Andrew is showing his work in simplifying −4.5 + 4.2 + 5.6 − 7.3. Identify any errors in his work or in his reasoning. Write feedback to Andrew explaining the mistake he made and how to correct his work. (5 points)
Step Work Reasoning
−4.5 + 4.2 + 5.6 − 7.3 Original problem
1 −4.5 + 4.2 + 5.6 + (−7.3) Additive inverse
2 −4.5 + (−7.3) + 4.2 + 5.6 Commutative property
3 (−4.5 + (−7.3)) + (4.2 + 5.6) Associative property
4 −11.8 + 9.8 Simplify
5 −21.6 Simplify
Please show error
The error in Andrew's work is in step 2. In this step, he incorrectly applies the commutative property when rearranging the terms. The correct rearrangement should be (-4.5 + 5.6) + (4.2 + (-7.3)).
To correct this mistake, Andrew should switch the order of the terms, but he should not change the signs. The correct equation should be: -4.5 + (-7.3) + 4.2 + 5.6.
By following this correction, Andrew will arrive at the correct answer.
The error in Andrew's work is in step number 2 where he applies the commutative property incorrectly.
To correct his work, Andrew needs to rearrange the order of the terms properly before he can apply the commutative property. The correct step would be:
2: -4.5 + 5.6 + 4.2 + (-7.3)
By properly rearranging the terms, Andrew will then be able to apply the commutative property correctly:
-4.5 + 5.6 + 4.2 + (-7.3) = -4.5 + 5.6 + 4.2 - 7.3
From this point, Andrew's work can continue with step 3 and so on.
Andrew made an error in step 2 of his work. He incorrectly applied the commutative property when rearranging the terms. The correct order of the terms should be: -4.5 + 4.2 + 5.6 - 7.3.
To correct his work, Andrew should proceed as follows:
Step 1: -4.5 + 4.2 + 5.6 - 7.3 (Original problem)
Step 2: -4.5 + 4.2 + 5.6 - 7.3 (No changes needed)
Step 3: (-4.5 + 4.2) + 5.6 - 7.3 (Associative property)
Step 4: (-0.3) + 5.6 - 7.3 (Simplify within parentheses)
Step 5: 5.3 + 5.6 - 7.3 (Simplify)
Step 6: 10.9 - 7.3 (Add the remaining terms)
Step 7: 3.6 (Simplify)
Therefore, the correct simplified expression is 3.6.