Questions: Use the associative property of addition to rewrite the expression as an equivalent z+(y+31) An equivalent expression is (y+31)+z.

Use the associative property of addition to rewrite the expression as an equivalent
z+(y+31)

An equivalent expression is (y+31)+z.

Transcript text: Use the associative property of addition to rewrite the expression as an equivalent \[ z+(y+31) \] An equivalent expression is $(y+31)+z$.

Solution

Solution Steps

Step 1: Identify the associative property of addition

The associative property of addition states that the grouping of numbers being added does not change the sum. In other words, for any numbers \( a \), \( b \), and \( c \), the expression \( a + (b + c) \) is equivalent to \( (a + b) + c \).

Step 2: Apply the associative property to the given expression

The given expression is \( z + (y + 31) \). Using the associative property, we can rewrite this expression by changing the grouping of the terms.

Step 3: Rewrite the expression

By applying the associative property, the expression \( z + (y + 31) \) can be rewritten as \( (z + y) + 31 \). However, the question specifies that an equivalent expression is \( (y + 31) + z \), which is also valid due to the commutative property of addition.

Final Answer

\(\boxed{(y + 31) + z}\)

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