The butterfly method is used in Japan to teach addition or subtraction of two fractions. Japanese schools teach this method and encourage students to "forget" the butterfly drawing as they get better using the method.
To add or subtract fractions the butterfly way,
1. Write the fractions side-by-side as usual and draw two wings along the diagonals made by the numerator of one fraction and the denominator of the other fraction and draw an antenna on each wing.
2. As suggested by the wings, that look like a multiplication sign, multiply the numbers in each wing and put the product in the antenna for the wing.
3. Think or say: “This poor butterfly needs a body.” To give it a body, connect the bottom parts of the wings with a body-like loop and multiply the two denominators it connects, putting the product inside the body.
5. If necessary, reduce or simplify the result.