Whole Numbers Operations
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Questions and Answers

Which operation guarantees that the result will always be an integer when applied to any two integers?

  • Subtraction
  • Multiplication
  • Addition
  • All of the above (correct)

    • What is the result of -6 - (-8)?

  • -14
  • -2
  • 2 (correct)
  • 14

    • If a is an integer and b is an integer, what can be concluded about the expression a x b?

  • It can only be positive.
  • It can be a non-integer.
  • It is guaranteed to be an integer. (correct)
  • It is guaranteed to be zero.

    • Which of the following does not yield an integer result when performed on integers?

    <p>None of the above</p> Signup and view all the answers

    What is the outcome of -7 + (-5)?

    <p>-12</p> Signup and view all the answers

    Which operation is commutative for whole numbers?

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

    Which of the following statements is true regarding the commutative property?

    <p>Multiplication is commutative.</p> Signup and view all the answers

    What is the outcome when applying the commutative property to addition of whole numbers?

    <p>The sum remains unchanged regardless of the order.</p> Signup and view all the answers

    For which operation is the following statement true: 'Changing the order of numbers does not change the result'?

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

    Which of these illustrates that division is not commutative?

    <p>8 / 4 = 2 and 4 / 8 = 0.5</p> Signup and view all the answers

    Which operation demonstrates closure under the operation of whole numbers?

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

    What is the result of subtracting two whole numbers if one is larger than the other?

    <p>An integer</p> Signup and view all the answers

    If a and b are whole numbers, what can be inferred about the expression a / b?

    <p>It is never a whole number.</p> Signup and view all the answers

    What is the product of two whole numbers always regarded as?

    <p>An integer</p> Signup and view all the answers

    Which of the following operations is NOT closed with respect to whole numbers?

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

    Which of the following statements is true about the closure property of rational numbers?

    <p>Rational numbers are closed under addition, subtraction, and multiplication.</p> Signup and view all the answers

    What is the result of the operation $2/7 - 3/5$ as expressed by the division of rational numbers?

    <p>The result is $6/35$.</p> Signup and view all the answers

    Which of the following combinations results in a rational number when multiplied?

    <p>1/2 and 1/4.</p> Signup and view all the answers

    What is the outcome of $1 + 3$ in relation to rational numbers?

    <p>It is equal to $4$, which is a rational number.</p> Signup and view all the answers

    How does the operation $12 - 3$ demonstrate the properties of rational numbers?

    <p>It results in $9$, showing closure under subtraction.</p> Signup and view all the answers

    What is the result of $rac{4}{7} - rac{5}{7}$ expressed in simplest form?

    <p>$rac{-1}{7}$</p> Signup and view all the answers

    Which operation is described as not commutative in the context of rational numbers?

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

    What is the result of $rac{8}{6} imes rac{6}{4}$ in simplest form?

    <p>$rac{19}{12}$</p> Signup and view all the answers

    Which of the following multiplications produces the smallest value?

    <p>$rac{9}{7} imes rac{0}{1}$</p> Signup and view all the answers

    What simplified result follows from the addition $rac{2}{5} + rac{3}{5}$?

    <p>$1$</p> Signup and view all the answers

    Which operation is considered associative?

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

    Which expression demonstrates the non-associativity of subtraction?

    <p>(7 - 6) - 5</p> Signup and view all the answers

    What is the result of the expression (8 ÷ 2) ÷ 2?

    <p>2</p> Signup and view all the answers

    Which of the following operations is not associative?

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

    Which expression illustrates the associative property of multiplication?

    <p>4 x (3 x 7)</p> Signup and view all the answers

    Which of the following statements regarding addition of integers is true?

    <p>Addition of integers is commutative.</p> Signup and view all the answers

    Which of the following expressions demonstrates the non-commutative property of subtraction?

    <p>2 - 3 ≠ 3 - 2</p> Signup and view all the answers

    Which of the following statements about multiplication of integers is correct?

    <p>Multiplying any integer by zero results in zero.</p> Signup and view all the answers

    Which of the following is true about the division of integers?

    <p>Dividing a positive integer by a negative integer results in a negative number.</p> Signup and view all the answers

    Which operation among the following is not commutative?

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

    Which of the following statements about addition and subtraction of rational numbers is correct?

    <p>Addition can produce a non-integer result.</p> Signup and view all the answers

    What is the result of the addition operation (5 + 17) + (14/4) when calculated stepwise?

