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 sho divided 20 by 2 before multiplying. the order of operations says t and divide from left to right.
no, doug made a mistake going from step 4 to step 5. doug sho subtracted 20 from 65 before dividing. the order of operations s and subtract from left to right.
yes, dougs work is correct.

Explanation:

Step1: Calculate the exponent

$$7^{2}=49$$

Step2: Calculate inside the innermost parentheses

$$49 - 45+1=5$$

Step3: Calculate division and multiplication from left - to - right inside the brackets

$$20\div2\times5 = 10\times5=50$$

Step4: Calculate the subtraction

$$65 - 50=15$$

Doug made a mistake in Step 4. In the expression $20\div2\times5$, according to the order of operations (division and multiplication from left - to - right), we should first do $20\div2 = 10$, then $10\times5=50$, not $20\div(2\times5)$.

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.