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## Ordering Rational Numbers

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6.NS.7
Understand ordering and absolute value of rational numbers.

8.NS.1
Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

## Rational Numbers

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Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

Understand ordering and absolute value of rational numbers.

## Rational Numbers : Fraction and Decimal Conversions

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Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

## Polynomial Long and Synthetic Division and Rational Root and Factor Theorem

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Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).

## Simplifying, Adding and Subtracting Rational Expressions

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Interpret expressions that represent a quantity in terms of its context.

Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P.  Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

## Multiplying and Dividing Rational Expressions

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Interpret expressions that represent a quantity in terms of its context.

Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P.  Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

## Translating and Graphing Rational Functions

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Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

## Solving Rational Equations

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Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.  Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

## Graphing Rational Functions F(x) = a/x

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Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.  Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

## Modeling with Rational Functions

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Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.  Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.