Difficulty: Medium
Correct Answer: 50
Explanation:
Introduction / Context:
This expression again uses the same number, 7, combined with different operations. The question is meant to reinforce the rule that division and multiplication must be executed before addition and subtraction, even when the numbers look symmetric and tempting to combine in other ways.
Given Data / Assumptions:
Concept / Approach:
We first identify the division 7 ÷ 7 and the multiplication 7 × 7. Once these are simplified, we are left with a straightforward combination of additions and subtractions. Evaluating systematically from left to right after resolving multiplication and division ensures accuracy.
Step-by-Step Solution:
Start with 7 + 7 ÷ 7 + 7 × 7 − 7.Compute division: 7 ÷ 7 = 1.Compute multiplication: 7 × 7 = 49.Substitute back: the expression becomes 7 + 1 + 49 − 7.Now evaluate left to right: 7 + 1 = 8.Then 8 + 49 = 57.Finally, 57 − 7 = 50.
Verification / Alternative check:
We can group as (7 − 7) + (7 ÷ 7) + 7 × 7. Here, 7 − 7 = 0, 7 ÷ 7 = 1 and 7 × 7 = 49.Summing yields 0 + 1 + 49 = 50, which is identical to the previous result, confirming our calculation.
Why Other Options Are Wrong:
An answer of 42 might come from incorrectly evaluating 7 × 7 − 7 as 42 and ignoring the other terms or combining them incorrectly.A value like 57 would appear if the subtraction of 7 at the end is mistakenly omitted.Zero would require all terms to cancel out perfectly, which obviously does not happen in this expression.
Common Pitfalls:
Performing operations strictly from left to right without regard to precedence can lead learners to compute (7 + 7) ÷ 7, which changes the structure of the expression.Another pitfall is to misread the expression as 7(1 + 1 + 7 − 1), which is not equivalent to the given question and thus yields the wrong answer.
Final Answer:
Applying the correct order of operations, the expression evaluates to 50.
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