Questions: Answer the questions below. Be sure to show your work. 1. Which example shows the associative property of multiplication? A. a(b+c)=ab+a0 B. (a+b)+9=a(b+a) C. (a * b) * 5=a *(b * 5) D. (a * b) * 5=(a * (1/5)) * b 2. Which example does NOT show the commutative property of addition? A. 4+x=x+4 B. ab=ba C. a+b=b+a D. 3x+4y=4y+3x 3. Complete the table below to show an equivalent expression. ORIGINAL EXPRESSION PROPERTY EQUIVALENT EXPRESSION ------------------------------------------------------ 15+0 Additive Identity 4 * 6 * 7 Commutative Property 9+(5+3) Associative Property 11 * 1 Identity Property (1/4) * (4/9) Inverse Property 9+(-9) Inverse Property 4. Describe how you know that (8+9)+3 is equivalent to 8+(9+3). What is the benefit to using this property? 5. Describe how you know that q+7+1 is equivalent to 9+1+7. What is the benefit to using this property?

Answer the questions below. Be sure to show your work. 1. Which example shows the associative property of multiplication? A. a(b+c)=ab+a0 B. (a+b)+9=a(b+a) C. (a * b) * 5=a *(b * 5) D. (a * b) * 5=(a * (1/5)) * b 2. Which example does NOT show the commutative property of addition? A. 4+x=x+4 B. ab=ba C. a+b=b+a D. 3x+4y=4y+3x 3. Complete the table below to show an equivalent expression. ORIGINAL EXPRESSION PROPERTY EQUIVALENT EXPRESSION ------------------------------------------------------ 15+0 Additive Identity 4 * 6 * 7 Commutative Property 9+(5+3) Associative Property 11 * 1 Identity Property (1/4) * (4/9) Inverse Property 9+(-9) Inverse Property 4. Describe how you know that (8+9)+3 is equivalent to 8+(9+3). What is the benefit to using this property? 5. Describe how you know that q+7+1 is equivalent to 9+1+7. What is the benefit to using this property?
Transcript text: Answer the questions below. Be sure to show your work. 1. Which example shows the associative property of multiplication? A. $a(b+c)=ab+a0$ B. $(a+b)+9=a(b+a)$ C. $(a \cdot b) \cdot 5=a \cdot(b \cdot 5)$ D. $(a \cdot b) \cdot 5=\left(a \cdot \frac{1}{5}\right) \cdot b$ 2. Which example does NOT show the commutative property of addition? A. $4+x=x+4$ B. $ab=ba$ C. $a+b=b+a$ D. $3x+4y=4y+3x$ 3. Complete the table below to show an equivalent expression. | ORIGINAL EXPRESSION | PROPERTY | EQUIVALENT EXPRESSION | |---------------------|----------|-----------------------| | $15+0$ | Additive Identity | | | $4 \cdot 6 \cdot 7$ | Commutative Property | | | $9+(5+3)$ | Associative Property | | | $11 \cdot 1$ | Identity Property | | | $\frac{1}{4} \cdot \frac{4}{9}$ | Inverse Property | | | $9+(-9)$ | Inverse Property | | 4. Describe how you know that $(8+9)+3$ is equivalent to $8+(9+3)$. What is the benefit to using this property? 5. Describe how you know that $q+7+1$ is equivalent to $9+1+7$. What is the benefit to using this property?
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Solution

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Solution Steps

Step 1: Identify the Associative Property of Multiplication
  • The associative property of multiplication states that the way in which numbers are grouped does not change their product.
  • Look for an expression where the grouping of numbers changes but the order of multiplication remains the same.
  • Option C: \((a \cdot b) \cdot 5 = a \cdot (b \cdot 5)\) shows the associative property of multiplication.
Step 2: Identify the Example That Does Not Show the Commutative Property of Addition
  • The commutative property of addition states that the order of numbers does not change their sum.
  • Check each option to see if the order of addition is changed.
  • Option B: \(\mathrm{ab} = \mathrm{ba}\) does not involve addition, so it does not show the commutative property of addition.
Step 3: Complete the Table for Equivalent Expressions
  • For the expression \(15 + 0\) with the Additive Identity property, the equivalent expression is \(15\).
  • For the expression \(4 \cdot 6 \cdot 7\) with the Commutative Property, rearrange the numbers: \(6 \cdot 4 \cdot 7\).
  • For the expression \(9 + (5 + 3)\) with the Associative Property, change the grouping: \((9 + 5) + 3\).

Final Answer

  1. The correct answer is C.
  2. The correct answer is B.
  • Equivalent expression for \(15 + 0\): \(15\)
  • Equivalent expression for \(4 \cdot 6 \cdot 7\): \(6 \cdot 4 \cdot 7\)
  • Equivalent expression for \(9 + (5 + 3)\): \((9 + 5) + 3\)
  1. The benefit of using the associative property is that it allows for easier computation by changing the grouping of numbers.
  2. The benefit of using the commutative property is that it allows for flexibility in the order of addition, making calculations simpler.
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