Sadlier-Oxford - Foundations of Algebra - Ch. 1
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Questions and Answers

What is a rational number?

  • A number that can be written in fractional form (correct)
  • A number that is always positive
  • A number that is an integer
  • A number that is not a fraction

    • Which of the following are natural numbers?

  • 2 (correct)
  • 0
  • Negative numbers
  • 1 (correct)

    • What are whole numbers?

    Set of natural numbers and zero.

    What are integers?

    <p>Set of whole numbers and their opposites.</p> Signup and view all the answers

    What is a terminating decimal?

    <p>A decimal whose digits end.</p> Signup and view all the answers

    What is a repeating decimal?

    <p>A decimal that has a digit or group of digits that repeat.</p> Signup and view all the answers

    What are opposites in terms of rational numbers?

    <p>Rational numbers that are additive inverses.</p> Signup and view all the answers

    What is absolute value?

    <p>The distance of a number from zero on a number line.</p> Signup and view all the answers

    What is the greatest common factor?

    <p>The largest number that is a common factor of all the numbers.</p> Signup and view all the answers

    What is prime factorization?

    <p>The process of writing a number as the product of prime numbers.</p> Signup and view all the answers

    What is the simplest form of a fraction?

    <p>A fraction in lowest terms.</p> Signup and view all the answers

    What does equivalent mean?

    <p>The same.</p> Signup and view all the answers

    What is the least common multiple?

    <p>The least nonzero multiple that is common to all of the numbers.</p> Signup and view all the answers

    What is the least common denominator?

    <p>The LCM of the denominators.</p> Signup and view all the answers

    What are algebraic fractions?

    <p>A fraction that has a variable in the numerator or denominator.</p> Signup and view all the answers

    What is the Cross-Products Rule?

    <p>The products obtained by multiplying the numerator of one fraction and the denominator of the other and vice versa. If the products are equal then the fractions are equal.</p> Signup and view all the answers

    What does the Distributive Property state?

    <p>2*(a+b) = 2<em>a + 2</em>b.</p> Signup and view all the answers

    What are complex fractions?

    <p>Fractions that have one or more fractions in the numerator or denominator.</p> Signup and view all the answers

    What is the Density Property of Rational Numbers?

    <p>An infinite number of rational numbers can be found between any two rational numbers.</p> Signup and view all the answers

    What is the Multiplicative Property of -1?

    <p>When a number or expression is multiplied by -1, the product is the opposite.</p> Signup and view all the answers

    What is exponential form?

    <p>A number written with a base and an exponent.</p> Signup and view all the answers

    What is a power in terms of numbers?

    <p>A number in exponential form or its equivalent standard form.</p> Signup and view all the answers

    What is the correct order of operations?

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

    Study Notes

    Rational Numbers

    • Defined as numbers that can be expressed in fractional form.

    Natural Numbers

    • Refers to the set of counting numbers, starting from 1 and increasing indefinitely.

    Whole Numbers

    • Comprises all natural numbers along with zero.

    Integers

    • Includes all whole numbers as well as their negative counterparts.

    Decimals

    • Terminating Decimal: A decimal number that has a finite number of digits.
    • Repeating Decimal: A decimal that features a digit or a sequence of digits that repeats infinitely.

    Opposites

    • Rational numbers that are additive inverses of each other (e.g., 5 and -5).

    Absolute Value

    • Measures the distance of a number from zero on the number line, always resulting in a non-negative value.

    Greatest Common Factor (GCF)

    • Identified as the largest number that evenly divides all numbers in a given set.

    Prime Factorization

    • Involves expressing a number as the product of its prime factors.

    Simplest Form

    • A fraction is in simplest form when it is expressed in its lowest terms.

    Equivalence

    • The term "equivalent" signifies equality in value or representation.

    Least Common Multiple (LCM)

    • The smallest non-zero multiple that two or more numbers share.

    Least Common Denominator (LCD)

    • Denotes the LCM of the denominators in a set of fractions.

    Algebraic Fractions

    • Defined as fractions that incorporate a variable in either the numerator or denominator.

    Cross-Products Rule

    • States that for two fractions, if the cross-products are equal, the fractions themselves are equal.

    Distributive Property

    • Mathematical principle stated as: ( a(b + c) = ab + ac ).

    Complex Fractions

    • A fraction that contains one or more fractions in its numerator or denominator.

    Density Property of Rational Numbers

    • Indicates that between any two rational numbers, an infinite number of rational numbers exists.

    Multiplicative Property of -1

    • If a number or expression is multiplied by -1, the outcome is the additive inverse (opposite) of that number or expression.

    Exponential Form

    • Representation of a number using a base and an exponent (e.g., ( a^n )).

    Power

    • Refers to a number presented in exponential form or its equivalent standard form.

    Order of Operations

    • Sequence of calculations:
      • Grouping Symbols
      • Exponents
      • Multiplication or Division (from left to right)
      • Addition or Subtraction (from left to right).

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    Description

    This quiz focuses on Chapter 1 of the Sadlier-Oxford Foundations of Algebra, covering key concepts related to rational numbers. You'll explore definitions of rational numbers, natural numbers, whole numbers, integers, and terminating decimals through flashcards. Test your understanding and strengthen your algebraic foundation.

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