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Odd fishing

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An old man lived by the river Kaveri.

He used to catch fish for a living. But he did not eat fishhimself.

Everyday he caught fish and sold them in the evening atthe market.

He was not a greedy man.

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One day his grandson saw him throwing back a fish into the river.“Grandpa, why did you do that?” he asked.

“Little one, I need to earn, so I catch fish.But I don’t need too much money.So I put back some fish into the river.”

“And how do you decide which fishto put into the basket and which fishto throw back into the river?”

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“Each day, I make up a rule for myself. Yesterday,I threw back the first fish I caught, kept the second,threw back the third, kept the fourth…”

“I know, you threw back Fish 1, Fish 3, Fish5………..You threw back the Odd-numbered fish!”

“That’s right. Today, I kept the first fish, threw back the second, kept the third, threw back the fourth…”

“All the even-numbered ones went back into the river. Poor odd-numbered ones!”

“Tomorrow, I’m going to need a little more money. So I’ll have a new system. Fish numbers 2, 3, 5, 7, 11, 13, 17, 19, 23, and soon will go back into the river. The rest will get into my basket.

“Grandpa, how many fishes do you sell each day?”
“About 50.”

1 is an odd number. 2 is an even number.

Numbers that cannot be divided by 2 are called odd numbers.

Numbers that can be divided by 2 are called even numbers.

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According to the story, how many fish went back into the river yesterday?

50. To sell 50 fishes, Grandpa would have to catch 100 fishes on Day 1. The odd ones went back into the river.

Did he throw back more or less number of fish today? How many fish went into the basket today?

Less. He threw back 49 fishes. 50 fishes went into the basket.

They are prime numbers. 2 can be divided by 1 and 2. 3 can be divided by 1 and 3. Four can be divided by 1, 2, and 4. 4 is not aPrime number.

Tomorrow, Grandpa has to really think hard before throwing back the fish. There is something special about thenumbers 2, 3, 5, 7, …. Can you guess what?

How many fishes did Grandpa catch today?

99 fishes. When he caught the 99th fish and put it in his basket, 4. , he had 50 fishes in the basket. So he did not have to catch the 100thfish to throw back!

A prime number is a number that can be divided exactly by two numbers,1 and by itself.1 can be divided ONLY by 1. So 1 is not a prime number. 13 can be divided by 1. It can be divided by 13. So it is aprime number. 15 can be divided by 1, 3, 5, and 15. So it is not a prime number. Can you count the number of primenumbers between 1 and 50?

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15 prime numbers. In a grid, write numbers 1 to 50. After 3, cut out all the even numbers (They can all be divided by 1,2 and themselves.So they are not prime). Cut out all the numbers that can be divided by 3. (6, 12 etc. They are all divisible by 1, 3 and themselves.So they are not prime.) Cut out all the multiples of 5. (Why?) Then finally, cut out all the numbers that can be divided by 10. Theremaining numbers are prime numbers.

Bits and pieces

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Eka, have you seen the Hindi film ‘Sholay’?

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Source:  OpenStax, Class. OpenStax CNX. Dec 24, 2010 Download for free at http://cnx.org/content/col11261/1.3
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