Find a common denominator: \( \frac{2d}{120} + \frac{3d}{120} = 5 \).

["Finding the Common Denominator: Solving the Equation ( \frac{2d}{120} + \frac{3d}{120} = 5 )", "Mastering algebra often begins with understanding the concept of common denominators, especially when solving equations involving fractions. One clear example is solving:", "[\n\frac{2d}{120} + \frac{3d}{120} = 5\n]", "In this equation, both terms share the same denominator—120—making it a perfect candidate for simplification using the common denominator approach. Let’s walk through the step-by-step solution in a clear, effective way that also boosts your understanding.", "---", "### Why Common Denominator Matters in Algebra", "When working with fractions, combining terms becomes straightforward only when they share a common denominator. In this equation, since both fractions have the same denominator, we can combine the numerators directly:", "[\n\frac{2d + 3d}{120} = 5\n]", "This simplification is the first critical step that simplifies the problem:", "[\n\frac{5d}{120} = 5\n]", "---", "### Step 1: Simplify the Fraction", "Now that the fractions are combined, reduce the fraction ( \frac{5d}{120} ) by dividing both numerator and denominator by their greatest common divisor (GCD), which is 5:", "[\n\frac{d}{24} = 5\n]", "This reduced form makes the equation easier to solve and clearly expresses ( d ) in terms accessible to typical problem-solving contexts.", "---", "### Step 2: Solve for ( d )", "To isolate ( d ), multiply both sides of the equation by 24:", "[\nd = 5 \ imes 24\n]", "[\nd = 120\n]", "---", "### Final Verification", "Plug ( d = 120 ) back into the original equation to confirm correctness:", "[\n\frac{2(120)}{120} + \frac{3(120)}{120} = \frac{240}{120} + \frac{360}{120} = 2 + 3 = 5\n]", "The equation balances perfectly—our solution is correct.", "---", "### Why This Example Matters for Students and Learners", "This problem demonstrates foundational algebraic skills: combining fractions with a common denominator, simplifying rational expressions, and isolating variables. Understanding common denominators is crucial for correctly adding or subtracting fractions—skills necessary not just in math, but in science, finance, and everyday calculations.", "Key Takeaways:", "- Always combine fractions first only when they share the same denominator.\n- Simplify fractions afterward by dividing numerator and denominator by their GCD.\n- Multiply both sides of an equation by the denominator to eliminate the fraction.\n- Always verify your solution by substituting back into the original equation.", "---", "### Bottom Line", "Solving ( \frac{2d}{120} + \frac{3d}{120} = 5 ) teaches you how to find a common denominator effortlessly, simplify expressions, and solve linear equations with clarity. Whether you're preparing for exams, tackling homework, or building algebraic intuition, mastering this technique empowers you to handle more complex equations with confidence.", "Practice Tip: Try rewriting the equation using a different common denominator first—though unnecessary here—to reinforce the core concept before applying it alone.", "---", "Keywords for SEO:\nfind a common denominator, solve (\frac{2d}{120} + \frac{3d}{120} = 5), algebra tutorial, simplifying fractions, combine fractions, solve linear equations, math education, rational expressions, algebra practice\nMeta Description:\nMaster how to solve (\frac{2d}{120} + \frac{3d}{120} = 5) by finding a common denominator, simplifying expressions, and isolating variables. Step-by-step algebra guide for students and learners."]