Sum = $ \frac{5}{2}(70 + 134) = \frac{5}{2}(204) = 5 \times 102 = 510 $

["Understanding the Sum: $ \frac{5}{2}(70 + 134) = 510 — A Step-by-Step Breakdown", "Calculating a sum efficiently is a common task in mathematics, finance, and everyday problem-solving. One example that often comes up involves breaking down expressions to simplify complex sums — like computing $ \sum = \frac{5}{2}(70 + 134) = \frac{5}{2}(204) = 5 \ imes 102 = 510 $. In this article, we’ll explore this calculation in detail, uncover its structure, and explain how such computations apply in real-world contexts.", "---", "### How to Calculate the Sum Step-by-Step", "The sum in question is:", "$$\n\sum = \frac{5}{2}(70 + 134)\n$$", "This expression uses two mathematical principles:", "1. Distributive Property and Addition Inside Parentheses\n The sum inside the parentheses — $ 70 + 134 $ — simplifies directly:", "$$\n 70 + 134 = 204\n $$", "Now substitute back:", "$$\n \sum = \frac{5}{2} \ imes 204\n $$", "2. Multiplying by a Fraction\n Instead of multiplying $ \frac{5}{2} $ directly, it’s often easier to compute:", "$$\n \frac{5}{2} \ imes 204 = 5 \ imes \left(\frac{204}{2}\right) = 5 \ imes 102 = 510\n $$", "Alternatively, you can multiply 204 by 5 first, then divide by 2:", "$$\n\frac{5}{2} \ imes 204 = \frac{5 \ imes 204}{2} = \frac{1020}{2} = 510\n$$", "This demonstrates the commutative and associative properties of arithmetic, where order and grouping do not change the result.", "---", "### Why This Calculation Matters", "Understanding this type of sum has practical applications in:", "- Financial calculations: Calculating average earnings, investment returns, or distributing costs evenly over time.\n- Data analysis: Simplifying aggregated data trends where values are scaled or weighted.\n- STEM subjects: Foundational arithmetic underpins more complex operations in algebra, physics, and engineering.", "---", "### Final Result", "$$\n\boxed{510}\n$$", "The sum $ \frac{5}{2}(70 + 134) $, when expanded and simplified, equals 510 — a clear example of how breaking a problem into manageable steps leads to quick and accurate results.", "---", "Keywords for SEO:\n- How to calculate $ \frac{5}{2}(70 + 134) $\n- Simplify sum using distributive property\n- Mathematical calculation step-by-step\n- Real-world applications of fractions in sums\n- Step-by-step arithmetic example", "Meta Title:\nUnderstanding $ \frac{5}{2}(70 + 134) = 510 — Step-by-step breakdown and real-world use", "Meta Description:\nLearn how to simplify $ \frac{5}{2}(70 + 134) $ using the distributive property and fractions. A clear example showing how to calculate the sum and arrive at 510 quickly. Ideal for math students and practical problem solvers."]