"k[subscript cat]/K[subscript M]" is a fundamental kinetic parameter as important as "k[subscript cat]" in enzyme kinetics. Although the parameter provides critical information on how the enzyme lowers the energy barriers along the reaction pathway for catalysis, "k[subscript cat]/K[subscript M]" is frequently considered as a composite or derived parameter to assess both "k[subscript cat]" and "K[subscript M]" together rather than as a fundamental kinetic parameter. The main challenge of teaching the meaning and the value of "k[subscript cat]/K[subscript M]" to students is the difficulty in explaining how the reaction energetics of enzyme catalysis determine "k[subscript cat]/K[subscript M]." This report demonstrates a step-by-step process to visualize the meaning of "k[subscript cat]/K[subscript M]" on the reaction free energy diagram. The reciprocal form of the expression of "k[subscript cat]/K[subscript M]" shows that "k[subscript cat]/K[subscript M]" is a harmonic sum of kinetic terms that correspond to the heights of the transition states relative to the free enzyme. Then, it is demonstrated that the height of the highest transition state has the dominant influence on "k[subscript cat]/K[subscript M]." The visualization of the meaning of "k[subscript cat]/K[subscript M]" on the reaction free energy diagram offers an intuitive way to understand all the known properties of "k[subscript cat]/K[subscript M]," including the Haldane relationship, which will greatly enhance the students' learning of the fundamental concepts in enzyme kinetics.