Question

part c – properties of real numbers

1. simplify using the commutative and/or associative property:

(3 + a) + 5

Explanation:

Step1: Recall associative property of addition

The associative property of addition states that \((x + y) + z = x + (y + z)\). For \((3 + a) + 5\), we can apply the associative property to regroup the terms.
\((3 + a) + 5 = 3 + (a + 5)\)

Step2: Apply commutative property of addition

The commutative property of addition states that \(x + y = y + x\). So, \(a + 5 = 5 + a\). Substituting this back, we get \(3 + (5 + a)\).

Step3: Apply associative property again (or just add the constants)

Now, using the associative property (or simply adding the constant terms), we have \(3 + 5 + a\). And \(3 + 5 = 8\), so the simplified form is \(8 + a\) (or \(a + 8\) by commutative property, but typically written as \(a + 8\) or \(8 + a\)).

Answer:

\(a + 8\) (or \(8 + a\))