    <p>5 + 17 + 3.5</p> Signup and view all the answers

    Which of the following operations demonstrates that subtraction is not associative?

    <p>(5 - 17) - 14/4</p> Signup and view all the answers

    When adding 21/5 and 35/15, what is the first step to ensure correct addition?

    <p>Convert both fractions to a common denominator.</p> Signup and view all the answers

    In the expression 3/6 + (12 + 28/3) / 5, what must be evaluated first according to the order of operations?

    <p>Evaluate 12 + 28/3 first.</p> Signup and view all the answers

    Which operation does not exhibit the associative property?

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

    What is the result of applying the operation 9 ÷ (-3 + 6)?

    <p>3</p> Signup and view all the answers

    What is the result of the subtraction operation (-6 - (4 - (3)))?

    <p>-13</p> Signup and view all the answers

    Which statement about multiplication is true?

    <p>It is associative regardless of the integers' signs.</p> Signup and view all the answers

    What can be inferred about the statement (4 x -7) x 2 = 28 x 2?

    <p>It demonstrates the associative property of multiplication.</p> Signup and view all the answers

    What is the result of the expression $(1/4 - 2/3)/1/4$?

    <p>-5/3</p> Signup and view all the answers

    Which of the following represents a correct evaluation of the expression $(1/4 - 3/2) / 1/4$?

    <p>-5</p> Signup and view all the answers

    Which expression demonstrates that division is not associative?

    <p>1/2 - (2/3 - 1/4)</p> Signup and view all the answers

    Evaluate the expression $(1/2 + x/3) x 4/7$. What does it equate to?

    <p>4/7 + 4x/21</p> Signup and view all the answers

    What is the simplified form of the expression $2/7 / (1/4)$?

    <p>8/7</p> Signup and view all the answers

    Study Notes

    Whole Numbers

    • Whole numbers include 0 and positive integers.
    • Closed under addition: a + b is a whole number for any whole numbers a and b.
    • Not closed under subtraction: 5 - 7 = -2 is not a whole number.
    • Closed under multiplication: ab is a whole number for any whole numbers a and b.
    • Not closed under division: 5/8 is not a whole number.

    Integers

    • Integers include positive and negative whole numbers, as well as zero.
    • Closed under addition: a + b is an integer for any integers a and b.
    • Closed under subtraction: a - b is an integer for any integers a and b.
    • Closed under multiplication: ab is an integer for any integers a and b.

    Rational Numbers

    • Rational numbers include any number expressible as a fraction where numerator and denominator are integers.
    • Closed under addition: the sum of any two rational numbers is a rational number.
    • Closed under subtraction: the difference of any two rational numbers is a rational number.
    • Closed under multiplication: the product of any two rational numbers is a rational number.
    • Not closed under division: caution with zero in the denominator.

    Commutative Property

    • Applies to addition and multiplication within whole numbers and integers.
    • Commutative in whole number addition: 5 + 9 = 14 and 9 + 5 = 14.
    • Not commutative for subtraction: a - b ≠ b - a.
    • Commutative in multiplication: 4 x 9 = 36 and 9 x 4 = 36.
    • Not commutative for division: 9 ÷ 3 ≠ 3 ÷ 9.

    Associative Property

    • Addition of whole numbers is associative: (a + b) + c = a + (b + c).
    • Subtraction is not associative; changing grouping alters the result.
    • Multiplication of whole numbers is associative: (a x b) x c = a x (b x c).
    • Division is not associative; altering grouping can lead to different results.

    Summary of Arithmetic Operations

    • Addition: Always commutative and associative across whole numbers, integers, and rational numbers.
    • Subtraction: Not commutative or associative for any number category.
    • Multiplication: Always commutative and associative across whole numbers, integers, and rational numbers.
    • Division: Not commutative or associative in any number category.

    Operations with Rational Numbers

    • Addition and multiplication of rational numbers maintain their property of closure.
    • Detailed examples demonstrate the addition and multiplication processes.
    • Subtraction and division examples illustrate the properties and results of rational numbers.

    General Insights

    • Numbers can be categorized into whole numbers, integers, and rational numbers.
    • Each number type has specific closure properties and operational characteristics.
    • Understanding the commutative and associative properties aids in simplifying calculations and developing mathematical reasoning.

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    Quiz Team

    Description

    Understanding properties of whole numbers under basic arithmetic operations like addition, subtraction, and multiplication. Learn about closure properties of whole numbers.

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