Question

Blake is showing his work in simplifying (4.6 − 9.2) − 0.8 + 5.4. identify any error in his work or reasoning. step 1: (4.6 − 9.2) − 0.8 + 5.4 step 2: 4.6 + (− 9.2 − 0.8) + 5.4 (associative property) step 3: 4.6 − 10 + 5.4 step 4: 4.6 + 5.4 − 10 (associative property) step 5: 10 − 10 = 0

Answer 1

In mathematics, when you are presented with multiple operations in one equation, you follow the PEMDAS rule. This rule assigns which operation should be the first priority. The P means parenthesis. So, any expression inside the parenthesis should be calculated first. This is followed by Exponent(E), Multiplication (M), Division (D), Addition (A) and lastly, Subtraction (S). Technically, when all you have left is addition and subtraction, priority doesn't matter because of associative property.

Step 1: Nothing has change. Blake just copied the original equation.
Step 2: Blake changed the placing of the parenthesis. As mentioned earlier, you have to prioritize what's inside the parenthesis first. You can't change the position of the parenthesis. It will matter. Good thing, the answer, in this case, does not matter. But this does not apply to all situations.
Step 3: Blake was correct. He prioritize the (− 9.2 − 0.8) term which is equal to -10.
Step 4: Associative property allows you interchange the order of the operations without changing the final answer. This is applicable to addition and subtraction operations. Hence, this was used correctly.
Step 5: Technically, this was correct because addition is prioritized more than subtraction.

Therefore, Blake's error was in Step 2.