Elementary Algebra Unit I
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Questions and Answers

What is the process for multiplying fractions?

  • Reduce by multiplying across (correct)
  • Multiply by the reciprocal
  • Add the fractions
  • Use a common denominator

    • How do you divide fractions?

    Multiply by the reciprocal

    What is needed to add fractions?

    Like terms or a common denominator

    What is required to subtract fractions?

    <p>Like terms or a common denominator</p> Signup and view all the answers

    What do exponents represent?

    <p>Shorthand for repeated multiplication of the same number</p> Signup and view all the answers

    What does PEMDAS stand for?

    <p>Parentheses, Exponents, Multiply/Divide, Addition/Subtraction</p> Signup and view all the answers

    What is a variable?

    <p>A placeholder for an unknown value</p> Signup and view all the answers

    What is an algebraic expression?

    <p>A number/variable put together and separated by addition or subtraction symbols</p> Signup and view all the answers

    What does evaluating expressions involve?

    <p>Substituting and simplifying</p> Signup and view all the answers

    Which of the following are names for addition? (Select all that apply)

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

    Which of the following are names for subtraction? (Select all that apply)

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

    Which of the following are names for multiplication? (Select all that apply)

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

    Which of the following are names for division? (Select all that apply)

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

    What are real numbers?

    <p>All rational and irrational numbers</p> Signup and view all the answers

    What are rational numbers?

    <p>Any number that can be expressed as a fraction</p> Signup and view all the answers

    What are irrational numbers?

    <p>Any real number which can't be expressed as a fraction of two integers</p> Signup and view all the answers

    What are natural numbers?

    <p>Counting numbers (1, 2, 3, 4, 5, etc.)</p> Signup and view all the answers

    What are whole numbers?

    <p>Natural numbers and zero (0, 1, 2, 3, etc.)</p> Signup and view all the answers

    What are integers?

    <p>Natural and whole numbers including negatives (-3, -2, -1, 0, 1, 2, 3, etc.)</p> Signup and view all the answers

    What is the distributive property?

    <p>Not defined in the provided content.</p> Signup and view all the answers

    What is the identity property of addition?

    <p>Not defined in the provided content.</p> Signup and view all the answers

    What is the identity property of multiplication?

    <p>Not defined in the provided content.</p> Signup and view all the answers

    What is the multiplication property of zero?

    <p>Not defined in the provided content.</p> Signup and view all the answers

    What is the multiplication property of -1?

    <p>Any number multiplied by -1 is always its opposite</p> Signup and view all the answers

    What is the inverse property of addition?

    <p>Not defined in the provided content.</p> Signup and view all the answers

    What is the inverse property of multiplication?

    <p>Not defined in the provided content.</p> Signup and view all the answers

    What is the commutative property of addition?

    <p>When adding, changing the order does not change the sum</p> Signup and view all the answers

    What is the commutative property of multiplication?

    <p>When multiplying, changing the order does not change the product</p> Signup and view all the answers

    What are terms in an expression?

    <p>A number, a variable, or a product of numbers and variables</p> Signup and view all the answers

    What are coefficients?

    <p>A term with a variable</p> Signup and view all the answers

    What is a constant?

    <p>Terms without a variable (e.g., 2 or 45)</p> Signup and view all the answers

    What are like terms?

    <p>Expressions that contain the same variables to the same power</p> Signup and view all the answers

    Study Notes

    Multiplying and Dividing Fractions

    • Multiply fractions directly across; no need for common denominators.
    • Dividing fractions involves multiplying by the reciprocal of the second fraction.

    Adding and Subtracting Fractions

    • Addition and subtraction require common denominators, referred to as "Like Terms."

    Exponents

    • Exponents serve as shorthand for repeated multiplication of a number.

    Order of Operations

    • Follow PEMDAS: Parentheses, Exponents, Multiply/Divide, Addition/Subtraction.

    Variables

    • Variables, such as "x" and "y," act as placeholders for unknown values.

    Algebraic Expression

    • Composed of numbers and variables combined with addition or subtraction; for example, x + 3.

    Evaluating Expressions

    • Involves substituting values for variables and simplifying.

    Terminology for Operations

    • Addition: Add, Sum, Plus, More than, Increase.
    • Subtraction: Subtract, Difference, Minus, Take away, Decrease.
    • Multiplication: Multiply, Product, Times, Doubled, Tripled.
    • Division: Divide, Quotient, Split, Halved.

    Types of Numbers

    • Real Numbers: Include all rational and irrational numbers.
    • Rational Numbers: Can be expressed as a fraction.
    • Irrational Numbers: Cannot be expressed as a fraction of two integers.
    • Natural Numbers: Counting numbers; starts at 1.
    • Whole Numbers: Natural numbers including zero.
    • Integers: Includes natural numbers, whole numbers, and their negative counterparts.

    Properties in Algebra

    • Distributive Property: Allows multiplication over addition or subtraction.
    • Identity Property of Addition: Adding zero to a number keeps it unchanged.
    • Identity Property of Multiplication: Multiplying by one keeps the number unchanged.
    • Multiplication Property of Zero: Any number multiplied by zero results in zero.
    • Multiplication Property of -1: Multiplying by -1 changes a number's sign.
    • Inverse Property of Addition: A number plus its opposite equals zero.
    • Inverse Property of Multiplication: A number times its reciprocal equals one.

    Commutative and Associative Properties

    • Commutative Property of Addition: Order of addition does not affect the sum.
    • Commutative Property of Multiplication: Order of multiplication does not affect the product.
    • Associative Property of Addition: Changing grouping of terms does not affect the sum.
    • Associative Property of Multiplication: Changing grouping of factors does not affect the product.

    Terms and Components of Expressions

    • Terms: Include numbers, variables, or products of numbers and variables.
    • Coefficients: Terms that include variables, representing the factor of those variables.
    • Constant: Terms without variables, such as integers.
    • Like Terms: Expressions that have the same variables raised to the same powers.

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    Test your knowledge of basic fraction operations with this flashcard quiz on Elementary Algebra Unit I. Topics include multiplying, dividing, adding, and subtracting fractions with a focus on the necessary conditions for each operation. Perfect for students looking to reinforce their understanding of fractions.

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