Eva is showing her work in simplifying (7.3 − 7.2) − 3.8 + 3.7. In which step did Eva make an error?

Step 1: (7.3 − 7.2) − 3.8 + 3.7

Step 2: 7.3 + (−7.2 − 3.8) + 3.7 (commutative property)

Step 3: 7.3 − 11 + 3.7

Step 4: 7.3 + 3.7 − 11 (commutative property)

Step 5: 11 − 11 = 0

Step 2; she wrote commutative instead of distributive
Step 4; she wrote commutative instead of distributive
Step 4; she wrote commutative instead of associative
Step 2; she wrote commutative instead of associative

Answer:

Step 2; she wrote commutative instead of associative.

Explanation:

An associative property of addition is a rule that states that, the sum of three (3) or more numbers will always be the same irrespective of how these numbers are grouped.

This ultimately implies that, re-grouping three (3) or more numbers and adding them will give the same answer or end result (outcome).

Mathematically, the associative property of addition is given by the formula;

[tex] a + (b + c) = (a + b) + c [/tex]

Applying the above rule to the question, we have;

[tex] (7.3 - 7.2) - 3.8 + 3.7 = 7.3 + (-7.2 - 3.8) + 3.7 [/tex]

Hence, we would have the correct step written as;

Step 2: 7.3 + (-7.2 − 3.8) + 3.7 (associative property of addition).

In conclusion, Eva should have written associative property in Step 2 instead of commutative property.

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