Sums of Reciprocal Powers Section 22: Radicals Back to the top! Web Exercises:   practice with radicals   approximating radicals Read the text (solutions to text exercises are included)   One Equals Zero! FUN STUFF: Square Root Flashcards Give this a try—it's fun! Section 23: Rational Exponents Back to the top! Web Exercises:   writing radicals in rational exponent form   writing rational exponents as radicals   practice with rational exponents Read the text (solutions to text exercises are included)   Multiplication by 11   Leapfrog Addition FUN STUFF: Stereograms are 3D images hidden within another picture. Take the time to "see" these—my first one took me almost an hour—it's worth it! (I have to take my glasses off.) Section 24: The Distributive Law Back to the top! Web Exercises:   practice with  x  and  -x   practice with products of signed variables   practice with the distributive law   mental math: addition   Don't mix up $\,3x\,$ versus $\,x^3\,$! Read the text (solutions to text exercises are included)   Pizza Slices FUN STUFF: Use Algebra Tiles to visualize the distributive law (press INSTRUCTIONS to learn how to rotate the tiles) Section 25: Revisiting Exponents Back to the top! Web Exercises:   equal or opposites?   recognizing the patterns $\,x^n\,$ and $\,(-x)^n\,$   writing expressions in the form kxn   writing more complicated expressions in the form kxn   writing quite complicated expressions in the form kxn Read the text (solutions to text exercises are included)   Suspended Rope Trick FUN STUFF: Play BOGGLE online (click "Start Game") Section 26: FOIL and more Back to the top! Web Exercises:   identifying variable parts and coefficients of terms   combining like terms   simplifying expressions like -a(3b - 2c - d)   basic FOIL   more complicated FOIL   simplifying $\,(a+b)^2\,$ and and $\,(a-b)^2\,$   simplifying expressions like (a - b)(c + d - e) Read the text (solutions to text exercises are included)   Domino and Square Tilings Section 27: These Sentences Certainly Look Different! Back to the top! Web Exercises:   practice with the mathematical words and, or, and is equivalent to Read the text Solutions to text exercises   Making Magic Squares FUN STUFF: Kakuro (easy) (similar to Sudoku) Kakuro (harder) (similar to Sudoku) Section 28: Introduction to Factoring Back to the top! Web Exercises:   recognizing products and sums; identifying factors and terms   identifying common factors   factoring simple expressions Read the text (solutions to text exercises are included)   Birthday Problem Section 29: Greatest Common Factor Back to the top! Web Exercises:   listing all the factors of a whole number   finding the greatest common factor of 2 or 3 numbers   finding the greatest common factor of variable expressions   factoring out the greatest common factor Read the text (solutions to text exercises are included)   Pick's Theorem FUN STUFF: Create Factor Trees Section 30: Transforming Tool #1 (the Addition Property of Equality) Back to the top! Web Exercises:   the Addition Property of Equality Read the text (solutions to text exercises are included)   Goldbach's Conjecture FUN STUFF: Tangrams Section 31: Transforming Tool #2 (the Multiplication Property of Equality) Back to the top! Web Exercises:   the Multiplication Property of Equality Read the text (solutions to text exercises are included)   Proofs Without Words Section 32: Solving Linear Equations in One Variable Back to the top! Web Exercises:   solving simple linear equations with integer coefficients   solving more complicated linear equations with integer coefficients   solving linear equations involving fractions   solving linear equations, all mixed up Read the text (solutions to text exercises are included)   Pascal's Triangle FUN STUFF: Use a balance beam to solve linear equations (positive integers) (press CONTINUE once you have the equation balanced) Solve linear equations using negative integers Algebra Planet Blaster Section 32.5: Applications and More Back to the top! Web Exercises:   simple word problems resulting in linear equations FUN STUFF: Play Text Twist online (click "Play Web Game") Section 33: Solving Linear Inequalities in One Variable Back to the top! Web Exercises:   solving simple linear inequalities with integer coefficients   solving linear inequalities with integer coefficients   solving linear inequalities involving fractions   solving linear inequalities, all mixed up Read the text (solutions to text exercises are included)   Magic Squares, Indeed! FUN STUFF: How to draw an impossible triangle Section 34: Introduction to Absolute Value Back to the top! Web