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Math Fundamentals

Math Review of Applications of Percents

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Overview Percents are based on the decimal system and have many useful applications in business, sales, and finance. Other applications of percents include percent increase and decrease. Estimating Percentages Many of the most useful applications of percents involve estimating and calculating percentages for sales tax and tips at a restaurant. Suppose the sales tax is…

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Math Review of Percents

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Overview Percents are special types of ratios that compare the number to 100. Similar to any ratio, a percent can be expressed as a fraction. Since percents compare to 100, they can also be expressed in decimal form. Fractions to Percents Percent or the percent sign (%) means “per 100,” so 5% means the same…

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Math Review of Two-Step and Multi-Step Equations

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Overview Not all equations can be solved in one step. Many take several steps to solve, but the principles of solving one-step equations can be applied. Use the order of operations to simplify the equation; math properties to combine like terms; then apply inverses to isolate the variable on one side of the equation in…

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Math Review of One-Step Equations

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Overview Some algebra equations can be solved with one step, using operations such as addition, subtraction, multiplication, and division. In order to solve them, use inverse operations so that the variable is on one side and real numbers are on the other side. Then, solve the problem with arithmetic. Balanced Equations An equation is solved…

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Math Review of Simplifying Expressions

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Overview Students can use the commutative, associative, and distributive properties of addition and multiplication to simplify algebraic expressions. Problems are more easily solved if compatible terms can be combined first. Some problems can then be solved mentally. Compatible Terms Real numbers, whether whole or mixed, are constants that can be added, subtracted, multiplied or divided.…

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Math Review of Operations with Real Numbers

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Overview Operations with real numbers are the most familiar types in mathematics. Those numerical expressions with constants and operations include such actions as addition, subtraction, multiplication, and division.   Many algebraic expressions are usually operations with real numbers. Real Numbers The set of real numbers include the entire set of rational numbers, such as positive and…

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Math Review of Variables and Expressions

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Overview The language of algebra is written in symbols, numerals, variables, constants, and expressions. In order to be successful in math, students should be able to translate its language into words and words into math language. Numerals and many symbols should already be familiar, as well as many operations with real numbers. Common Symbols and…

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Application of Binary Math to Computers

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Overview The binary (Base 2) system is based upon powers of 2. It has many applications to situations that have only two alternatives, such as off and on, 0 and 1, yes and no. Electronics, computers, and computer-based hardware such as cell phones and satellites use the binary system. Switching The binary system was adapted…

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Review of Mathematical Patterns in Art, Music, and Dance

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Overview Mathematical patterns underlie everything in the natural world, including those human extensions of the natural world that surround us. Some of those mathematical patterns are expressed in the arts, including visual arts such as painting and sculpture, and the physics and mathematics of music. Other mathematical patterns are expressed in performance arts, such as…

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Review of Mathematical Patterns and Archaeology

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Overview Mathematical patterns underlie human activity, as far back as we can discover ancient artifacts. Architectural wonders such as the Parthenon, the Pyramids, and other ruins show that civilizations were able to apply geometric and mathematical relationships. Neolithic sites as far away as Newgrange, Stonehenge, and many others around the world, show an ancient grasp…

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