9. Use the commutallve property lo make numbor sentences true. Example: \[ \begin{array}{c} a \times b=\square \\ a \times b=b \times a \\ a b=b a \end{array} \] a. \( x \times c= \) b. \( m \times n= \) \( \square \) \( \square \) 10. Use zero as the idenitity element for addilion, or 1 as the identity element for multiplication to simplity the following: a. \( a \times 1= \) b. \( b \times \) \( \qquad \) \( =b \) c. \( c+0= \) \( \square \) \( \square \) \( \square \)

Sure, I can help you complete questions 9 and 10 by applying the commutative property and the identity elements for addition and multiplication. Let's go through each part step by step. --- ### **Question 9: Use the Commutative Property to Make Number Sentences True** The **commutative property** states that the order of numbers does not change the result of the operation. This property applies to both addition and multiplication. **Example:** \[ \begin{array}{c} a \times b = \square \\ a \times b = b \times a \quad \text{(Commutative Property)} \\ ab = ba \end{array} \] **a. \( x \times c = \square \)** **Solution:** Apply the commutative property to switch the order of the operands. \[ x \times c = c \times x \] **Filled-In Sentence:** \[ \begin{array}{c} x \times c = c \times x \end{array} \] --- **b. \( m \times n = \square \)** **Solution:** Apply the commutative property to switch the order of the operands. \[ m \times n = n \times m \] **Filled-In Sentence:** \[ \begin{array}{c} m \times n = n \times m \end{array} \] --- ### **Question 10: Use Identity Elements to Simplify the Following** - The **identity element for addition** is **0**, because adding 0 to any number does not change its value. - The **identity element for multiplication** is **1**, because multiplying any number by 1 does not change its value. **a. \( a \times 1 = \)** **Solution:** Since 1 is the identity element for multiplication: \[ a \times 1 = a \] **Filled-In Sentence:** \[ a \times 1 = a \] --- **b. \( b \times \quad = b \)** **Solution:** To find what to multiply \( b \) by so that the product is \( b \), use the identity element for multiplication, which is 1: \[ b \times 1 = b \] **Filled-In Sentence:** \[ b \times 1 = b \] --- **c. \( c + 0 = \)** **Solution:** Since 0 is the identity element for addition: \[ c + 0 = c \] **Filled-In Sentence:** \[ c + 0 = c \] --- ### **Summary of Answers** **Question 9:** - **a.** \( x \times c = c \times x \) - **b.** \( m \times n = n \times m \) **Question 10:** - **a.** \( a \times 1 = a \) - **b.** \( b \times 1 = b \) - **c.** \( c + 0 = c \) --- Feel free to ask if you need further clarification or additional examples!