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>$a + 0 = a$ (D)</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. (A)</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. (D)</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. (C)</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. (B)</p> Signup and view all the answers

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

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

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

<p>To simplify multiplication calculations (D)</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 (C)</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 (B)</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 (D)</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 (C)</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 (C)</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 (D)</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 (A)</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 (D)</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 (A)</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 (C)</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 (D)</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 (A)</p> Signup and view all the answers

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