One day my tenth-grade math teacher walked into our classroom and said, "Class, today to start off the class I've got an addition problem for you. Give me any two positive proper fractions and I'll add them up."
Some of us were a bit bewildered at that, but one of the students decided to bite. "1/2 plus 1/2", he said.
"11/20", answered our teacher.
We were a bit surprised. "Shouldn't that be 1, teacher?"
"Nope," he said. "I'm not using your standard addition algorithm today."
"Alright, what about 1/3 + 2/3"?
"That's 4/11", said the teacher.
"How about 2/9 + 7/9?"
"That's 3/11."
The teacher wrote our questions and his answers on the board along with a few more:
1/2 + 1/2 = 11/20
1/3 + 2/3 = 4/11
2/9 + 7/9 = 3/11
3/20 + 4/20 = 1/8
1/9 + 1/9 = 1/9
1/30 + 5/6 = 1/12
Can you figure out what addition algorithm the teacher was using?