\[ p = \frac{2\left(\frac{49}{29}\right) + 8}{3} \]

["Simplify the Expression: Step-by-Step Solution for ( p = \frac{2\left(\frac{49}{29}\right) + 8}{3} )", "Understanding how to simplify complex fractions and expressions is essential in algebra, math education, and real-world problem solving. One such expression commonly encountered involves arithmetic operations and division:\n[\np = \frac{2\left(\frac{49}{29}\right) + 8}{3}\n]", "This article walks you through the step-by-step simplification of this expression, breaking down each operation to help you master similar algebraic manipulations.", "---", "### Step 1: Evaluate the Parentheses\nStart by simplifying the numerator:\n[\n2\left(\frac{49}{29}\right) + 8\n]\nMultiplying the fraction first is clearer:\n[\n2 \ imes \frac{49}{29} = \frac{98}{29}\n]\nNow add the whole number 8. To add, convert 8 to a fraction with denominator 29:\n[\n8 = \frac{8 \ imes 29}{29} = \frac{232}{29}\n]\nNow add:\n[\n\frac{98}{29} + \frac{232}{29} = \frac{98 + 232}{29} = \frac{330}{29}\n]", "---", "### Step 2: Divide by 3\nNow substitute the simplified numerator back into the original expression:\n[\np = \frac{\frac{330}{29}}{3}\n]\nDividing by 3 is the same as multiplying by (\frac{1}{3}):\n[\np = \frac{330}{29} \ imes \frac{1}{3} = \frac{330}{29 \ imes 3} = \frac{330}{87}\n]", "---", "### Step 3: Simplify the Fraction\nReduce (\frac{330}{87}) by finding the greatest common divisor (GCD) of numerator and denominator. The number 87 factors into (3 \ imes 29), and 330 is divisible by 3:\n[\n330 \div 3 = 110, \quad 87 \div 3 = 29\n]\nSo:\n[\n\frac{330}{87} = \frac{110}{29}\n]", "---", "### Final Answer:\n[\n\boxed{p = \frac{110}{29}}\n]", "---", "### Why This Matters\nThis problem illustrates key algebraic skills:\n- Dominating fractions: Correctly multiplying across denominators.\n- Adding mixed expressions: Combining fractions and whole numbers via common denominators.\n- Simplifying rational expressions: Reducing fractions to lowest terms using prime factorization.", "Mastering such steps builds confidence for advanced algebra, scientific calculations, financial modeling, and more.", "---", "Keywords for SEO:\np = (\frac{2\left(\frac{49}{29}\right) + 8}{3}), algebraic expression simplification, solving fractions, intermediate algebra, step-by-step math solving, how to simplify rational expressions, math tutorial, fractional arithmetic, division of fractions, reducing fractions to simplest form.", "---", "Turn simplifying ( p ) into a habit — and unlock clearer thinking in every equation!"]