Children love it when teacher tells a story instead of giving the usual lesson. This class of 9 year olds was thrilled when the teacher said that today it was story time.
“Long time ago, there was a king who worshipped the sun every morning. He was named Maharaja Suryaman. He was tall and good looking. He was also very brave like a king should be. The people loved the king but his enemies feared him because he also had a large army.
Maharaja Suryaman respected intellectuals (smart and wise people with knowledge). To show his respect for them, he called them Buddhiman (one who has intellect). He used to meet with them once a month. At the end of each meeting, every Buddhiman received a good meal and a gift. If they told him something he liked, he gave them big prizes.
One day, a Buddhiman raised his hand and asked the king: Great Maharaja, may I ask your highness what is the exact size of your army?
Maharaja: Buddhiman, I am very proud of our army of brave soldiers. We have three units of 9 horseback soldiers with swords, three units of 9 foot soldiers who carry bows and arrows, and another three units of 9 foot soldiers who carry spears. We have a very strong army.
The king had to count this way. At that time, 9 was the largest number known. He would have to say how many nines or how many nines of nines. He couldn’t even properly count his wealth or the number of people living in his kingdom.
Buddhiman gifted the king an egg
Buddhiman: I have a gift for your highness – an egg.
Maharaja’s face turned red with anger. He said: Buddhiman, remain within your limits. Don’t insult me with this small gift. I have nines of nines of nines of eggs in my farm.
Buddhiman: Your greatness, this is not just an ordinary egg from a farm. It is a new symbol. I will name it after your wisdom, and call it Surya. Based on this egg, I propose a new counting system. We will use the numbers 1 to 9 but we will also have a next number which will be called ten and written as 10. Then you can write 11, 12 and so on until you reach 19. Again you can use Surya to make 20 as the next number after 19. You can continue the same way as 90, 91, 92 and so on then after 99, you could write 100.
Now the king could count his army
The king was confused and said: Buddhiman, what does this symbol have to do with the size of my army?
Buddhiman: Brave Maharaja, using this system two nines will become 18 and three nines will be 27. Therefore, your army would consist of 27 horseback soldiers, 27 foot soldiers with bows and arrows and another 27 with spears. Then you can add all of them and say that there are 81 soldiers in your army. Very simple, no confusion of how many nines.
The king thought for a moment and then he said happily: If I add 9 more soldiers, I will have 90 soldiers in the army. Buddhiman, is that what you are saying?
Buddhiman: Yes, your highness. See the simplicity. Nine plus one will become 10, and then will come 11, 12 and so on until 19 which will be followed by 20. The sum of 10 tens will be 100, the sum of 10 hundreds will become 1000 and so on. You could keep going and writing bigger numbers. This counting system will allow you to count your enormous wealth, and you could also determine the number of subjects in your kingdom.
The king was thrilled at this invention. He saw wisdom in this counting system. He gave the Buddhiman a big prize: a house, a farm and some cattle. However, he told the court that the egg symbol will not be called Surya but Shunya. Then onwards shunya became a popular concept in India, and in other places it was also called a zero or a cipher.
The king gave the prize but he also asked the Buddhiman to explain to everyone how they would use this system for adding, multiplying and dividing . It was a huge task. Buddhiman had his honour to save. He had already been given a reward to last him his whole life.
In the next meeting, the king asked Buddhiman to show how to add using this system. The king said, “The farmer has only ten fingers. How will he add numbers bigger than 10 in your system.”
Buddhiman: For 9 + 2, the farmer will first add one and get 10. From 10, he can carry over the 1 to the left side with his shovel. On the right side, he can add the remaining 1 to the 0 to get 1. This way he will have 11. Your highness has 81 soldiers. If you were to conquer an empire with 69 soldiers, you could say that 69 = 60 + 9 and then add them like this:
|Add 1+9 to get 10, carry over 1 to the left||1||0|
|Add the carry over 1 to 8||9||0|
|Carry over 1 to the left to get the final answer||1||5||0|
The king looked at the other Buddhimans. They liked the system but said that the farmer would have to be taught how to use it. The subtraction was also done the same way because the farmer could borrow a carry over “1” if needed.
Peter: Sir, this was not a story. You just tricked us into learning addition and subtraction.
Teacher: Peter, you catch on fast. Come to the board and show us how to use this idea for multiplication. Multiply 63 by 12 using the carry over.
Peter: 10 + 2 = 12. So I will first multiply 63 by 2, this will give me 126 because 1 will be carried over from 6 x 2 to become 12. Now 63 x 10 is 630. Adding 630 and 126 will give me 756.
Teacher: The farmer will also have to do the division. Tanya, can you show us the long division now? Show us how to divide 425 by 25.
Tanya: I would not do the long division. I know that 25 x 4 = 100 and 425 x 4 = 1700. So the answer will be the same as 1700 divided by 100 which is 17.
The long division
Tinku: Sir, Tanya loves short cuts. I can do the long division step by step.
Here, I will write the dividend 425, and on the left side I will write the divisor 25. First, I try to find 4 divided by 25. Because 4 is smaller than 25, I will write 0 (or nothing) in the answer on top of the line. Then I will bring down 5 to get 42. 25 times 1 is 25. Therefore, in the answer I will add 1. Calculating 42 minus 25 gives me 17. Now I will bring down 5 to make it 175. Now 25 x 7 = 175. Therefore, in the answer I will add 7 on the right hand side. Subtracting 175 from 175 gives me a zero. That means there is no remainder, and the answer is 17.
Teacher: Tinku. Very good. As you pointed out, sometimes even after the division you may have a remainder. Everyone should do some practice questions at home.
Harry went home and talked to his father: Dad, you used to get angry at me when I did the addition and subtraction using my fingers.
Harry’s father: That’s because you have only 10 fingers, and after that you were always stuck and had to remove your shoes.
Harry: Our math teacher told us a very good story today. Now I can do big sums too.
Then Harry told his father the whole story about the Maharaja Suryaman. The father was happy but he was even more impressed when the teacher used the story for a play at the annual school function.
A toy store has 3456 toys to give away. They give 9 toys to each person in the line. You are number 400 in the line. How many persons will get the toys? Some people are leaving because the line is too long. How many will have to leave for your chance to come?
Solution: There are 3456 toys and 9 toys per person. That means the dividend is 3456 and the divisor is 9. The long division shows that there are enough toys for 384 persons in the line. If you are 400th in line, that means 400 minus 384 or 16 persons will have to leave the line so that you get a chance to get your toys.