BJU Pre-Algebra Chapter 1 Flashcards

Mathematical Concepts and Definitions

• Absolute value: Measures the distance of a number from zero on a number line; always non-negative.
• Additive inverse: For any number 'a', 'b' is its additive inverse if a + b = 0; represented as -a.
• Cubed: Refers to raising any expression to the third power.
• Exponent: A superscript showing how many times the base is multiplied by itself.
• Integers: Include all whole numbers and their negatives; extend infinitely in both directions.
• Opposites: Numbers located an equal distance from zero but in opposite directions; examples include 5 and -5.
• Scientific notation: Format that expresses numbers as a product of a number between 1 and 10 and a power of ten.
• Squared: Indicates a number or expression multiplied by itself, represented by an exponent of two.

Arithmetic Operations and Properties

• Subtraction: Can be viewed as adding an opposite; for instance, a - b is equivalent to a + (-b).
• Variable: A symbol (usually a letter) that represents an unknown quantity in expressions or equations.
• Zero power: States that any non-zero number raised to the power of zero results in 1.
• Addend: Any number involved in an addition operation; e.g., in 3 + 5, both 3 and 5 are addends.
• Minuend: The number from which another is subtracted in a subtraction operation.
• Subtrahend: The number being subtracted from the minuend in a subtraction operation.
• Dividend: The quantity being divided in a division operation.
• Divisor: The number by which another number (the dividend) is divided.
• Quotient: The result of a division operation.

Exponents and Their Properties

• Base: The number that is raised to a power in exponential form and also indicates place values in a numeral system.
• Negative exponent: If 'x' is a non-zero number and 'a' is an integer, then x^-a = 1/x^a, reflecting division.

Operations with Integers

• Adding integers with like signs: Sum the absolute values and apply the common sign for the result.
• Adding integers with unlike signs: Compute the difference in absolute values and adopt the sign of the number with the larger absolute value.

Properties of Exponents

• Multiplication Property of Exponents: States that when multiplying like bases, add their exponents: x^a * x^b = x^(a+b).
• Power Property of Exponents: When raising a power to another power, multiply the exponents: (x^a)^b = x^(ab).
• Division Property of Exponents: Describes how to handle division with exponents.

Order of Operations

• Order of Operations: A set sequence to solve mathematical expressions:
  • Evaluate grouping symbols first.
  • Compute all exponents.
  • Perform multiplication and division from left to right.
  • Conduct addition and subtraction from left to right.