Algebra Basics Flashcards

Algebra Basics

• Algebra simplifies mathematical problems by using symbols instead of numbers.
• The term "algebra" originates from the Persian word "Aljabr."

Variables and Equations

• Literal numbers and variables are represented by letters that replace unknown quantities.
• An equation is a mathematical statement asserting the equality of two quantities.
• A solution to an equation is the value or values that make the equation true.
• To isolate a variable within an equation, apply inverse operations evenly on both sides.

Signed Numbers

• Directed numbers have positive or negative signs.
• Absolute value is the non-directed magnitude of a number.
• Adding signed numbers:
  • If both signs are the same, add absolute values and retain that sign.
  • If signs differ, subtract absolute values and take the sign of the larger value.
• Subtracting signed numbers involves changing the sign of the number being subtracted and applying the addition rules.
• Multiplying and dividing signed numbers:
  • Like signs yield a positive result.
  • Unlike signs yield a negative result.
• An even count of negative signs results in a positive product, while an odd count gives a negative product.

Algebraic Expressions and Terms

• An algebraic expression consists of numbers and variables linked through operators like addition and multiplication.
• Such expressions enable communication of concepts and simplification of ideas.
• A term is part of an expression formed solely by multiplication and division.
• Operations of addition and subtraction separate terms and create multi-term expressions.

Types of Expressions

• A monomial has one term.
• A binomial consists of two terms, separated by plus or minus signs.
• A trinomial has three terms, also separated by adding or subtracting operators.
• A polynomial contains more than one term, encompassing monomials.

Combining Like Terms

• Similar or like terms are those sharing constant values or identical literal factors with the same powers.
• Only like terms can be combined when adding algebraic expressions.

Number Sets

• An empty set contains no elements.
• Rational numbers are fractions with integer numerators and denominators, except when the denominator is zero.
• Natural numbers are the counting numbers from 1 to 9, excluding zero.
• The roster method entails listing all elements of a set within brackets.
• A set is a well-defined collection of distinct objects, often numbers, that share a common property.
• Set builder notation is another way to define a set, often summarizing its properties.