Examine these equations one by one, treating each after some such manner as follows:
How might we obtain the numerator 18 from the numerator 3? (Multiply by 6.)
The denominator 30 from the denominator 5? (Multiply by 6.)
If we multiply both the numerator and the denominator of the fraction 3/5 by 6, what will be the effect upon the value of the fraction? (It will be unchanged.)
What have we done with the numerator and denominator in every case? How has the fraction been affected? What rule may we infer from these examples? (Multiplying the numerator and denominator by the same number does not alter the value of the fraction.)
THE FORMAL STEPS
In describing the process of acquiring either a general notion or a general truth, the psychologist and logician usually divide it into four parts as follows:
1. The person is said to analyse a number of particular cases. In the above examples this would mean, in the conceptual lesson, noting the various characteristics of the several words, John, Toronto, desk, etc.; and in the second lesson, noting the facts involved in the several cases of shading.