Elementary Algebra Unit I

Multiplying and Dividing Fractions

• Multiply fractions directly across; no need for common denominators.
• Dividing fractions involves multiplying by the reciprocal of the second fraction.

Adding and Subtracting Fractions

• Addition and subtraction require common denominators, referred to as "Like Terms."

Exponents

• Exponents serve as shorthand for repeated multiplication of a number.

Order of Operations

• Follow PEMDAS: Parentheses, Exponents, Multiply/Divide, Addition/Subtraction.

Variables

• Variables, such as "x" and "y," act as placeholders for unknown values.

Algebraic Expression

• Composed of numbers and variables combined with addition or subtraction; for example, x + 3.

Evaluating Expressions

• Involves substituting values for variables and simplifying.

Terminology for Operations

• Addition: Add, Sum, Plus, More than, Increase.
• Subtraction: Subtract, Difference, Minus, Take away, Decrease.
• Multiplication: Multiply, Product, Times, Doubled, Tripled.
• Division: Divide, Quotient, Split, Halved.

Types of Numbers

• Real Numbers: Include all rational and irrational numbers.
• Rational Numbers: Can be expressed as a fraction.
• Irrational Numbers: Cannot be expressed as a fraction of two integers.
• Natural Numbers: Counting numbers; starts at 1.
• Whole Numbers: Natural numbers including zero.
• Integers: Includes natural numbers, whole numbers, and their negative counterparts.

Properties in Algebra

• Distributive Property: Allows multiplication over addition or subtraction.
• Identity Property of Addition: Adding zero to a number keeps it unchanged.
• Identity Property of Multiplication: Multiplying by one keeps the number unchanged.
• Multiplication Property of Zero: Any number multiplied by zero results in zero.
• Multiplication Property of -1: Multiplying by -1 changes a number's sign.
• Inverse Property of Addition: A number plus its opposite equals zero.
• Inverse Property of Multiplication: A number times its reciprocal equals one.

Commutative and Associative Properties

• Commutative Property of Addition: Order of addition does not affect the sum.
• Commutative Property of Multiplication: Order of multiplication does not affect the product.
• Associative Property of Addition: Changing grouping of terms does not affect the sum.
• Associative Property of Multiplication: Changing grouping of factors does not affect the product.

Terms and Components of Expressions

• Terms: Include numbers, variables, or products of numbers and variables.
• Coefficients: Terms that include variables, representing the factor of those variables.
• Constant: Terms without variables, such as integers.
• Like Terms: Expressions that have the same variables raised to the same powers.

Test your knowledge of basic fraction operations with this flashcard quiz on Elementary Algebra Unit I. Topics include multiplying, dividing, adding, and subtracting fractions with a focus on the necessary conditions for each operation. Perfect for students looking to reinforce their understanding of fractions.