Consider the following phrases: "4 by 6" and "3 into 12." To which of the four arithmetic operations are these referring? If you said, multiplication and division, respectively, I can conclude one thing. You are not from India.
I recently began tutoring a young woman who immigrated here from India last year. Through a series of unfortunate events, she has experienced a 6 year gap in her education. At 18 years old, she is only eligible to attend public school for one more year. After that, she must pursue a GED. She is actually a very capable young mathematician, although she needs to build confidence.
During our first few lessons, she appeared to be confusing multiplication with division. After speaking with her father, I discovered that I was the one who was confused. Or rather, we were suffering from a miscommunication. Evidently, in India, the word "by" denotes division and "into" refers to multiplication.
Isn't that delightfully fascinating? I think so.