\frac{1}{2} \left( \frac{3}{2} - \frac{103}{2652} \right) = \frac{1}{2} \left( \frac{3978 - 103}{2652} \right) = \frac{1}{2} \cdot \frac{3875}{2652} = \frac{3875}{5304}

["Understanding the Equation: \frac{1}{2} \left( \frac{3}{2} - \frac{103}{2652} \right) = \frac{3875}{5304}", "Solving mathematical expressions step by step not only clarifies the solution but also improves understanding for learners and professionals alike. This article explains how to simplify and evaluate the equation:", "[\n\frac{1}{2} \left( \frac{3}{2} - \frac{103}{2652} \right) = \frac{3875}{5304}\n]", "---", "### Step 1: Rewrite the Subtraction Using a Common Denominator", "To subtract (\frac{3}{2}) and (\frac{103}{2652}), we first convert (\frac{3}{2}) into a fraction with denominator 2652.", "[\n\frac{3}{2} = \frac{3 \ imes 1326}{2 \ imes 1326} = \frac{3978}{2652}\n]", "Now substitute back:", "[\n\frac{1}{2} \left( \frac{3978}{2652} - \frac{103}{2652} \right) = \frac{1}{2} \cdot \frac{3978 - 103}{2652}\n]", "---", "### Step 2: Perform the Subtraction in the Parentheses", "Subtract the numerators:", "[\n3978 - 103 = 3875\n]", "So the expression becomes:", "[\n\frac{1}{2} \cdot \frac{3875}{2652}\n]", "---", "### Step 3: Multiply by (\frac{1}{2})", "Multiplying by (\frac{1}{2}) is equivalent to dividing by 2, which means dividing numerator by 2:", "[\n\frac{1}{2} \cdot \frac{3875}{2652} = \frac{3875}{2 \ imes 2652} = \frac{3875}{5304}\n]", "---", "### Final Result", "[\n\boxed{ \frac{1}{2} \left( \frac{3}{2} - \frac{103}{2652} \right) = \frac{3875}{5304} }\n]", "This final form is reduced and also verified algebraically, offering clarity for students, educators, and anyone who values exact, well-explained math.", "---", "### Why This Process Matters", "Step-by-step simplification improves accuracy and comprehension. By expressing fractions with common denominators and carefully combining terms, we ensure the result is precise and transparent. This kind of detailed breakdown helps learners grasp not just the answer, but how to achieve it reliably.", "Whether you're studying math for school, solving real-world problems, or enhancing your analytical skills, understanding how to manipulate and simplify fractions is essential. Breaking equations like this one step by step builds confidence and competence in mathematical reasoning."]