Smarty Pants lessons
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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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A replacement set is a group of numbers that is substituted into an equation or expression to achieve a mathematically correct statement. In this lesson by Eric Buffington, learn how to write out replacement sets, solve equations using a predetermined series, and write out answers when more than one number is correct.

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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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Implicit differentiation can be tricky, so improve your understanding of the idea and work through an example equation with Krista King from IntegralCalc. Krista shows how to take the derivative of both sides of the equation, starting with the left. Then, learn to use the product and chain rule rules. Learn when you must multiply by dy/dx. Once you’ve simplified the equation and separated terms, you’ll be left with your final answer. With Krista’s help, implicit differentiation is simple!

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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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Learn to divide out derivatives with help from this video on evaluating difference quotients. This lesson from IntegralCALC’s Calculus I Essentials series teaches you how to use the definition of a derivative to find the value of a derivative at a particular point. See how to plug in values and functions, simplify your formula, and then cancel out variables and numbers to make solving a confusing equation easy.

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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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You've got a graph, but how do you know whether or not it represents a function? Use the vertical line test! This lesson from IntegralCALC's Calculus I Essentials series teaches you all about the vertical line test: if you draw a vertical line anywhere on the graph and it crosses more than two points, then the graph fails the test and is not a function. This handy mathematical trick even can apply to discontinuous graphs!

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Calculus can be frustrating if you don’t have a thorough grasp of the concepts. Build your confidence and improve your test scores with lessons from integralCALC! In this lesson, Krista discusses limits: learn how to solve for them, as well as three helpful shortcuts to help you find infinite limits. Stick around for the whole lesson and watch Krista demonstrate what to do in the event of a point discontinuity or a jump discontinuity. Calculus doesn’t have to be difficult—demystify limits!

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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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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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Take your math skills to the limit! The general limit exists only if the left-hand and right-hand limits exist, and the two are equal. This lesson from IntegralCALC's Calculus I Essentials series teaches you how to find the left-hand and right-hand limits (negative and positive limits), and then use those limits to prove that the general limit does not exist. Although this lesson uses a specific example, the technique shown here can be applied to finding or disproving the limit of any formula.

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Learn how to find the equation of a line that is tangent to a particular function! In this example from IntegralCalc, Krista shows you how to begin plugging in known variables. Then, Krista demonstrates how to simplify the equation once you’ve got your formulas and variables figured out, and eliminate the variable in the denominator of the equation. Next, learn how simplify to find the slope, and the point on the line. With the slope and a point, finding the final answer couldn’t be simpler!

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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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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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Lost in the world of calculus? Start at the beginning with integralCALC’s online tutorials. The first in a series, this lesson introduces the idea of functions - number ‘machines’ that describe a relationship between two or more variables (like ‘x’ and ‘y'). Learn how functions differ from equations, what it means to find a function’s domain and range, and how to use the vertical line test to check a function’s validity.

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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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Know your limits! But what is a limit in mathematical terms? This lesson from IntegralCALC's Calculus I Essentials series introduces you to the precise definition (or epsilon delta definition) of a limit. The introductory video explains the definition in detail, and then walks you through the step-by-step process of using that definition to prove a limit is true.

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One of the most universally frustrating parts about math is working with negative numbers. Join Eric Buffington to learn the ins and outs of adding integers. This lesson includes examples with adding negatives, variables, replacement sets, inequalities, and absolute values. Once you've mastered adding negative numbers, check out Mr. Buffington's lessons on subtracting, multiplying and dividing negative numbers!

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