Series: Pre-Algebra Review

Ugh, surface area!

06/01/2009

~ brittanie

This video is a great visual resource to find the surface area of a cylinder! It's a much better way to learn surface area than from my teacher's textbook.

lcm

04/15/2009

~ monique

this really hepled me understand better than my college prep teacher

Thanks!

01/29/2009

~ hmaryt

very clear explanations of how to approach dependent probabilities... which always seem to baffle me. Thanks, Prof Burger!

Below are the descriptions for each of the lessons included in the series:

• Pre-Algebra: Exponent Intro - Evaluating Powers

  Large numbers can be more easily expressed with a power. A power is an expression written with a base and an exponent (or the value of such an expression that includes both a base and an exponent). The base is a number in a power that is used as a factor. The exponent is a superscript number that indicates how many times the base is used as a factor. For example, 3^5 (or three to the power of five or three-to-the-fifth) can also be written as the product of five factors of three, or 3*3*3*3*3, or 243.

  Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Pre Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/prealgebra. The full course covers whole numbers, integers, fractions and decimals, variables, expressions, equations and a variety of other pre algebra topics.

  Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

  He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".

  Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

  Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

• Pre-Algebra: Writing a Decimal as a Percent

  A percent gives us a sense of how much of something a number is. Professor Burger shows us that converting a decimal to a percentage is pretty simple. In prior lessons, we've learned how to convert a percentage to a decimal (by dividing by one hundred). In this lesson, we will learn how to convert a decimal to a percentage. To do so, you will multiply the decimal by 100. This is the same as moving the decimal point over two places to the right.

  Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Pre Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/prealgebra. The full course covers whole numbers, integers, fractions and decimals, variables, expressions, equations and a variety of other pre algebra topics.

  Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

  He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".

  Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

  Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

• Pre-Algebra: Volume of a Cylinder

  To find the volume for a cylinder, you will use the same volume formula that you would use to calculate the volume of a rectangular prism, V=Bh. However, for a cylinder, the area of the base, B, is equal to Pi * r^2, where r is the radius of the base. This is because the base is circular in shape, and the area of a circle is equal to pi*r^2 whereas the area of a rectangle (the shape of the base of a rectangular prism) is equal to length*width.

  Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Pre Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/prealgebra. The full course covers whole numbers, integers, fractions and decimals, variables, expressions, equations and a variety of other pre algebra topics.
  Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

  He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".

  Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

  Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

• Pre-Algebra: Probability of Dependent Events

  Dependent events, in terms of probability, are instances in which the occurrence of one event has an effect on the probability that a second event will occur. Professor Burger uses the example of pulling 2 dimes from a pocket full of coins. If I pull a dime out the first time, I'm less likely to pull a dime out the second time given that there is one less dime in the pocket which I can pull out. The probability can be computed P(A and B) = P(A) * P(B after A). This means that the last part of the equation is computed, given that the first event has occurred. It is ready, 'The probability of A and B is equal to the probability of A times the probability of B given A.'

  Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Pre Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/prealgebra. The full course covers whole numbers, integers, fractions and decimals, variables, expressions, equations and a variety of other pre algebra topics.

  Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

  He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".

  Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

  Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

• Pre-Algebra: Converting Fractions and Decimals

  Fractions can be converted into decimals by simply dividing the numerator by the denominator. This can be done easily with a calculator or it can be done by hand using long division. Professor Burger shows how this is done both with numbers that divide evenly, and numbers that don't divide evenly. Sometimes, when numbers don't divide evently, you are left with a result that has a decimal. In this lesson, you will also learn shorthand for writing numbers with repeating decimals.

  Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Pre Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/prealgebra. The full course covers whole numbers, integers, fractions and decimals, variables, expressions, equations and a variety of other pre algebra topics.

  Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

  He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".

  Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

  Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

• Pre-Algebra: Subtracting Integers

  To subtract integers, you can simply add the opposite. In a previous lesson, Professor Burger taught us how to add integers, and in this lesson he will show how subtracting two integers is the same as adding the integers with the opposite sign. For example, 10-14 is equal to 10 + (-14). If the number being subtracted is less than the the number it is being subtracted from, the answer will be positive. If the number being subtracted is greater, the answer will be negative.

  Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Pre Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/prealgebra. The full course covers whole numbers, integers, fractions and decimals, variables, expressions, equations and a variety of other pre algebra topics.

  Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

  He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".

  Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

  Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

• Pre-Algebra: Volume of a Prism

  Professor Burger teaches how to find the volume of a prism. For a rectangular prism, you will take the length * width * height of the prism. Units will always be expressed as cubed as volume describes a trhee-dimensional space. Professor Burger also explains how to find the volume of a prizm that is not rectangular. For this formula, V, volume, equals B, the area of the base, multiplied by the height, V=Bh.

  Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Pre Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/prealgebra. The full course covers whole numbers, integers, fractions and decimals, variables, expressions, equations and a variety of other pre algebra topics.

  Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

  He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".

  Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

  Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

• Pre-Algebra: Finding Greatest Common Factors (GCF)

  Factors shared by two or more numbers are called common factors. The largest common factor shared by two or more numbers is known as the Greatest Common Factor, or GFC, of the numbers. There are several methods to find the GFC, which Professor Burger will show you. The first is to simply list out the factors for each number. This is easiest for small numbers. For larger numbers, or groups of numbers, using prime factorization or a ladder diagram will work better. Professor Burger demonstrates how to do both of these methods to find the GFC for 3 numbers. If using a ladder diagram, you will have to multiply the factors together to find the Greatest Common Factor.

  Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Pre Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/prealgebra. The full course covers whole numbers, integers, fractions and decimals, variables, expressions, equations and a variety of other pre algebra topics.

  Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

  He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".

  Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

  Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

• Pre-Algebra: Adding Integers Using Absolute Value

  Professor Burger shows you how to add positive and negative integers together. To add two integers with the same sign (both positive or both negative), you will add their absolute values and keep the sign. To add two integers with different signs, you will take the difference of their absolute values and use the sign of the integer with the greater absolute value. Thus because -3 and -4 have the same sign, we will add their absolute values (3 and 4 respectively) to get 7. We will then apply the sign of both -3 and -4 to the 7 to arrive at -7 as our final answer. If we were adding +5 and -8, we would notice that they have different signs. Thus, we start by taking the difference of their absolute values (8-5), which turns out to be 3. In order to decide what the correct sign is for 3, we'll pick the sign of the number with the larger absolute value, which in this case is 8. Since 8 has a negative sign assigned to it, our answer will also have a negative sign. Thus, the answer is -3.

  Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Pre Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/prealgebra. The full course covers whole numbers, integers, fractions and decimals, variables, expressions, equations and a variety of other pre algebra topics.

  Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

  He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".

  Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

  Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

• Pre-Algebra: Simplifying Algebraic Expressions

  You can simplify algebraic expressions by combining like terms. Terms are the part of an expression to be added or subtracted. Terms are called 'like terms' if the variables are the same. A coefficient is the number that is multiplied by a variable in an algebraic expression. In this lesson, Professor Burger demonstrates the commutative, associative, and distributive properties by simplifying several algebraic expressions involving like and unlike terms.

  Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Pre Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/prealgebra. The full course covers whole numbers, integers, fractions and decimals, variables, expressions, equations and a variety of other pre algebra topics.

  Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

  He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".

  Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

  Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

• Pre-Algebra: Writing & Solving Two-Step Equations

  This lesson outlines the process for solving two step equations, which are equations that involve more than one operation to solve for the variable. First, Professor Burger teaches you to isolate the variable terms. Remember that you will use the reverse order of operations to solve an equation with more than one operation involved. Once you have isolated the variable term on one side of the equation, you can solve for it.

  Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Pre Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/prealgebra. The full course covers whole numbers, integers, fractions and decimals, variables, expressions, equations and a variety of other pre algebra topics.

  Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

  He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".

  Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

  Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

• Pre-Algebra: Multiplying Decimals

  In this lesson, Professor Burger demonstrates how to multiply numbers with decimals. Start out by multiplying as if the numbers were whole numbers. Then, place the decimal point in the product so that the number of decimal places is equal to the total number of decimal places in the factors. Thus, the product of 3.47 times 5.1 will have 3 digits to the right of the decimal place given that 3.47 have 2 digits to the right and 5.1 has 1 digit to the right. Pay particular attention to the sign of the product; make sure it is correct if you are multiplying with a single or double negative.

  Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Pre Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/prealgebra. The full course covers whole numbers, integers, fractions and decimals, variables, expressions, equations and a variety of other pre algebra topics.

  Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

  He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".

  Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

  Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

• Pre-Algebra: Using the Order of Operations

  When evaluating numerical expressions, the set of rules that must be followed to ensure that everyone get the same answer is called the Order of Operations. The Order of Operations is as follows:
  1) Parentheses
  2) Exponents
  3) Multiply/Divide
  4) Add/Subtract

  What this means is that operations involving parentheses should be done first. Next, you should perform any calculations or operations that involve exponents. After that, you'll want to perform any multiplication or division that is called for. Finally, you can finish up by performing any addition and subtraction operations. If you encounter multiple operations within a set of parentheses, you will follow the order of operations to simplify the expression within the parentheses.

  Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Pre Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/prealgebra. The full course covers whole numbers, integers, fractions and decimals, variables, expressions, equations and a variety of other pre algebra topics.

  Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

  He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".

  Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

  Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

• Pre-Algebra: Writing a Fraction as a Percent

  There are two different ways to convert a fraction to a percentage depending on how easy the problem is. If the denominator of the fraction is a multiple of 100, Professor Burger shows you how to multiply the fraction up so that the numerator is over 100, in which case it will be a percentage. Professor Burger also shows you how to use long division to find the decimal equivalent of the fraction, and then multiply by 100 to find the percentage.

  Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Pre Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/prealgebra. The full course covers whole numbers, integers, fractions and decimals, variables, expressions, equations and a variety of other pre algebra topics.

  Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

  He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".

  Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

  Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

• Pre-Algebra: Finding Least Common Multiples (LCM)

  Professor Burger will show you how to find the Least Common Multiple of two or more numbers. The Least Common Multiple, or LCM, of a set of two or more numbers is the smallest number that is a multiple of all of the numbers. To find the LCM, you can use skip counting on a number line, create a list, or use Prime Factorization. By skip counting, you will start by marking the number on the number line, and then 'skipping' to all the multiples of that number. You repeat this process for the second number, and the first place where the two intersect is the LCM. You can also use a list by listing out multiples of all the numbers. Find the smallest number that is in all the lists, and this is the LCM. Lastly, Professor Burger demonstrates using Prime Factorization to find the LCM. For this method, you will factor all the numbers. Then, you will multiply these factors, using just enough of them to account for each number.

  Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Pre Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/prealgebra. The full course covers whole numbers, integers, fractions and decimals, variables, expressions, equations and a variety of other pre algebra topics.

  Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

  He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".

  Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

  Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

• Pre-Algebra: Surface Area of a Prism

  Professor Burger explains how surface area is different than volume. The surface area of a prism is the sum of the area of each face. So, S= 2lw + 2lh + 2hw. Professor Burger reminds you that the units for surface area are squared. The volume of a prism is given by V=Bh, where B is the area of the base (l*w) and h is the height of the prism. Volume is a measure of how much space their is inside the prism, and it is measured in cubed units.

  Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Pre Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/prealgebra. The full course covers whole numbers, integers, fractions and decimals, variables, expressions, equations and a variety of other pre algebra topics.

  Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

  He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".

  Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

  Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

• Pre-Algebra: Probability of Independent Events

  In probability, an independent event is one in which the occurrence of one event has no effect on the probability that a second event will occur. Professor Burger uses the example of a die and a coin to determine the probability of independent events, P(A and B)=P(A) * P(B). This is read, 'The probability of both A and B is equal to the probability of A times the probability of B.'

  Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Pre Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/prealgebra. The full course covers whole numbers, integers, fractions and decimals, variables, expressions, equations and a variety of other pre algebra topics.

  Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

  He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".

  Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

  Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

• Pre-Algebra: Surface Area of a Cylinder

  To find the surface area of a cylinder, you will need to add the surface area of the base, top, and curved surface. The area of both the base and the top will each be Pi * r^2 (the formula for the area of a circle). The area of the curved surface will be the height multiplied by the circumference of the base, 2*Pi*r. The equation for the Surface area is S=(2*Pi*r^2) + (2*Pi*r*h).

  Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Pre Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/prealgebra. The full course covers whole numbers, integers, fractions and decimals, variables, expressions, equations and a variety of other pre algebra topics.

  Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

  He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".

  Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

  Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

• Pre-Algebra: Rounding and Estimating Decimals

  This lesson is an example of rounding a number to the nearest tenth. Rounding is a way to shorten a number by approximating. To round to a particular decimal place, you'll learn to check the number directly to the right of the place you are rounding to see if you will round up or down. A value of 5 or greater in this place means that you should round up, where as a number less than 5 will round down. Thus, when 1.24 is rounded to the nearest tenth, it will become 1.2 given that 4 is less than 5. However, 1.25 would round up to 1.3 given that a value of 5 or more in the decimal place to the right (the hundredths place when we're rounding to tenths) indicates that you should round up.

  Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Pre Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/prealgebra. The full course covers whole numbers, integers, fractions and decimals, variables, expressions, equations and a variety of other pre algebra topics.

  Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

  He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".

  Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

  Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

• Pre-Algebra: Writing, Solving Multi-Step Equations

  A multi-step equation is an equation that calls for more than two operations to be performed. It will require forethought to solve and careful consideration of the order of operations. In this lesson, Professor Burger shows you how to use properties, such as the distributive property, to simplify the equation. Then you will want to combine like terms to further simplify the equation. Once you have isolated the variable term, you can finally solve the equation.

  This lesson is perfect for review for a CLEP test, mid-term, final, summer school, or personal growth!

  Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Pre Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/prealgebra. The full course covers whole numbers, integers, fractions and decimals, variables, expressions, equations and a variety of other pre algebra topics.

  Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

  He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".

  Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

  Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

• Pre-Algebra: Volume of a Pyramid

  It appears that finding the volume of a pyramid would be tricky, but Professor Burger teaches a simple formula, V=(1/3)Bh. The height, h, in the case of a pyramid, is in the very center of the pyramid, from the peak to the base. B is equal to the area of the base of the pyramid. This formula is similar to the formula used to calculate the volume of a rectangular prism (V=Bh, where B is the area of the base and h is the height of the prism) or cylinder (also V=Bh, where B is the area of the base and h is the height of the cylinder).

  Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Pre Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/prealgebra. The full course covers whole numbers, integers, fractions and decimals, variables, expressions, equations and a variety of other pre algebra topics.

  Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

  He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".

  Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

  Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

• Pre-Algebra: Multiplying Fractions & Mixed Numbers

  In this lesson, Professor Burger demonstrates two ways to multiply mixed numbers (numbers that contain both a fraction less than one and a whole number that is greater than or equal to one). In the first method, you will learn to convert the mixed numbers into improper fractions (fractions that are in fraction form but equal to an amount in excess of one). Then, you will learn that there is a way to simplify these numbers by canceling in the numerator and denominator. Next, you will multiply the two fractions together and write either as an improper fraction, or convert back to a mixed number. In the event a problem involves multiplying a whole number and a mixed number, Professor Burger shows you how to use the distributive property to solve it. Begin by writing the mixed number as a sum, and then distribute the whole number to both parts of the sum. Simplify and multiply the numbers to find your answer.

  Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Pre Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/prealgebra. The full course covers whole numbers, integers, fractions and decimals, variables, expressions, equations and a variety of other pre algebra topics.

  Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

  He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".

  Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

  Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

• Pre-Algebra: Quotient Properties of Exponents

  In this lesson, Professor Burger teaches us about the quotient properties of exponents. Exponential properties dictate that a^m/a^n = a^(m-n). Basically, if the bases of two exponential expressions are the same, we can simply subtract the exponent of the denominator from the exponent of the numerator to write the result of dividing one of these expressions by the other. In this lesson, Professor Burger shows you several examples to make sure you are comfortable subtracting exponents in equations that involve exponents, both positive and negative, in fractions.

  Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Pre Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/prealgebra. The full course covers whole numbers, integers, fractions and decimals, variables, expressions, equations and a variety of other pre algebra topics.

  Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

  He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".

  Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

  Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

• Pre-Algebra: Equations with Variables on 2 Sides

  Equations get a little more complicated when there are variables on both sides, but in this lesson, Professor Burger shows us that the process remains the same. Start by simplifying the equation and combining like terms. When there are variables on both sides of the equation, simplify each side, and then isolate the like variables to one side of the equation. Once the variable term is isolated, solve the equation. Professor Burger demonstrates this process with two examples, including one that involved fractions and thus requires finding the Least Common Denominator.

  Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Pre Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/prealgebra. The full course covers whole numbers, integers, fractions and decimals, variables, expressions, equations and a variety of other pre algebra topics.

  Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

  He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".

  Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

  Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

• Pre-Algebra: Fraction & Mixed Number Arithmetic

  Adding or subtracting fractions or mixed numbers can become tricky if the denomintators are not the same. Professor Burger shows us how to find common denominators by finding common multiples of the denominators. First, he shows us that we can use the product of the two denominators as a common denominator. To do this, we must also multiply the numerators by the same numbers by which we are multiplying the denominators. (Effectively, we will be multiplying each fraction by X/X, which is equal to one, in which X is equal to a common multiple of both denominators). Then, we will rewrite both fractions with the common denominators and add them together, simplifying if needed. This process can also be done by finding the Least Common Multiple or Least Common Denominator (LCD), which is the least common multiple of the two denominators. By using the LCD, you will often have less work to do simplifying your answer once the math operation is performed.

  Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Pre Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/prealgebra. The full course covers whole numbers, integers, fractions and decimals, variables, expressions, equations and a variety of other pre algebra topics.

  Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

  He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".

  Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

  Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

• Pre-Algebra: Prime Factorization

  In this lesson, Professor Burger introduces Prime numbers and prime factorization. A Prime number is any whole number greater than one whose only factors are one and itself, for example, 2 and 5. All whole numbers greater than one are either prime, or can be broken down into prime factors. Prime factorization is a way to represent a number as the product of its factors (thus, the prime factorization of 9 would be 3*3 given that the number 3 is prime and the product of 3 and 3 is 9). Professor Burger shows you two simple, visual ways to find a number's prime factorization: a factor tree and a ladder diagram. The factor tree pulls the numbers out, creating a diagram that looks like a family tree. The ladder diagram starts with dividing the number by prime factors until you get to 1, creating a stair-step diagram as you go.

  Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Pre Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/prealgebra. The full course covers whole numbers, integers, fractions and decimals, variables, expressions, equations and a variety of other pre algebra topics.

  Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

  He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".

  Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

  Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

• Pre-Algebra: Finding an Unknown in a Proportion

  A proportion states that 2 ratios are equivalent. To solve an equation involving proportions, Professor Burger shows you a method called the Cross-Product method (or cross-multiplication). Cross multiplication is simply the application of the Cross-Product method. A cross-product is found by multiplying along the diagonals of a proportion. Once you have an equation that no longer involves fractions, you can solve for the variable. For instance, when you get an equation like x/2 = 32/x, you can use cross-multiplication to turn the equation into x^2 = 64. From here, the equation will be much simpler to solve for x.

  Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Pre Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/prealgebra. The full course covers whole numbers, integers, fractions and decimals, variables, expressions, equations and a variety of other pre algebra topics.

  Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

  He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".

  Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

  Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

• Pre-Algebra: Simplifying with Negative Exponents

  In this lesson, Professor Burger explains what to do when you have a negative exponent. When there is a negative exponent, the expression will need to be set up as a reciprocal in order to evaluate and simplify the expression. A term with a negative exponent is equal to the reciprocal of the same term with a positive exponent. Thus, x^(-2) = 1/(x^2). Professor Burger explains examples of how to do this with negative integers, subtracting terms, and using variables.

  Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Pre Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/prealgebra. The full course covers whole numbers, integers, fractions and decimals, variables, expressions, equations and a variety of other pre algebra topics.

  Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

  He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".

  Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

  Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

• Pre-Algebra: Finding a Percent of a Number

  In this lesson, Professor Burger introduces percentages. He begins by reminding us that a percent is read "5 percent of 20," and the word "of" indicates multiplication. To multiply, we will need to convert the percent into a fraction or a decimal. He does examples using both methods. To convert a percentage to a fraction, you set the percentage over 100 and continue multiplying. To convert the percentage to a decimal, you will move the decimal point over two places to the left, and then continue multiplying. You can check your work by doing the problem both ways. Thus, our example, "5 percent of 20," can be written as 5/100*20 or .05*20.

  Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Pre Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/prealgebra. The full course covers whole numbers, integers, fractions and decimals, variables, expressions, equations and a variety of other pre algebra topics.

  Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

  He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".

  Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

  Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

• Pre-Algebra: Simplifying Fractions

  Once you have learned how to find the Greatest Common Factor (GCF) of a set of numbers, you can simplify fractions by factoring the numerator and denominator until they are relatively prime. Numbers are relatively prime when they have no common factors, other than 1. To do this, you will need to find the GCF for the numerator and denomentator, and then divide them both by this factor. This will effectively simplify the fraction to its most simplified form.

  Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Pre Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/prealgebra. The full course covers whole numbers, integers, fractions and decimals, variables, expressions, equations and a variety of other pre algebra topics.

  Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

  He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".

  Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions. Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

• Pre-Algebra: Dividing Decimals (Long Division)

  Numbers with decimals can be divided using long division, and Professor Burger shows you how in this lesson. You will first set up the problem, moving the decimal point in the divisor to the right or left until the number no longer has a decimal. You will then move the decimal in the number being divided the same number of places to the right or left. Then, you will begin the process of long division. Make sure that you transfer the decimal into the correct place in the quotient, and that the quotient has the correct sign.

  Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Pre Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/prealgebra. The full course covers whole numbers, integers, fractions and decimals, variables, expressions, equations and a variety of other pre algebra topics.

  Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

  He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".

  Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

  Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.