\[ 2 \left( \frac{1}{4} + \frac{1}{6} \right) = 2 \left( \frac{3}{12} + \frac{2}{12} \right) = 2 \times \frac{5}{12} = \frac{10}{12} = \frac{5}{6} \text{ of the tank} \]

["Mastering Basic Fraction Addition: Solving ( 2 \left( \frac{1}{4} + \frac{1}{6} \right) = \frac{5}{6} ) of the Tank", "Understanding how to add fractions and apply operations is essential in mathematics and real-life problem solving—especially when managing fractions in practical scenarios like filling a tank. Today, we explore the step-by-step breakdown of the equation:", "[\n2 \left( \frac{1}{4} + \frac{1}{6} \right) = 2 \left( \frac{3}{12} + \frac{2}{12} \right) = 2 \ imes \frac{5}{12} = \frac{10}{12} = \frac{5}{6}\n]", "This simple expression reveals how combining parts of a whole yields precise results—perfect for understanding tank capacity, resource allocation, or any proportion-based calculation.", "### Breaking Down the Equation Step by Step", "#### Step 1: Add the Fractions Inside the Parentheses\nTo sum ( \frac{1}{4} + \frac{1}{6} ), find the least common denominator (LCD).\nThe denominators are 4 and 6. The least common multiple of 4 and 6 is 12.", "Convert each fraction:\n- ( \frac{1}{4} = \frac{3}{12} )\n- ( \frac{1}{6} = \frac{2}{12} )", "Now add:\n[\n\frac{3}{12} + \frac{2}{12} = \frac{5}{12}\n]", "#### Step 2: Multiply by the Outer Coefficient\nNext, multiply the result by 2:\n[\n2 \ imes \frac{5}{12} = \frac{10}{12}\n]", "#### Step 3: Simplify the Fraction\nReduce ( \frac{10}{12} ) to lowest terms:\n[\n\frac{10 \div 2}{12 \div 2} = \frac{5}{6}\n]", "So,\n[\n2 \left( \frac{1}{4} + \frac{1}{6} \right) = \frac{5}{6} \ ext{ of the tank}\n]", "### Why This Matters in Real Life", "Imagine you're filling a water tank in a construction or automotive context. If two pipes together fill ( \frac{1}{4} + \frac{1}{6} ) of the tank per hour, multiplying by 2 hours means the tank reaches exactly ( \frac{5}{6} )—meaning just five-sixths full. This kind of math helps professionals estimate completion time, capacity usage, and fluid distribution with precision.", "### Visualize It with Practical Examples", "- Fractional tank filling: Two pumps working together fill ( \frac{1}{4} + \frac{1}{6} = \frac{5}{12} ) of the tank in one hour. After two hours, total fill is ( 2 \ imes \frac{5}{12} = \frac{10}{12} = \frac{5}{6} ).\n- Volume calculations: If a tank’s total capacity is 1 (full), pouring ( \frac{1}{4} + \frac{1}{6} ) each hour accumulates quickly; knowing ( 2 \ imes \frac{5}{12} = \frac{5}{6} ) tells exactly when it’s nearly full.", "### Key Takeaways", "- Always find a common denominator before adding fractions.\n- Multiplying a sum of fractions by a coefficient adjusts the total proportion quickly.\n- Simplifying fractions ensures clarity and accuracy in calculations.\n- This method applies directly to real-life tank or volume management across industries.", "Understanding these principles removes complexity from fraction-based problems and empowers precise, confident decision-making.", "---", "In summary:\n[\n2 \left( \frac{1}{4} + \frac{1}{6} \right) = \frac{5}{6} \ ext{ of the tank}\n]\nMaster fraction arithmetic—because every part counts!", "Keywords: fraction addition, simplifying fractions, common denominator, tank capacity calculation, real life math, arithmetic steps, practical fractions, online math tutorial"]