h = \frac{84 \cdot 2}{15} = \frac{168}{15} = 11.2 \text{ cm}

["Understanding the Calculation: ( h = \frac{84 \cdot 2}{15} = \frac{168}{15} = 11.2 , \ ext{cm} )", "In mathematical problem-solving, breaking down complex expressions into simple steps enhances clarity and comprehension. One such calculation is solving for ( h ) in the equation:", "[\nh = \frac{84 \cdot 2}{15} = \frac{168}{15} = 11.2 , \ ext{cm}\n]", "This formula appears straightforward but involves key arithmetic principles—multiplication, division, and simplification—that are essential in both academic and real-world applications. Below, we explore how this calculation unfolds and why mastering such steps matters.", "### Breaking Down the Equation", "The expression begins with a multiplication and a division:", "1. Multiplying the Numerator:\n First, we compute ( 84 \ imes 2 = 168 ). This step demonstrates basic multiplication, a foundational operation in algebra and arithmetic.", "2. Dividing by the Denominator:\n Next, we divide 168 by 15, yielding ( \frac{168}{15} = 11.2 ). Simplifying fractions or converting fractions to decimals ensures easy interpretation—particularly important when measuring physical dimensions.", "3. Final Value:\n The result, ( h = 11.2 , \ ext{cm} ), represents a precise, practical measurement.", "### Why This Calculation Matters", "While the equation may seem abstract, similar calculations underpin tasks like architectural design, engineering measurements, or optimizing material use. For example:\n- If ( 84 ) represents a known benchmark (e.g., a frame length), doubling it to assess twice the size ensures accurate scaling.\n- Dividing by ( 15 ) could correspond to standard unit conversion or adjustment, such as fine-tuning dimensions for compatibility with machinery or ergonomic standards.", "### Practical Applications of the Result", "Measuring ( h = 11.2 , \ ext{cm} ) is useful in:\n- Craftsmanship: Cutting materials to exact sizes for construction or furniture assembly.\n- Packaging: Determining optimal box dimensions for shipping delicate items.\n- Science: Calibrating experimental apparatus or validating formulas in physics and geometry.", "### Simplifying the Computation", "For fast mental math or quick verification, note that ( \frac{168}{15} ) can be simplified:\n[\n\frac{168 \div 3}{15 \div 3} = \frac{56}{5} = 11.2\n]\nThis simplification confirms the accuracy of the result while reinforcing fraction division rules.", "### Conclusion", "The equation ( h = \frac{84 \cdot 2}{15} = \frac{168}{15} = 11.2 , \ ext{cm} ) exemplifies how simple math enables precise measurements in everyday life. Whether scaling components, designing structures, or solving equations, understanding each step affords confidence and accuracy. By mastering operations like multiplication, division, and fraction simplification, anyone can tackle practical problems with precision—making seemingly abstract math immediately relevant.", "So next time you encounter ( h = \frac{84 \cdot 2}{15} ), remember: it’s not just a calculation—it’s a tool for clear, effective measurement."]