.(1 point)
11 answers
The Commutative Property of Addition states that the order in which two numbers are added does not affect the sum. Therefore, to rewrite the expression \(4x^2 + 8x\) using the Commutative Property, you can simply rearrange the terms.
So, \(4x^2 + 8x\) can be rewritten as:
\[ 8x + 4x^2 \]
Both forms represent the same expression.
Using the Commutative Property of Addition, which states that the order of addition does not affect the sum, you can rearrange the terms in the expression \( ab^2 + c^3 \).
So, the rewritten expression can be:
\[ c^3 + ab^2 \]
Both forms represent the same expression.
The Commutative Property of Multiplication states that the order in which two numbers are multiplied does not affect the product.
Using this property, you can rewrite the expression \( a^{20} \cdot x^{3} \) by switching the order of the factors:
\[ x^3 \cdot a^{20} \]
Both forms represent the same product.
To make the two expressions \( 14 \cdot (__) \cdot 2 \) and \( 7 \cdot (__) \cdot 14 \) equivalent using the Commutative Property, we can find the appropriate value for the blanks.
We can rewrite \( 7 \) in terms of \( 14 \) because \( 14 = 2 \cdot 7 \).
Thus, we can fill in the blanks using \( 1 \) for both blanks:
\[ (14) \cdot (1) \cdot (2) = (7) \cdot (2) \cdot (14) \]
So the filled expressions would be:
\[ (14)(1)(2) = (7)(2)(14) \]
Both sides equal \( 28 \).
To fill in the blank so that the two expressions \( 14 \cdot (__) \cdot 2 = 7 \cdot 2 \cdot 14 \) are equivalent, we can start simplifying the right side.
First, let's calculate the right side:
\[ 7 \cdot 2 \cdot 14 = 14 \cdot 2 \cdot 7 \] which simply rearranges using the Commutative Property.
Now, we want the left side to equal the right side. We can express \( 7 \) in terms of multiplication:
Notice that: \[ 7 = \frac{14}{2} \]
So we can fill in the blank with \( \frac{14}{2} \) or just \( 7 \).
Thus, the complete expression is:
\[ (14)(7)(2) = (7)(2)(14) \]
In summary, you can fill in the blank with 7.
You're welcome! If you have any more questions or need further assistance, feel free to ask. Happy studying!
