Finding a common denominator, we get \(\frac{2d}{120} + \frac{3d}{120} = 5\).
["Finding a Common Denominator: Solving (\frac{2d}{120} + \frac{3d}{120} = 5)", "In algebra, one of the essential skills is learning how to combine fractions by finding a common denominator. This concept becomes especially valuable when solving equations like:\n[\n\frac{2d}{120} + \frac{3d}{120} = 5\n]", "At first glance, working with fractions may seem challenging, but with a clear process, solving for the variable becomes straightforward. Let’s walk through the steps to solve this equation and understand why finding a common denominator is a critical first move.", "### Step 1: Combine Like Terms Using a Common Denominator\nBoth fractions in the equation share the same denominator—120—so adding them is simple:\n[\n\frac{2d}{120} + \frac{3d}{120} = \frac{2d + 3d}{120} = \frac{5d}{120}\n]\nSince the denominators are identical, we combine the numerators directly.", "### Step 2: Set the Simplified Fraction Equal to the Right Side\nNow the equation looks like:\n[\n\frac{5d}{120} = 5\n]", "### Step 3: Eliminate the Denominator\nTo eliminate the fraction, multiply both sides of the equation by 120:\n[\n5d = 5 \ imes 120\n]\n[\n5d = 600\n]", "### Step 4: Solve for (d)\nNext, divide both sides by 5:\n[\nd = \frac{600}{5} = 120\n]", "### Final Answer\nThe solution to the equation is (d = 120). By first finding a common denominator and simplifying the fractions, the problem becomes manageable and easily solvable.", "---", "### Why Finding a Common Denominator Matters\nFinding a common denominator ensures that fractions have identical bases, allowing direct addition or subtraction. This foundational technique not only simplifies complex fraction problems but also strengthens logical reasoning in algebra. Whether you’re solving linear equations or more advanced mathematical models, mastering this step simplifies the process and reduces errors.", "So next time you encounter a sum of fractions with the same denominator, remember: combining them first is a smart move that unlocks clarity and simplicity in algebraic problem-solving.", "---", "Keywords: Finding a common denominator, algebra, solving equations, (\frac{2d}{120} + \frac{3d}{120} = 5), step-by-step math, simplify fractions, algebra tip, solving linear equations.\nMeta Description: Learn how to find a common denominator and solve (\frac{2d}{120} + \frac{3d}{120} = 5) with clear steps and detailed explanation.\nSuggested Tags: #Algebra #FractionMath #SolvingEquations #CommonDenominator #MathTutorial #HighSchoolMath"]
