Math Gr 8 Ch 1: Properties of Whole Numbers
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Questions and Answers

What is the commutative property of addition?

  • $a + b = a - b$
  • $a + b = 2a$
  • $a + b = a imes b$
  • $a + b = b + a$ (correct)

    • What is the associative property of multiplication?

  • $a imes (b imes c) = (a imes b) imes c$ (correct)
  • $a imes b imes c = a imes (b + c)$
  • $a imes b + a imes c = a imes (b + c)$
  • $a imes (b + c) = a imes b + a imes c$

    • What is the distributive property of multiplication over addition?

  • $a imes (b + c) = a imes b imes a imes c$
  • $a imes (b + c) = a imes (b - c)$
  • $a imes (b + c) = a imes b - a imes c$
  • $a imes (b + c) = a imes b + a imes c$ (correct)

    • What is the additive property of 0?

    <p>$a + 0 = a$</p> Signup and view all the answers

    What is the benefit of using the commutative and associative properties in calculations?

    <p>It helps to simplify the calculations and makes them more efficient.</p> Signup and view all the answers

    What is the purpose of using a summary table for multiplication?

    <p>To practice and reinforce the multiplication of various numbers.</p> Signup and view all the answers

    What is the benefit of using the distributive property in calculations?

    <p>It helps to break down complex multiplications into simpler parts.</p> Signup and view all the answers

    What is true about the commutative property of multiplication?

    <p>It states that the order of numbers in multiplication does not change the result.</p> Signup and view all the answers

    Which of the following properties is true for both addition and multiplication?

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

    What happens when the order of numbers in addition or multiplication is changed?

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

    When adding or multiplying three or more numbers, what does the associative property ensure?

    <p>The way the numbers are grouped does not affect the result</p> Signup and view all the answers

    What is the purpose of the distributive property of multiplication over addition?

    <p>To simplify multiplication calculations</p> Signup and view all the answers

    What is the result of multiplying a number by 1?

    <p>The result is the same as the original number</p> Signup and view all the answers

    What is the purpose of using a summary table for multiplication?

    <p>To practice and reinforce multiplication facts</p> Signup and view all the answers

    What happens when 0 is added to a number?

    <p>The result is the same as the original number</p> Signup and view all the answers

    Why is it important to understand the properties of whole numbers?

    <p>To simplify calculations and solve problems efficiently</p> Signup and view all the answers

    If $a + b = 12$ and $a + c = 15$, which of the following can be concluded using the commutative property of addition?

    <p>b + c = 27</p> Signup and view all the answers

    What is the value of $(a + b) + (a - b)$, using the distributive property of multiplication over addition?

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

    If $(a + 2) × (a + 3) = 24$, what is the value of $a$, using the distributive property of multiplication over addition?

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

    Which of the following expressions is equivalent to $a × (b + c)$, using the distributive property of multiplication over addition?

    <p>a × b + a × c</p> Signup and view all the answers

    If $a + (b + c) = 12$, what is the value of $a + b + c$, using the associative property of addition?

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

    What is the value of $a × (1 + 1)$, using the distributive property of multiplication over addition?

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

    If $a × b = 12$ and $a × c = 15$, what is the value of $b + c$, using the commutative property of multiplication?

    <p>27</p> Signup and view all the answers

    What is the value of $(a × b) × (a × c)$, using the associative property of multiplication?

    <p>a^2 × b × c</p> Signup and view all the answers

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