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

Question

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

Answer 1

To make the two expressions equivalent using the Commutative Property, we can rearrange the terms. The Commutative Property states that for addition, the order of adding numbers does not change the sum.

The given expressions are:

Left Side: \( 5 + _ + 1 + 7 \)
Right Side: \( 4 + _ + 7 + 1 \)

For the left side, we know \(5 + 1 + 7 = 13\). We need to find a value to fill in the blank that makes both sides equal.

Let’s evaluate both sides step by step by filling in the blanks.

1. We know that \(5 + _ + 1 + 7\) should equal \(4 + _ + 7 + 1\).
2. The left side begins with 5 and sums with 1 and 7. Thus:
   • We can directly sum \(5 + 1 + 7 = 13\).
3. The right side must also equal 13. So we look at \(4 + _ + 7 + 1\):
   • The sum \(4 + 7 + 1 = 12\).
   • To equal 13, \(_ \) must be \(1\).

So by filling in both blanks with \(1\):

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

This gives:

Left Side: \( 5 + 1 + 1 + 7 = 14\)
Right Side: \( 4 + 1 + 7 + 1 = 14\)

The completed expressions are:

\(5 + 1 + 1 + 7 = 4 + 1 + 7 + 1\)

Thus, the blanks are filled with 1.