Algebra Class: Expressions and Operations

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Questions and Answers

What is an algebraic expression?

  • A statement that two expressions are equal.
  • An equation with no variables.
  • A group of numbers and symbols that express an operation. (correct)
  • A single number.

What is a coefficient?

A number which multiplies a variable.

What is a constant?

A number with a value that is always the same.

What is a dependent variable?

<p>A variable whose value is determined by the value of the independent variable.</p> Signup and view all the answers

What is the definition of an expression?

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

What is an equivalent expression?

<p>The same number or equal to one another.</p> Signup and view all the answers

What does it mean to evaluate an expression?

<p>To replace an expression with a number and then solve it.</p> Signup and view all the answers

What is an exponent?

<p>A number that tells how many equal factors there are.</p> Signup and view all the answers

What is a formula in mathematics?

<p>A set of numbers that express a mathematical rule.</p> Signup and view all the answers

What is an independent variable?

<p>A variable whose value determines that of a dependent variable.</p> Signup and view all the answers

What is an inequality?

<p>A mathematical sentence that compares two unequal expressions.</p> Signup and view all the answers

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Study Notes

Algebraic Expressions

  • Algebraic expressions consist of numbers, symbols, and variables representing one or more operations.
  • Example: In the expression 7x + 8, both the variable x and the number 8 are part of the expression.

Coefficient

  • A coefficient is a numerical factor that multiplies a variable within an expression.
  • In the expression 7x + 8, the coefficient is 7.

Constant

  • A constant is a specific numerical value that remains unchanged.
  • In the expression 7x + 8, the constant term is 8.

Dependent Variable

  • The dependent variable in a function is determined by the value of the independent variable.
  • Its value changes in response to modifications of the independent variable.

Expression

  • An expression signifies that two mathematical quantities or operations are equivalent.
  • Example: 3 * 5 = 7 + 8 demonstrates that both sides yield the same value.

Equivalent Expression

  • Equivalent expressions yield the same result or value despite having different appearances.
  • Example: Both 4 * 4 and 9 + 7 equal 16.

Evaluate

  • Evaluating an expression involves substituting variables with numbers and performing the operations to simplify.
  • For instance, replacing 'a' in 4 + a when a = 2 results in 4 + 2 = 6.

Exponent

  • An exponent indicates how many times a number (the base) is multiplied by itself.
  • For example, in ( x^3 ), the exponent is 3, denoting ( x \times x \times x ).

Formula

  • A formula is a mathematical statement or equation that expresses a rule or relationship between variables.
  • An example is the area of a rectangle, represented by A = l * w, where l is the length and w is the width.

Independent Variable

  • The independent variable is the input value in a function that influences the dependent variable's output.
  • It is the variable that stands alone and isn't affected by other variables in the equation.

Inequality

  • An inequality is a mathematical statement that compares two non-equal expressions using symbols, such as >, <, or ≠.
  • Inequalities demonstrate relational differences between quantities.

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