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Math Review of Equivalent Sentences 150 150 Deborah

Math Review of Equivalent Sentences

  Overview: Solving equations in algebra depends on using equivalent sentences until the solution is found.  Sentences are equivalent if they have the same solution.  For example, sentences such as x +3 = 8 and 2x = 10 are equivalent because in both of them x = 5. How to Use Equivalent Sentences When solving…

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Identity and Equality Properties in Algebra 150 150 Deborah

Identity and Equality Properties in Algebra

Overview: Identity and equality properties in mathematics are some of the keys to solving algebraic equations.  Those properties allow operations to be performed with numbers and variables.  Some of them may have been learned in lower grades, without symbols to represent them. What Are Some Identity Properties? Zero in addition has a special property.  Any…

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Addition and Subtraction of Radicals 150 150 Deborah

Addition and Subtraction of Radicals

Overview: Addition and subtraction of radicals is similar to addition and subtraction of polynomials.  First, like terms must be identified.  Some expressions may have to be simplified before they are in like terms.  Then, they are added or subtracted as needed. What Are Like Terms for Radicals? Monomials such as 5ab and 3ab can be…

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Using Formulas to Solve Math Problems 150 150 Deborah

Using Formulas to Solve Math Problems

  Overview: Some relationships between variables can be solved for in terms of common formulas.  For example, the formula for the circumference of a circle is C=πd.  This equation shows the relationship between the circumference of a circle and the diameter of the circle. What Is a Formula? A formula is an equation or inequality…

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Multiplication and Division of Radicals 150 150 Deborah

Multiplication and Division of Radicals

Overview: Multiplication and division of radicals use the same properties as other types of multiplication.  It is much easier to simplify expressions before they are used in an expression.  Also, the result needs to be checked carefully to make sure the expression is in its simplest form. Factoring a Radical Multiplying a radical is defined…

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Math Review of Simplifying Radicals 150 150 Deborah

Math Review of Simplifying Radicals

Overview: Before many operations can be performed with expressions involving radicals, the radicals must be simplified.  This ensures that they are factored so that there are no perfect square factors under the radical sign.  Approximations of the nonnegative square root can then be calculated. How Are Radicals Factored? The process of factoring radicals is similar…

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Chemistry Review of Solids 150 150 Deborah

Chemistry Review of Solids

Overview: The solid state of matter is one of the three states of matter, along with liquids and solids.  In the solid state of matter, particles are in fixed positions, compared to their movement in liquids or gases.  Solids can be crystalline or amorphous, depending on the structure that molecules form.  Various types of bonds…

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Chemistry Review of Liquids 150 150 Deborah

Chemistry Review of Liquids

Overview: The liquid state is one of the three states of matter, between the gaseous state and the solid state.  Molecules still move freely, although the density is higher than in the gaseous state.  Many substances occur in the liquid state at room temperature. How Does the Kinetic-Molecular Theory Account for Liquids? The particles in…

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Chemistry Review of Gases 150 150 Deborah

Chemistry Review of Gases

  Overview: As one of the three states of matter, gases have chemical and physical properties of their own. The particles that make up gases are the most diffuse and are able to move freely.  Some gases are made up of compounds and mixtures of different kinds of molecules, while a few, the noble or…

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Math Review: Fractions to Decimals 150 150 Deborah

Math Review: Fractions to Decimals

Overview: Simple fractions and mixed numbers are often turned into equivalent decimals for ease of operations in addition, subtraction, multiplication, and division.  They are easier to use on a calculator or with a computer, they are always in the same terms, so it is easier to compare them.  When they are translated into decimals, some…

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