Question

Mateo begins his dive at sea level. He dives down 15 meters, and then rises up 4 meters. He dives again, going down 7 meters. Which equation models Mateo’s movements, and uses the commutative property?
(–15) + 4 + (–7) = (–7) + (–15) + (–4)
(–15) + 4 + (–7) = 7 + 15 + (–4)
(–15) + 4 + (–7) = 4 + (–15) + (–7)
(–15) + 4 + (–7) = 4 + 15 + 7

Answer 1

To find the correct equation that models Mateo’s movements while using the commutative property, let's break down his movements:

1. He begins at sea level, which we can consider as 0.
2. He dives down 15 meters, which would be represented by -15.
3. He then rises up 4 meters, which is +4.
4. Lastly, he dives down another 7 meters, represented by -7.

We can express Mateo's total movement with the equation:
\[
(-15) + 4 + (-7)
\]

Now, applying the commutative property means rearranging the terms in the expression without changing the result.

Analyzing the options:

1. **Option 1**: \((-15) + 4 + (-7) = (-7) + (-15) + (-4)\)
- This is incorrect because it mistakenly changes +4 to -4 on the right side.

2. **Option 2**: \((-15) + 4 + (-7) = 7 + 15 + (-4)\)
- This is incorrect because it introduces positive values incorrectly and changes the terms inaccurately.

3. **Option 3**: \((-15) + 4 + (-7) = 4 + (-15) + (-7)\)
- This is correct because it properly rearranges the terms using the commutative property.

4. **Option 4**: \((-15) + 4 + (-7) = 4 + 15 + 7\)
- This is incorrect, as it mistakenly changes -15 to +15 and -7 to +7.

Therefore, the correct equation modeling Mateo's movements while using the commutative property is:

**Option 3**: \((-15) + 4 + (-7) = 4 + (-15) + (-7)\)