Question

which expression uses the communtative property of addition and the associate property of multiplication to rewrite the expression 3x(2x8)+7

Answer 1

To rewrite the expression \(3x(2 \times 8) + 7\) using the commutative property of addition and the associative property of multiplication, we can first recognize what those properties entail:

- **Commutative Property of Addition** states that \(a + b = b + a\).
- **Associative Property of Multiplication** states that \(a(bc) = (ab)c\).

Let's first calculate \(2 \times 8\):

\[
2 \times 8 = 16
\]

Substituting that back into the expression gives us:

\[
3x(16) + 7
\]

Now we apply the properties:

1. **Using the associative property within the multiplication**:
We can express \(3x(16)\) in a different way:
\[
= (3x \times 16)
\]

2. **Now, let’s apply the commutative property** so that we can rearrange the addition:
\[
3x(16) + 7 = 7 + 3x(16)
\]

So, rewriting the expression while utilizing both properties, we have:

\[
7 + 3x(16)
\]

In its final form, the expression is \(7 + 3x(16)\), which incorporates both the commutative property of addition and the associative property of multiplication.