Simplify: \(S_5 = \frac{5}{2}(6 + 8) = \frac{5}{2} \times 14 = 35\).

["Simplify: How to Solve ( S_5 = \frac{5}{2}(6 + 8) = \frac{5}{2} \ imes 14 = 35 ) Step-by-Step", "Understanding how to simplify complex expressions like ( S_5 = \frac{5}{2}(6 + 8) ) is essential for mastering basic algebra. In this article, we break down the step-by-step process to solve this equation efficiently and confidently.", "---", "### What Is ( S_5 = \frac{5}{2}(6 + 8) )?", "At first glance, ( S_5 = \frac{5}{2}(6 + 8) ) might look intimidating, but it’s simply a multiplication problem wrapped in parentheses. Algebra teaches us that simplification means breaking down the expression into smaller, manageable parts.", "---", "### Step 1: Simplify Inside the Parentheses\nThe expression starts with:\n[\nS_5 = \frac{5}{2}(6 + 8)\n]", "Inside the parentheses, we add:\n[\n6 + 8 = 14\n]", "So the expression becomes:\n[\nS_5 = \frac{5}{2} \ imes 14\n]", "---", "### Step 2: Multiply ( \frac{5}{2} ) by 14\nNext, replace the parentheses with the simplified value:\n[\nS_5 = \frac{5}{2} \ imes 14\n]", "Instead of multiplying a fraction by a whole number directly, multiplication of fractions and integers follow a clear rule:\n[\n\frac{a}{b} \ imes c = \frac{a \ imes c}{b}\n]", "Here, ( a = 5 ), ( b = 2 ), and ( c = 14 ). So:\n[\nS_5 = \frac{5 \ imes 14}{2} = \frac{70}{2}\n]", "---", "### Step 3: Simplify the Fraction\nNow simplify ( \frac{70}{2} ):\n[\n\frac{70}{2} = 35\n]", "---", "### Final Result:\n[\nS_5 = 35\n]", "---", "### Why Simplifying Such Expressions Matters\nSimplifying expressions like ( S_5 = \frac{5}{2}(6 + 8) ) helps students develop fluency in fraction arithmetic, order of operations, and algebraic manipulation. This foundational skill appears in everyday problems—from calculating ratios and growth rates to solving real-life equations.", "---", "### Quick Recap of the Simplification Steps\n1. Inside parentheses: ( 6 + 8 = 14 )\n2. Rewrite expression: ( S_5 = \frac{5}{2} \ imes 14 )\n3. Multiply numerator and denominator: ( \frac{5 \ imes 14}{2} = \frac{70}{2} )\n4. Final simplification: ( \frac{70}{2} = 35 )", "---", "Mastering these steps opens the door to solving more complex algebra problems with ease. The key takeaway: breaking down expressions step by step leads to confident and accurate answers.", "---", "Keywords: simplify algebra, solve fractions, algebraic expression, step-by-step math, how to simplify, arithmetic steps, solve ( S_5 ), mathematics tutorial, basic algebra, simplifying fractions, multiplication of fractions, step-by-step simplification.", "---", "If you want more step-by-step principles in algebra, dive into fraction multiplication rules, distributive property, and working with parentheses—the building blocks of clear mathematical thinking."]