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. (B)</p> Signup and view all the answers

What is the additive inverse of an integer?

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

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

<p>Multiplication distributes over addition. (B)</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) (C)</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. (C)</p> Signup and view all the answers

What is the additive inverse of 5?

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

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

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

What is the absolute value of -3?

<p>3 (A)</p> Signup and view all the answers

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

<p>A negative product (A)</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 (D)</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 (C)</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 (D)</p> Signup and view all the answers

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

<p>Zero (A)</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 (C)</p> Signup and view all the answers

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

<p>We get zero (A)</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 (C)</p> Signup and view all the answers

What is the result of adding zero to any integer?

<p>The original integer (B)</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 (D)</p> Signup and view all the answers

What happens when we multiply any integer by one?

<p>We get the original integer (A)</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. (A)</p> Signup and view all the answers

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

<p>A negative difference (D)</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. (C)</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. (B)</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 (D)</p> Signup and view all the answers

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

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

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

<p>Commutative Property (B)</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 (D)</p> Signup and view all the answers

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

<p>0 (B)</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 (A)</p> Signup and view all the answers

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

<p>-0 (A), 0 (B)</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 (D)</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 (C)</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 (C)</p> Signup and view all the answers

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

<p>Negative (A)</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 (A)</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 (C)</p> Signup and view all the answers

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

<p>Positive (C)</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 (B)</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 (C)</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 (A)</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 (A)</p> Signup and view all the answers

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

<p>Always zero (B)</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 (C)</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 (A)</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 (C)</p> Signup and view all the answers

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

<p>Zero (A)</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 (C)</p> Signup and view all the answers

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

<p>One (D)</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 (B)</p> Signup and view all the answers

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