Question

doug tried to evaluate an expression. here is his work:
$65 - 20 \div 2 \cdot (7^2 - 45 + 1)$
$= 65 - 20 \div 2 \cdot (49 - 45 + 1)$ step 1
$= 65 - 20 \div 2 \cdot (4 + 1)$ step 2
$= 65 - 20 \div 2 \cdot 5$ step 3
$= 65 - 20 \div 10$ step 4
$= 65 - 2$ step 5
$= 63$ step 6
is dougs work correct?
no, doug made a mistake going from step 3 to step 4. doug should have divided 20 by 2 before multiplying. the order of operations says to multiply and divide from left to right.
no, doug made a mistake going from step 4 to step 5. doug should have subtracted 20 from 65 before dividing. the order of operations says to divide and subtract from left to right.
yes, dougs work is correct.

Explanation:

Step1: Evaluate Step 3 to Step 4

Original Step 3: $65 - [20 \div 2 \cdot 5]$
Order of operations (left to right for multiply/divide): First calculate $20 \div 2 = 10$, then $10 \cdot 5 = 50$. Doug incorrectly calculated $2 \cdot 5 = 10$ first, then $20 \div 10 = 2$.

Step2: Correct the calculation

$65 - [20 \div 2 \cdot 5] = 65 - [10 \cdot 5] = 65 - 50 = 15$

Step3: Identify Doug's error

Doug violated left-to-right order for multiply/divide in Step 3 to 4.

Answer:

No, Doug made a mistake going from Step 3 to Step 4. Doug should have divided 20 by 2 before multiplying. The order of operations says to multiply and divide from left to right.