Algebra Basics Flashcards
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Questions and Answers

What is Algebra?

It is essentially a way to reduce a math problem down to a small set of symbols.

The term algebra is derived from the Persian ______________.

Aljabr

What is a literal number and a variable?

Both are a letter that stands for a number.

What is an equation?

<p>A mathematical statement that two quantities are equal.</p> Signup and view all the answers

What is the solution?

<p>It is the number or numbers which, when used as the value of a variable or variables, makes the statement true.</p> Signup and view all the answers

The variable must be ______________ on one side of the equation.

<p>isolated</p> Signup and view all the answers

How is a variable isolated in an equation?

<p>Apply any inverse operations to both sides of the equation until the variable is isolated.</p> Signup and view all the answers

What is a directed or signed number?

<p>A number that has negative or positive sign.</p> Signup and view all the answers

What is the absolute value of a number?

<p>It is the unsigned or undirected value of a number.</p> Signup and view all the answers

What are the rules of adding signed numbers and subtracting signed numbers?

<p>If adding, like signs add their absolute values and use the common sign. If opposite signs, subtract absolute values and keep the sign of the largest.</p> Signup and view all the answers

What are the rules of multiplying and dividing signed numbers?

<p>With like signs, the result is positive; with unlike signs, the result is negative.</p> Signup and view all the answers

When dealing with negative numbers, what is an easy way to determine the sign of the product?

<p>An even number of minus signs multiplied will result in a positive product while an odd number will yield a negative product.</p> Signup and view all the answers

What is an algebraic expression?

<p>A collection of numbers and variables separated by normal operators; addition, subtraction, multiplication, and division.</p> Signup and view all the answers

What do algebraic expressions allow us to do?

<p>They allow us to communicate ideas and generalize (simplify) big ideas.</p> Signup and view all the answers

What is a term?

<p>An algebraic expression connected only by the operations of multiplication and division.</p> Signup and view all the answers

Since terms are formed using only multiplication and division, plus and minus signs _____________ terms and make expressions with more than one term.

<p>separate</p> Signup and view all the answers

What is a monomial?

<p>An algebraic expression with only one term.</p> Signup and view all the answers

What is a binomial?

<p>An algebraic expression with only two terms separated by plus or minus signs.</p> Signup and view all the answers

What is a trinomial?

<p>An algebraic expression with only three terms separated by plus or minus signs.</p> Signup and view all the answers

What is a polynomial?

<p>Any algebraic expression with more than one term (monomial).</p> Signup and view all the answers

What are similar or like terms?

<p>Terms that are similar or like because they are both constant terms or they have the same literal factors raised to the same powers.</p> Signup and view all the answers

When adding algebraic expressions, only ____ terms can be combined.

<p>like or similar.</p> Signup and view all the answers

What is an empty set?

Signup and view all the answers

What are rational numbers?

<p>Fractions where the numerator and denominator are integers as long as the bottom integer (divisor) is not 0.</p> Signup and view all the answers

What are natural numbers?

<p>1 through 9, excluding 0.</p> Signup and view all the answers

What is the roster method?

<p>The method of writing a set by listing its elements.</p> Signup and view all the answers

What is a set?

<p>An organized collection of objects, such as numbers.</p> Signup and view all the answers

What is set builder notation?

Signup and view all the answers

Study Notes

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.

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Description

This quiz explores fundamental concepts in algebra through flashcards. Test your knowledge on what algebra is, its origin, and key terms like literals, variables, and equations. Perfect for beginners looking to strengthen their understanding of algebraic principles.

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