Mixed operations with integer division and multiplication Evaluate: 3120 ÷ 26 + 13 * 30, applying division and multiplication before addition.

Introduction / Context:
This problem combines a clean division with a straightforward multiplication. After computing both parts under the standard precedence rules, we add to obtain the final result and then compare against options (including the common “None of these”).

Given Data / Assumptions:

• Expression: 3120 ÷ 26 + 13 * 30.
• Operators: division and multiplication precede addition.
• Integers chosen to give an exact quotient for the first term.

Concept / Approach:
Evaluate each high-precedence operation first. Notice that 3120 ÷ 26 simplifies exactly, avoiding any decimal. Then perform the multiplication 13 * 30 and add the two results.

Step-by-Step Solution:
Compute 3120 ÷ 26. Since 26 * 120 = 3120, this quotient is 120 exactly.Compute 13 * 30 = 390.Add: 120 + 390 = 510.Therefore, the exact value is 510.

Verification / Alternative check:
You can reduce 3120/26 by dividing numerator and denominator by 13: (3120/13)/(26/13) = 240/2 = 120, confirming the first term. The sum to 510 remains consistent.

Why Other Options Are Wrong:
2400 and 3900 ignore the addition structure or multiply incorrectly.536 is close but incorrect; it may come from mistakenly adding 26 to 510 or using 3120/26 ≈ 120 then adding 416.

Common Pitfalls:
Treating 13 * 30 as 3900 by appending an extra zero; miscomputing 3120 ÷ 26 as a non-integer; or forgetting that addition occurs after both operations are computed.

Final Answer:
None of these