Math Gr 8 Ch 2: Properties of Integers
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Math Gr 8 Ch 2: Properties of Integers

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Questions and Answers

What is a fundamental property of addition in integers?

  • The order of numbers changes the sum.
  • The order of numbers does not change the sum. (correct)
  • The grouping of numbers changes the sum.
  • Addition is only possible with positive integers.

    • Which of the following is a property of multiplication in integers?

  • Multiplication is only possible with positive integers.
  • The grouping of numbers changes the product.
  • The order of numbers changes the product.
  • The order of numbers does not change the product. (correct)

    • What is the result of adding zero to any integer?

  • The number remains the same. (correct)
  • The number increases by one.
  • The number decreases by one.
  • The number becomes negative.

    • What is the result of multiplying any integer by one?

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

    What is the additive inverse of an integer?

    <p>A number that when added results in zero.</p> Signup and view all the answers

    What is a consequence of the distributive property of multiplication over addition?

    <p>Multiplication distributes over addition.</p> Signup and view all the answers

    Which of the following is an example of the associative property of addition?

    <p>(2 + 3) + 4 = 2 + (3 + 4)</p> Signup and view all the answers

    What is a consequence of the commutative property of multiplication?

    <p>The order of numbers in multiplication does not affect the product.</p> Signup and view all the answers

    What is the additive inverse of 5?

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

    What is the result of subtracting a negative integer from a positive integer?

    <p>A positive difference</p> Signup and view all the answers

    What is the absolute value of -3?

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

    What is the result of multiplying two integers with different signs?

    <p>A negative product</p> Signup and view all the answers

    What is the result of adding a positive integer and a negative integer?

    <p>A sum that depends on the absolute values of the integers</p> Signup and view all the answers

    What is the property that states that multiplying a number by a sum of numbers is the same as multiplying each addend separately and then adding the products?

    <p>Distributive Property</p> Signup and view all the answers

    Which property of integers states that changing the order of the numbers does not change the sum?

    <p>Commutative Property</p> Signup and view all the answers

    What is the result of multiplying any integer by its additive inverse?

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

    Which property of integers allows us to regroup numbers when adding three or more integers?

    <p>Associative Property</p> Signup and view all the answers

    What happens when we add a positive integer and its additive inverse?

    <p>We get zero</p> Signup and view all the answers

    Which property of integers states that multiplying a number by a sum of numbers is the same as multiplying each addend separately and then adding the products?

    <p>Distributive Property</p> Signup and view all the answers

    What is the result of adding zero to any integer?

    <p>The original integer</p> Signup and view all the answers

    Which property of integers allows us to change the order of the numbers when multiplying?

    <p>Commutative Property</p> Signup and view all the answers

    What happens when we multiply any integer by one?

    <p>We get the original integer</p> Signup and view all the answers

    Which of the following is true about the product of three integers?

    <p>The product is positive if at least two integers have the same sign.</p> Signup and view all the answers

    What is the result of subtracting a positive integer from a negative integer?

    <p>A negative difference</p> Signup and view all the answers

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

    <p>The product of a positive and a negative integer is always negative.</p> Signup and view all the answers

    What is the relationship between the absolute value of an integer and its distance from zero on the number line?

    <p>The absolute value is equal to the distance from zero.</p> Signup and view all the answers

    Which of the following is an example of the distributive property of multiplication over addition?

    <p>2 × (3 + 4) = 2 × 3 + 2 × 4</p> Signup and view all the answers

    What is the result of adding a positive integer and its additive inverse?

    <p>A zero sum</p> Signup and view all the answers

    What is a common property shared by both addition and multiplication of integers?

    <p>Commutative Property</p> Signup and view all the answers

    Which property of integers allows us to rearrange the numbers when adding or multiplying three or more integers?

    <p>Associative Property</p> Signup and view all the answers

    What is the result of adding a negative integer to its additive inverse?

    <p>0</p> Signup and view all the answers

    Which property of integers states that the order in which two numbers are added or multiplied does not change the result?

    <p>Commutative Property</p> Signup and view all the answers

    What is the result of multiplying an integer by its additive inverse?

    <p>-0</p> Signup and view all the answers

    Which property of integers allows us to multiply a number by a sum of numbers?

    <p>Distributive Property</p> Signup and view all the answers

    What is the purpose of the additive inverse of an integer?

    <p>To find the sum of an integer and its opposite</p> Signup and view all the answers

    Which property of integers states that changing the grouping of numbers does not change the result?

    <p>Associative Property</p> Signup and view all the answers

    When multiplying three negative integers, what is the sign of the product?

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

    What is the result of adding a positive integer and a negative integer with the same absolute value?

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

    Which of the following is equivalent to subtracting a negative integer from a positive integer?

    <p>Adding a positive integer to a positive integer</p> Signup and view all the answers

    When multiplying two integers with the same sign, what is the sign of the product?

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

    What is the relationship between the absolute value of an integer and its distance from zero on the number line?

    <p>The absolute value is equal to the distance from zero</p> Signup and view all the answers

    What is the result of multiplying a negative integer by a sum of positive integers?

    <p>A negative product</p> Signup and view all the answers

    What is the result of multiplying an integer by the sum of its additive inverse and 1?

    <p>Always zero</p> Signup and view all the answers

    Which of the following statements is true about the multiplication of integers with different signs?

    <p>The product is always negative</p> Signup and view all the answers

    What is the result of subtracting an integer from its additive inverse?

    <p>Always zero</p> Signup and view all the answers

    What is the relationship between the absolute value of an integer and its distance from zero on the number line?

    <p>The absolute value is equal to the distance from zero</p> Signup and view all the answers

    What is the result of adding a positive integer and a negative integer with the same absolute value?

    <p>Always zero</p> Signup and view all the answers

    Which property of integers allows us to extend the distributive property to three or more addends?

    <p>Distributive Property of Multiplication over Addition</p> Signup and view all the answers

    What is the result of subtracting the additive inverse of an integer from itself?

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

    Which property of integers is used to simplify the expression $(a + b) + c$?

    <p>Associative Property of Addition</p> Signup and view all the answers

    What is the result of multiplying an integer by its multiplicative inverse?

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

    Which property of integers is used to simplify the expression $a imes (b + c + d)$?

    <p>Distributive Property of Multiplication over Addition</p> Signup and view all the answers

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