Question

part c – properties of real numbers 5. simplify using the commutative and/or associative property: (3 + a) + 5

Explanation:

Step1: Recall associative property

The associative property of addition states that \((x + y) + z = x + (y + z)\). We can apply this to \((3 + a) + 5\) by regrouping the terms.
So, \((3 + a) + 5 = 3 + (a + 5)\) (by associative property). But we can also use the commutative property of addition (\(x + y = y + x\)) to reorder \(a + 5\) as \(5 + a\), so we get \(3+(5 + a)\). Then, using the associative property again (or just adding the constants first), we have \((3 + 5)+a\).

Step2: Add the constants

Calculate \(3 + 5\), which equals \(8\). So now we have \(8 + a\), and by the commutative property, this is also equal to \(a + 8\) (but typically we write the constant first or keep the variable order as is, but simplifying the constants gives \(a + 8\) or \(8 + a\), and the simplified form by combining the constant terms is \(a + 8\) (or \(8 + a\)).

Answer:

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