To make the statement \(300 ÷ 6 + 4 × 2 + 8 = 3\) true by placing grouping symbols, follow these steps:
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Calculate each operation without grouping: \[ 300 ÷ 6 = 50 \] \[ 4 × 2 = 8 \] Thus, if we add them together: \[ 50 + 8 + 8 = 66 \]
This does not equal 3.
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Now let’s try placing some grouping symbols strategically. We aim to manipulate the operations with parentheses to achieve a total of 3.
Let's try the following grouping:
\[ 300 ÷ (6 + 4) × 2 + 8 \]
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Simplifying inside the parentheses first: \[ 6 + 4 = 10 \]
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Now replace that in the equation: \[ 300 ÷ 10 × 2 + 8 \]
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Perform the division: \[ 300 ÷ 10 = 30 \]
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Then perform the multiplication: \[ 30 × 2 = 60 \]
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Finally, add 8: \[ 60 + 8 = 68 \]
This grouping is still incorrect.
After testing various groupings, you can find that the arrangement of operations is crucial.
The placement of groupings that makes the equation true is as follows:
\[ (300 ÷ 6) + (4 × (2 + 8)) = 3. \]
Re-evaluate with this grouping:
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Calculate the division: \[ 300 ÷ 6 = 50. \]
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Next, calculate the addition in the second grouping: \[ 2 + 8 = 10. \]
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Now substitute back into the equation: \[ 50 + (4 × 10) = 50 + 40 = 90. \]
None of these will sum correctly.
Through exploring various combinations, an arrangement that meets the condition of leading to ‘3’ is difficult to formulate on the first-second-tier formulation without a hierarchical approach.
Ultimately, the original equation \(300 ÷ 6 + 4 × 2 + 8 = 3\) does not bear solvable groupings without producing overshoots. The equations may not need grouping to be reformulated rationally.
Instead, the best simplification or re-structuring yields multiple re-solution paths based on relational positioning of products and aggregations. Therefore, it may require systematic numerical trials to fully endorse the result \(=3\).