Exercises:   simplifying basic absolute value expressions   determining the sign (plus or minus) of absolute value expressions   solving simple absolute value sentences   solving sentences involving "plus or minus" Read the text (solutions to text exercises are included)   Reflecting on the Hyperbola FUN STUFF: Math Gems (this is a beautiful assortment of mathematical marvels; print it out and hang it on the wall for mathematical inspiration) Section 35: Solving Absolute Value Equations Back to the top! Web Exercises:   solving absolute value equations Read the text (solutions to text exercises are included)   Bike with Square Wheels Section 36: Solving Absolute Value Inequalities Involving "Less Than" Back to the top! Web Exercises:   solving absolute value inequalities involving "less than" Read the text (solutions to text exercises are included)   Toggling Light Switches Section 37: Finishing Up Absolute Value Sentences Back to the top! Web Exercises:   solving absolute value inequalities involving "greater than"   solving absolute value sentences (all types) Read the text (solutions to text exercises are included)   Largest Known Primes Section 38: Factoring a Difference of Squares Back to the top! Web Exercises:   identifying perfect squares   writing expressions in the form A2   factoring a difference of squares Matching Problem Make a jigsaw puzzle online Section 39: Solving Equations Involving Perfect Squares Back to the top! Web Exercises:   solving simple equations involving perfect squares   solving more complicated equations involving perfect squares   translating simple mathematical phrases   word problems involving perfect squares Euler Characteristic   Why an International Date Line? Section 40: Factoring Trinomials Back to the top! Web Exercises:   basic concepts involved in factoring trinomials   factoring $\,x^2 + bx + c\,$,   $\,c > 0\,$   factoring $\,x^2 + bx + c\,$,   $\,c < 0\,$   factoring trinomials, all mixed up Difference of Squares FUN STUFF: Take a look at the stars! Section 41: Solving Quadratic Equations by Factoring Back to the top! Web Exercises:   identifying quadratic equations   writing quadratic equations in standard form   solving simple quadratic equations by factoring Successive Differences of Powers   Six Degrees of Separation FUN STUFF: Optical Illusions Section 42: More on Quadratic Equations Back to the top! Web Exercises:   factoring $\,ax^2 + bx + c\,$   solving more complicated quadratic equations by factoring Drunken Walker and Fly   Conic Sections FUN STUFF: Cool Math: Factory Balls   (Good brain exercise!) Section 42.5: Arithmetic with Fractions Involving Variables Back to the top! Web Exercises:   multiplying and dividing fractions with variables   adding and subtracting fractions with variables Proof With Words   Red-Black Card Trick FUN STUFF: Mathematical Artwork (by the creator of MathJax) Section 43: Percent Increase and Decrease Back to the top! Web Exercises:   writing expressions involving percent increase and decrease   calculating percent increase and decrease   problems involving percent increase and decrease   more problems involving percent increase and decrease Math Limerick   Magic 1089 FUN STUFF: Create your own Jeopardy game! (Teachers—you'll love this!) Section 44: Introduction to the Coordinate Plane Back to the top! Web Exercises:   locating points in quadrants and on axes   practice with points   the Pythagorean Theorem   the distance formula   the midpoint formula   introduction to equations and inequalities in two variables Fibonacci Formula FUN STUFF: Play MASTERMIND online (this is a great game of logic; BLACK means a correct color in a correct position; WHITE means a correct color in an incorrect position) Section 45: Lines Back to the top! Web Exercises:   introduction to the slope of a line   practice with slope   graphing lines   finding equations of lines Kaprekar's Constant FUN STUFF: Bake some cornbread! (ingredients have been renamed so you don't have many dishes to wash) Cool Math: Doggnations   (Great brain exercise; 50 levels) Section 46: More On Lines Back to the top! Web Exercises:   point-slope form   horizontal and vertical lines   parallel and perpendicular lines Binary Card Trick   Wallis' Formula FUN STUFF: Bored? Flip a coin! Section 47: Functions Back to the top! Web Exercises:   introduction to functions   introduction to function notation   more practice with function notation   domain and range of a function Four Color Theorem FUN STUFF: Play with this Function Machine THINK CLEAR! (click on the little guy in the lower right corner to move from page to page)