1/2 + 1/2 = 1/4 + 1/4 + 1/4 + 1/4.
He also may say that two halves are equal to four fourths, and write accordingly:
2/2 = 4/4.
This is merely the expression of the same thing. Seeing the pieces, he has done an example mentally and then has written it out. Let us write it according to the first form, which is, in reality, an analysis of this example:
1/2 + 1/2 = 1/4 + 1/4 + 1/4 + 1/4.
When the denominator is the same, the sum of the fractions is found by adding the numerators:
1/2 + 1/2 = 2/2; 1/4 + 1/4 + 1/4 + 1/4 = 4/4.
The two halves make an entire circle, as do the four fourths.