Final answer:
The question is about simplifying a complex fraction by performing arithmetic operations with fractions and maintaining equality throughout the steps. The operations include finding common denominators, working with reciprocals, and understanding the relationship between multiplication and division.
Step-by-step explanation:
The student's question involves performing arithmetic operations with fractions to simplify an expression. The question shows a sequence of steps that simplifies the expression 54 + 1/6 * 9 + 5/13 into the fraction 25/12. To simplify the fraction 15, the approach would involve multiplying the numerator and denominator by the same factor to obtain common denominators, and applying the properties of reciprocal by flipping the fraction upside-down when dividing.
Understanding expressions and equations, as well as the property that implies any fraction with the same quantity in the numerator and denominator equals 1, are critical for apprehending the nature of the operations conducted in the problem.
Additionally, grasping the concept that multiplication and division are inversely related helps in simplifying fractions. Performing the equivalent function on both sides of an equation maintains equality, which is important when solving complex fractions. This knowledge is vital in different aspects of arithmetic operations and is often reinforced through practice.