\[ \frac{d}{80} + \frac{d}{60} = 7 \]

["# Solving the Equation: (\frac{d}{80} + \frac{d}{60} = 7) in Simple Steps", "Understanding how to solve equations involving fractions is a fundamental math skill, especially useful in algebra, physics, engineering, and everyday problem solving. This article walks you through solving the equation (\frac{d}{80} + \frac{d}{60} = 7), explaining each step clearly so you can build confidence in handling similar problems.", "---", "## What Is the Equation?", "We begin with:", "[\n\frac{d}{80} + \frac{d}{60} = 7\n]", "This equation involves two fractions with constants (d) in the numerator and fixed denominators (80 and 60). Our goal is to isolate (d) and find its numerical value.", "---", "## Step 1: Combine Like Terms", "Both terms on the left contain (d), so factor (d) out:", "[\nd\left(\frac{1}{80} + \frac{1}{60}\right) = 7\n]", "This turns the equation into a product: (d) multiplied by a sum of fractions.", "---", "## Step 2: Add the Fractions", "To add (\frac{1}{80}) and (\frac{1}{60}), find the least common denominator (LCD). The prime factors of 80 are (2^4 \cdot 5), and for 60: (2^2 \cdot 3 \cdot 5). The LCD is (2^4 \cdot 3 \cdot 5 = 240).", "Convert each fraction:", "[\n\frac{1}{80} = \frac{3}{240}, \quad \frac{1}{60} = \frac{4}{240}\n]", "Add them:", "[\n\frac{3}{240} + \frac{4}{240} = \frac{7}{240}\n]", "---", "## Step 3: Substitute and Simplify", "Now replace the sum in the equation:", "[\nd \cdot \frac{7}{240} = 7\n]", "---", "## Step 4: Solve for (d)", "Divide both sides by (\frac{7}{240}). Dividing by a fraction is the same as multiplying by its reciprocal:", "[\nd = 7 \cdot \frac{240}{7}\n]", "Cancel the 7 (assuming (d <br/>\ne 0)):", "[\nd = 240\n]", "---", "## Final Answer", "[\n\boxed{d = 240}\n]", "---", "## Why This Equation Matters", "Solving equations like (\frac{d}{80} + \frac{d}{60} = 7) is more than just homework — it's essential in:", "- Rate problems: When combining work rates or speed comparisons\n- Physics and engineering: For calculating combined resistances, capacitances, or rates\n- Financial math: When dealing with proportional dividends or shared costs", "Understanding how to combine fractions and isolate variables empowers problem-solving across disciplines.", "---", "## Pro Tips", "- Always find the least common denominator (LCD) before adding fractions.\n- Use reciprocal multiplication when dividing by a fraction.\n- Verify your solution by plugging (d = 240) back into the original equation.", "Check:\n[\n\frac{240}{80} + \frac{240}{60} = 3 + 4 = 7 \quad \checkmark\n]", "---", "By mastering this solving technique, you strengthen your algebraic foundation and become more confident in complex math scenarios. Keep practicing — every equation brings you one step closer to fluency!"]