Zero multiplied by anything is ZERO

I had mentioned about a Science Teacher who taught me an important lesson in English, in "You just killed John Milton."  Now I remember a Mathematics Teacher who taught me a secret of life. Through a formula of Mathematics.

I was in Standard IX and sitting in an Algebra class. The teacher was a short man but very strict as most teachers in that era were. Students were afraid of him even though he did not say or do anything to fear him. He was explaining solving a mathematical problem and writing on the blackboard. All the students were engrossed in the solution of the sum. He went step by step and came to the penultimate step. He said "Since a is zero, a multiplied by b is also zero,  since zero multiplied by anything is zero". A fundamental doubt crept up in my mind. How can it be? Zero multiplied by 10 is also zero. Zero multiplied by 100 is also zero. Zero multiplied by 1000 is also zero. Is it correct? Is it fair? Does the other number has no significance?

If I ask a question he may not like it. He may even say "Don't you know even this basic thing? How did you come to class IX?", like many other teachers. I had not raised this questions when the same issue was dealt in earlier classes. He may remind me of that and may admonish me for raising the question rather belatedly. He may get angry and throw the duster at me, as he did on students sleeping in his class. I somehow mustered courage, got up and asked him: "How is it possible? How is any number multiplied with zero is zero, Even when the other number is big or small?".

He stopped his lecture, looked at me for a moment. Like Bumble the Beadle looked at Oliver Twist when Oliver Twist asked for some more of the gruel. ( Oliver Twist, the famous novel by Charles Dickens was prescribed as a Non-detailed text for Standard IX and was being taught in parallel English classes). I froze where I stood.

He called me to where he was standing. I complied hesitantly. "Go out and bring a handful of Small stones.", he ordered. I went out immediately and collected a handful of small stones, each of the size of a groundnut. Why does he want small stones when he has a big duster with him?, I wondered. Sheepishly I came back to the class with a handful of the stones. "Put them on the table ", he commanded.  The classroom had a platform on which a table and chair were kept for the teachers. I put the pebbles on the table. "Turn around and face your friends" he said. I complied dutifully.

He divided the pebbles into heaps of four. Six heaps making a total of twenty four. Remaining pebbles were kept aside. Now I was confident that he would not throw the pebbles at me. Some cheer returned to my face. Oh, now I am a part of some experiment, I told myself. He asked me to open my right palm and and stretch it. "Look, here I have pebbles of four each in a group. I put them in your hand. Now count them.", he said and put the first lot of four in my hand.

"Four multiplied by one. How much?".  "Four" was the answer. All the students were watching us.
"Four multiplied by two. How much?"   "Eight"
"Four multiplied by Three..........."  "Twelve".
...............................................................................
"Four multiplied by six".    "Twenty four".

He took away all the pebbles. I was standing with outstretched right palm. "Now I will give you stones in lots of zero. Count", he said.

"Zero multiplied by one. How much?"   "Zero".
"Zero multiplied by two"             "Zero"
"Zero multiplied by three"    "Zero"
................................................
"Zero into ten"        "Zero"

"Zero multiplied by anything!"   The entire class shouted    "ZERO".

I was asked to get back to my seat. I went back like a hero and sat in my place.

He was now addressing the entire class. "Remember,  all of you. Do not hesitate to ask a question if you do not understand anything. Anything, however silly the question may appear. Do not worry about what others think. You are learning for yourself. Others are not going to help you when you go out in the world and are on your own. Now let us get back to Algebra!". He had read my mind perfectly!

When I was in college I met him once and reminded him about the incident. "Zero multiplied by anything is Zero. That I will never forget, Sir", I said.  "There is more to the formula than what you learnt that day. It is true of life as well. Returns in life are proportionate to the investment you make. If you make zero investment, however much you slog, returns are always  Zero. If you invest at least interest you will reap manifold returns, in proportion to your hard work. I am not referring to Principle and Interest of Mathematics. It is INTEREST in what you do", he said and winked in a rare moment of humour and affection.