Math 71

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This lesson explores the concept of absolute value, defined as the distance from zero on the number line. We delve into basic arithmetic operations involving real numbers, including addition, subtraction, multiplication, and their properties. Learn how to handle operations with similar and opposite signs, and understand the role of additive inverses. This foundational knowledge is essential for simplifying algebraic expressions and solving mathematical problems effectively.

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Jun 08, 2026

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Math 71

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Math 71 1.2 – Operations with Real Numbers and Simplifying Algebraic Expressions
Absolute Value There are two ways to define absolute value: 1. means the distance from 0 to on the number line. ex: 2. ex:
Absolute Value There are two ways to define absolute value: 1. means the distance from 0 to on the number line. ex: 2. ex:
Absolute Value There are two ways to define absolute value: 1. means the distance from 0 to on the number line. ex: 2. ex:
Absolute Value There are two ways to define absolute value: 1. means the distance from 0 to on the number line. ex: 2. ex:
Absolute Value There are two ways to define absolute value: 1. means the distance from 0 to on the number line. ex: 2. ex:
Absolute Value There are two ways to define absolute value: 1. means the distance from 0 to on the number line. ex: 2. ex:
Addition When adding same signs, we ___________, and when adding opposite signs, we ________________. ex:
Addition add When adding same signs, we ___________, and when adding opposite signs, we ________________. ex:
Addition add When adding same signs, we ___________, and when adding opposite signs, we ________________. ex: subtract
Addition add When adding same signs, we ___________, and when adding opposite signs, we ________________. ex: subtract Keep common sign
Addition add When adding same signs, we ___________, and when adding opposite signs, we ________________. ex: subtract Keep sign of
Addition add When adding same signs, we ___________, and when adding opposite signs, we ________________. ex: subtract Keep sign of
Addition add When adding same signs, we ___________, and when adding opposite signs, we ________________. ex: subtract Keep sign of
Addition Properties 1. and 2. and Note: and are called ________________________. ex: The additive inverse of is _______________. The additive inverse of is _______________. ex: Find if .
Addition Properties 1. and 2. and Note: and are called ________________________. ex: The additive inverse of is _______________. The additive inverse of is _______________. ex: Find if . additive inverses
Addition Properties 1. and 2. and Note: and are called ________________________. ex: The additive inverse of is _______________. The additive inverse of is _______________. ex: Find if . additive inverses
Addition Properties 1. and 2. and Note: and are called ________________________. ex: The additive inverse of is _______________. The additive inverse of is _______________. ex: Find if . additive inverses
Addition Properties 1. and 2. and Note: and are called ________________________. ex: The additive inverse of is _______________. The additive inverse of is _______________. ex: Find if . additive inverses
Addition Properties 1. and 2. and Note: and are called ________________________. ex: The additive inverse of is _______________. The additive inverse of is _______________. ex: Find if . additive inverses
Subtracting We can define subtraction in terms of addition: ex:
Subtracting We can define subtraction in terms of addition: ex:
Subtracting We can define subtraction in terms of addition: ex:
Subtracting We can define subtraction in terms of addition: ex:
Subtracting We can define subtraction in terms of addition: ex:
Subtracting We can define subtraction in terms of addition: ex:
Subtracting We can define subtraction in terms of addition: ex:
Subtracting We can define subtraction in terms of addition: ex:
Subtracting We can define subtraction in terms of addition: ex:
Multiplying When multiplying ___________signs, the result is _________________. When multiplying ___________ signs, the result is _________________. ex:
Multiplying When multiplying ___________signs, the result is _________________. When multiplying ___________ signs, the result is _________________. ex: same
Multiplying When multiplying ___________signs, the result is _________________. When multiplying ___________ signs, the result is _________________. ex: same positive
Multiplying When multiplying ___________signs, the result is _________________. When multiplying ___________ signs, the result is _________________. ex: same positive opposite
Multiplying When multiplying ___________signs, the result is _________________. When multiplying ___________ signs, the result is _________________. ex: same positive opposite negative
Multiplying When multiplying ___________signs, the result is _________________. When multiplying ___________ signs, the result is _________________. ex: same positive opposite negative
Multiplying When multiplying ___________signs, the result is _________________. When multiplying ___________ signs, the result is _________________. ex: same positive opposite negative
Multiplying When multiplying ___________signs, the result is _________________. When multiplying ___________ signs, the result is _________________. ex: same positive opposite negative
Multiplying When multiplying ___________signs, the result is _________________. When multiplying ___________ signs, the result is _________________. ex: same positive opposite negative
Multiplying When multiplying ___________signs, the result is _________________. When multiplying ___________ signs, the result is _________________. ex: same positive opposite negative
Multiplying When multiplying ___________signs, the result is _________________. When multiplying ___________ signs, the result is _________________. ex: same positive opposite negative
Multiplying When multiplying ___________signs, the result is _________________. When multiplying ___________ signs, the result is _________________. ex: same positive opposite negative
Multiplying When multiplying ___________signs, the result is _________________. When multiplying ___________ signs, the result is _________________. ex: same positive opposite negative
Multiplication Properties 1. ex: 2. ex:
Multiplication Properties 1. ex: 2. ex:
Multiplication Properties 1. ex: 2. ex:
Multiplication Properties 1. ex: 2. ex:
Multiplication Properties 1. ex: 2. ex:
Dividing We can define division in terms of multiplication: Note: and are ________________ of each other (also called _________________________) ex:
Dividing We can define division in terms of multiplication: Note: and are ________________ of each other (also called _________________________) ex: reciprocals
Dividing We can define division in terms of multiplication: Note: and are ________________ of each other (also called _________________________) ex: reciprocals multiplicative inverses