This topic covers various properties of arithmetic operations and integers. This series of seven lessons teaches various principles including how to find the reciprocal of a number, identity and inverse properties for multiplication and division and various properties of the arithmetic operations themselves, like commutativity.

The student will learn many important ideas with respect to arithmetic operations in the field of rational numbers.

### Finding the Reciprocal

This lesson shows the student how to find the reciprocal of a rational number. The topic teaches finding the reciprocal as solving a one-step linear equation, where the number we want to reciprocate times x equals one. Then, x is found and shown to be the reciprocal of the number.

### Identity Properties

This lesson teaches the student the identity properties of addition and multiplication. The student learns that adding zero to any number results in the sum being the original number. The student also learns that multiplying a number by one results in the product being the number.

### Inverse Properties

This lesson teaches the student the inverse properties of addition and multiplication. The student learns that adding the opposite of a number to itself results in zero. The student also learns that multiplying a number by the reciprocal results in a product of one.

### Distributive Property

This lesson introduces the idea of the distributive property. An array approach is used to show that a*(b+c) = a*b + a*c. The distributive property is shown in both numerical expressions and also with expressions that contain variables.

### Commutative Properties

This lesson explains the commutative property of addition and multiplication. The student sees examples of the commutative property at work.

### Associative Properties

This lesson explains the associative property of addition and multiplication.

### Simplify Using Properties

This lesson reviews the properties that the student has learned in this series.

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