Medium 1) \( 5 a-\frac{7}{8} k+\frac{4 k}{8} \) 1)

To simplify the expression \( 5a - \frac{7}{8}k + \frac{4k}{8} \), start by combining the terms involving \( k \). Notice that \( \frac{4k}{8} \) simplifies to \( \frac{1}{2}k \) or \( \frac{4}{8}k \). So, we can rewrite the expression like this: \[ 5a - \frac{7}{8}k + \frac{4}{8}k = 5a - \left(\frac{7}{8}k - \frac{4}{8}k\right) = 5a - \frac{3}{8}k. \] Thus, the simplified expression is \( 5a - \frac{3}{8}k \). Taking a look at real-world applications, simplifying algebraic expressions is crucial in fields like engineering and economics. Engineers often use algebra to model and solve problems related to forces and loads, while economists simplify expressions to analyze market trends and optimize resources. For problem-solving tips, it's important to carefully combine like terms and simplify fractions step-by-step to avoid mistakes. A common error is neglecting to convert coefficients to a common denominator, leading to incorrect summation of terms. Always double-check your calculations for accuracy!