Question

aiden tried to evaluate an expression. here is his work: \\\left8 + 24 \div \left(42 \div 3 \cdot 2 - 20\
ight)\
ight^2\\\\= \left8 + 24 \div \left(14 \cdot 2 - 20\
ight)\
ight^2\\ step 1\\= \left8 + 24 \div \left(28 - 20\
ight)\
ight^2\\ step 2\\= \left32 \div \left(28 - 20\
ight)\
ight^2\\ step 3\\= \left32 \div 8\
ight^2\\ step 4\\= 4^2\\ step 5\\= 16\\ step 6 is aidens work correct? no, aiden made a mistake going from the given expression to step 1. aiden should have multiplied 3 and 2 before dividing. the order of operations says to multiply before you divide. no, aiden made a mistake going from step 2 to step 3. aiden should have subtracted 20 from 28 instead of adding. the order of operations says to evaluate expressions in brackets and parentheses from the inside out. yes, aidens work is correct.

Explanation:

Step1: Evaluate inner parentheses (left to right)

First handle $42 \div 3 \cdot 2$:
$42 \div 3 = 14$, then $14 \cdot 2 = 28$. Subtract 20: $28 - 20 = 8$.
This matches Aiden's Steps 1-2.

Step2: Evaluate division before addition

Inside the brackets: $24 \div 8 = 3$, then $8 + 3 = 11$.
Aiden incorrectly added $8+24$ first in Step3.

Step3: Identify the error location

The mistake occurs between Step2 and Step3, as Aiden violated order of operations (division before addition).

Answer:

No, Aiden made a mistake going from Step 2 to Step 3. Aiden should have subtracted 20 from 28 instead of adding. The order of operations says to evaluate expressions in brackets and parentheses from the inside out.