Question

Using the Commutative Property, fill in the blanks so that the two algebraic expressions are equivalent.

5+_+1+7=4+_+7+1

Answer 1

To use the Commutative Property, we can rearrange the terms on either side of the equation without changing the overall value of the expressions.

The given equation is:

\[ 5 + \_ + 1 + 7 = 4 + \_ + 7 + 1 \]

We can start by rearranging the expressions and then filling in the blanks.

On the left side:
We have \(5, 1,\) and \(7.\)

Let’s rewrite it as:
\[ (5 + 7) + (1 + \_) \]

On the right side:
We have \(4, 7,\) and \(1.\)

Let’s choose \(2\) to fill in the blank:
\[ (4 + 1) + (7 + \_) \]

Thus we can fill the blanks with \(2\) on both sides:

So the expressions become:

\[ 5 + 2 + 1 + 7 = 4 + 2 + 7 + 1 \]

This way, both sides are equal and we used the Commutative Property to rearrange the terms.

The complete equation is:

\[ 5 + 2 + 1 + 7 = 4 + 2 + 7 + 1 \]

where the blanks are filled with \(2\).