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Everyone loves having choices in life. In this lesson, learn two methods for solving equivalent fractions with variables and choose the method you like best! After you pick your favorite method, Mr. Buffington provides a few practice problems so that you can cement your knowledge of this important skill.


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What happens if two suspects are taken in for questioning on suspicion of robbery? If everyone is looking out for their own interests, the results might surprise you! Follow along with William Spaniel as he explains this classic game theory scenario. Learn how to decide which outcomes are most likely and what it means for a person to have a ‘strategically dominant strategy’.

Continue with the rest of this series to understand how people behave in increasingly complicated scenarios.


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8 of 13

In part two of a three-part series, Eric Buffington breaks down several practice problems for adding and subtracting fractions and reviews reducing fractions to lowest terms. Whether you have never worked with fractions before or you want to brush up on old skills, this lesson has got you covered. Note: you’ll need to know how to reduce fractions to lowest terms and find the lowest common denominator.


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Have you ever struggled to know what gets done first in a math problem? This lesson outlines the correct order of operations, and many of the common challenges and mistakes people make when trying to solve math problems. Tackle your next math problem with the right strategy - and you'll have an easy time knowing when to add, subtract, multiply, and divide for the correct answer.


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Can war be mutually beneficial? Because the costs and benefits of war can be complex and dependent on the environment, you might think that a simple example couldn’t hold the answers to cost-benefit analyses used in real situations. Think again: this tutorial by William Spaniel provides a no-frills, theoretical example involving Colombia, Venezuela, and $80 billion worth of oil that confirms war inefficiency through simple mathematics.


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Do you know how to solve for outcomes in a two-player game, where there can only be one winner, and only one loser? In this lesson on mixed strategy Nash equilibrium from his series on game theory, William Spaniel explains how to solve a game with diametrically opposed interests (like soccer or football) when no pure strategy Nash equilibria exist.


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4 of 13

Never struggle with multiplying fractions again. In this quick and easy math lesson, Eric Buffington explains how to multiply several different kinds of fractions and get a simplified answer by reducing to lowest terms. You’ll also learn how to work with variables and negative fractions and cement your knowledge with several practice problems.


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9 of 13

You’ve already learned how to add and subtract fractions; but can you apply your skills to word problems? This lesson, the final part of a three-part series, breaks down three word problems that require you to find the least common multiple (LCM), add or subtract fractions, and reduce the answer to lowest terms. Each step is clearly explained and demonstrated so that you can solve similar questions on your own.


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13 of 13

In this lesson by Eric Buffington, learn how to solve algebraic equations that involve fractions. Whether you need to add, subtract, multiply, or divide, the process is just a combination of basic math skills. Get started with a few practice problems. As a bonus, you’ll learn about the property of equality and improve your understanding of equations.


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In the anarchic world of international relations, how can we predict and explain outcomes? In this lesson, William Spaniel applies game theory, a methodology created to study economic interdependence, to political science. With simple mathematical models, you too can turn assumptions into predictions of action in global politics.


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Keep your keys chained up with the threat of mutually assured destruction. Goofy scientist Myles Power shows off his radioactive keychain, and along the way explains how gaseous tritium, an isotope of hydrogen used to improve the explosive power of nuclear bombs, can serve as a light source through the power of radioluminscence. Warning: do not crack, swallow, or inhale!


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How can you win when playing Rock, Paper, Scissors? Not with a pure strategy, that’s for sure! This lesson from William Spaniel's Game Theory 101 series teaches you the theory behind this classic game. Do the math and check the payoffs to discover why you just can't beat randomness. Bummer, right? Learn about cycling arguments and why equal payoffs mean you can't easily pin down even a mixed strategy Nash equilibrium.


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The Sistine Chapel is one of the most famous pieces of art and architecture in the world, and in the center of Michelangelo’s enormous fresco is “The Creation of Adam,” a visual representation of the story of God creating Adam from the dust of the earth. Michelangelo’s portrayal of both Adam and God reflects the Neo-Platonic values of the time, but perhaps the most interesting interpretation of this painting is that of God’s vehicle being a brain, and the life he is giving Adam, consciousness.


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6 of 13

Want to compare, add, or subtract fractions? To complete any of these operations, you need to find a common denominator. In this quick and easy math lesson by Eric Buffington, learn how to find the least common multiple (LCM) and put two fractions on a level playing field. Finally, test your skills with several practice problems.


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7 of 13

Adding and Subtracting Fractions is the most difficult of the operations. In this lesson we go over, in a visual way, the basics of adding or subtracting fractions, then practice practice practice.


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You want to play golf, but your friend wants go surfing; you’d both rather be together than not. It is in your best interest to make the same decision, but you have a few options, and you have to decide without knowing your friend’s decision. Learn how to run a mixed strategy algorithm to determine if there is a mixed strategy equilibria. Once you can calculate the payoffs for a mixed strategy, you can make an educated decision and choose the option with the highest probability of success.


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5 of 13

You already know how to multiply fractions; what about division? In this basic math lesson, Mr. Buffington shows you a quick trick with reciprocals to help you divide fractions without a calculator. You’ll also work with negative fractions to practice your understanding of operators and their effect on a number’s positive or negative value.


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The conclusion set out in “War’s Inefficiency Puzzle” was that war is inefficient; this was proven using a theoretical example involving Colombia, Venezuela, and $80 billion worth of oil. However, what if we want a purer mathematical model with which to draw conclusions? This tutorial by William Spaniel demonstrates how to create an algebraic model of war, which reinforces the conclusion that war is inefficient.


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Learn to apply the Prisoner’s Dilemma strategy to a more complex game using a tactic called iterative elimination of strategically dominated strategies. In this lesson, William Spaniel will teach you how to identify scenarios that can be solved using this approach, and walk you through an example problem to get you on your way. Though not all games can be solved using this approach, it’s a good one to have in your game theory tool belt!


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