91Ó°ÊÓ

Evaluating expressions is a fundamental skill in mathematics. It involves replacing variables in an expression with specific numerical values. After substitution, you compute the result based on arithmetic rules. In this example, you start with the expression \( \frac{7x + 2y}{3x} \). The task is to substitute \( x = 2 \) and \( y = 5 \), while \( z \) is not relevant here. After substitution, the expression becomes \( \frac{7(2) + 2(5)}{3(2)} \). This replacement is crucial as it transitions an algebraic expression into a numerical form ready for computation.

Fractions can appear daunting, but they simplify magically with the right approach. After substituting the given variables, as in \( \frac{7(2) + 2(5)}{3(2)} \), simplifying involves two steps:

• Simplify the numerator and denominator separately.
• Perform division to simplify the fraction as a whole.

In our example, handle the numerator step-by-step: first, calculate \( 7 \times 2 = 14 \) and \( 2 \times 5 = 10 \). Combine these to make \( 24 \), turning the expression into \( \frac{24}{6} \). Finally, divide \( 24 \) by \( 6 \) to get \( 4 \). Simplifying fractions means getting to the core number representing your total value in a more comprehensible manner.

At the heart of evaluating expressions lies basic arithmetic—addition, subtraction, multiplication, and division.
In this problem, multiplication and addition are used in the numerator, while division simplifies the whole fraction. Start with multiplying the variable's coefficient with its substitution value: \( 7 \times 2 = 14 \) and \( 2 \times 5 = 10 \).

• Add these results to handle the numerator: \( 14 + 10 \).
• Result: \( 24 \).

Do not overlook division, which simplifies the final number: \( \frac{24}{6} = 4 \). Understanding these operations helps unravel any complex expression by boiling it down into simple, manageable tasks. Each step in performing basic arithmetic operations paves the way for an accurate solution, showing how math builds upon itself.