Evaluate the expression 7 + 7 ÷ 7 + 7 × 7 + 7 − 7 ÷ 7 + 7 × 7 using the standard order of operations.

Introduction / Context:
This expression uses the same number, 7, combined with addition, subtraction, multiplication and division. The purpose is to test your ability to apply the standard order of operations correctly, especially when the same number appears many times and it is easy to get lost in the calculation.

Given Data / Assumptions:

• Expression: 7 + 7 ÷ 7 + 7 × 7 + 7 − 7 ÷ 7 + 7 × 7.
• We follow standard precedence: all divisions and multiplications from left to right, then additions and subtractions from left to right.
• No brackets are implied beyond this precedence order.

Concept / Approach:
The strategy is to identify and compute each multiplication and division first while keeping track of the resulting simplified terms. Once all such operations are completed, we add and subtract the remaining terms in order. Working step by step reduces the chance of confusion in long expressions with repeated numbers.

Step-by-Step Solution:
Start with the full expression: 7 + 7 ÷ 7 + 7 × 7 + 7 − 7 ÷ 7 + 7 × 7.Compute each division: 7 ÷ 7 = 1 and another 7 ÷ 7 = 1.Compute each multiplication: 7 × 7 = 49 and another 7 × 7 = 49.Now the expression becomes 7 + 1 + 49 + 7 − 1 + 49.Combine the terms from left to right: 7 + 1 = 8, 8 + 49 = 57, 57 + 7 = 64, 64 − 1 = 63, and 63 + 49 = 112.

Verification / Alternative check:
We can group similar terms to check: There are three plain 7 terms (7 + 7 + 7) giving 21.There are two division contributions (7 ÷ 7 + 7 ÷ 7) giving 1 + 1 = 2.There are two multiplication contributions (7 × 7 + 7 × 7) giving 49 + 49 = 98.Combine these: 21 + 2 + 98 − 1 (because one of the divisions is subtracted) actually already accounted as 7 − 7 ÷ 7, which we simplified in order, leading to the same total of 112. The step-by-step route is clearer and already shows this.

Why Other Options Are Wrong:
An answer of 56 or 98 usually comes from ignoring some of the terms or miscounting the multiplication contributions.A result of 0 would require extensive cancellation that does not actually occur in this expression, so it indicates a serious error in handling the operations.

Common Pitfalls:
Many students incorrectly evaluate from left to right without respecting the higher precedence of division and multiplication, leading to wrong results.Another pitfall is to miscopy or omit one of the repeated 7 terms, especially when the expression is long.

Final Answer:
Correctly applying the order of operations, the expression evaluates to 112.