Divisio’s Problem
Long ago, in the distant land of Mathematica, there was a small town called Decimalia which was an elegant town of grand architecture with a beautiful clock tower at its centre.
Many years ago, an evil Maths Puzzler had cursed the town so that the people there only understood numbers to two decimal places and made it such that the clock would stop at 1 minute to twelve until someone could find the solution to a maths question.
The question was what is 4.65 divided by 7. For generations the townspeople could not begin to understand the answer to this as try as they might, all of the greatest mathematicians in the land did not have a technique that would work for such a sum.
During a gathering in the town square, the conversation went like, “So, 4.65 divided by would be 0.66 ... but … how can it be … there is some left over, a … remainder … what does that mean … how can it be … what unearthly science is this ? is it witchcraft ? Are we all going mad ?”.
A young boy, Divisio, shouted up from the back “what happens if you just keep on going ? why don't we add more decimal places ?”
This did not go down well and after much discussion by the town's leaders, Divisio was banished from the land and told to only return if he could explain how his crazy notion could help solve the problem.
Divisio was sad and set out to wander the land of Mathmatica alone.
The first town he came across was Guesstica a town where the shopkeepers just guessed the change they owed their customer and every one was not sure how much money they had and generally felt ‘ripped-off’ and gloomy.
When Divisio asked one of the townspeople how to work out the answer to his question the man just replied,
“Uh… I dunno… 21?”
Divisio could clearly see this was a total guessed so said,
“Thanks, but no thanks.” and walked away to set off on his journey again.
The next town Divisio came across was Estimatum a town where everything was roughly what it seemed, the houses were more or less houses, the roads more or less went to the right place, and everything seemed about the right size. More or less. When Divisio asked one of the members of this peculiar town they said,
“Hmmm…. Well if it was 4.2 divided by 7, that would be 0.6 so… AHA! The answer must be about 0.6.”
Divisio was stumped. How could this be? So instead of saying anything he just walked away, not listening to the man shouting after him, “I would estimate that you do not believe me.”
He was so annoyed that he shouted back.”Exactly correct!”
When Divisio stopped next, it was at a village called Fractopia. Tiring of his quest, he asked the first person he saw who was a grey haired woman.
“Old woman, Can you tell me, what is 4.65 divided by seven ?”.
The town's woman stared at him.
“Firstly I’m not old, I just haven't been sleeping well. Secondly, I never heard such talk, What does that mean ?”.
Divisio replied,
“You know numbers, division and all that”.
“Oh, numbers. You mean like 4 and 3 and, erm, 76.” said the woman knowingly.
“Yes, that sort of thing. But decimals, numbers less than 1.” exclaimed Divisio, getting irritated.
“Oh, you mean fractions. I know all about fractions. Hey, Numerallia. There’s a boy here wants to know about fractions.”
Another woman appeared.
“So, your sum, is gibberish.” said Numerallia laughing with Denomilicia. “A sum with numbers less than one would be something like a half times a half.”
“Two fifths !!!.” Denomilicia called out and as she did, a siren blared and two burly policemen leaped out of a passing car and dragged her away.
“I’m sorry M’am, but you are guilty of getting an answer wrong in public. You're nicked.”
“Errr, one fifth, 3 quarters, err, two and and a bit. Nooooooooo.”
And with that she was gone. Numeralia looked a bit stunned.
“Don’t worry miss.” said Divisio. “It’s probably for the best.”
He quickly made his way out of town not looking back.
Weary from his travels and meetings with people having bizarre views on numbers and calculations, Divisio happened upon a beautiful field with three goats who looked very strange but at the same time possibly helpful. One of them appeared to be giving a lecture to the other two, and was frantically waving a laser pointer.
“Hello” said Divisio,”Who are you?”
“We are three very wise goats.” said one of the goats.
“Yes, er… You do look wise.” replied Divisio.
“Very wise!” reminded another of the goats. “What is your name?”
“My name is Divisio.” said Divisio.
“We are too wise for that name, so we we shall change it to… Barbara” said the other goat.
Divisio was a bit taken aback but kept on going. “ Oh wise goats, I, Divi… er, I Barbara have a really hard question.” he said, “ What is 4.65 divided by 7? And how can I explain it to someone who can only cope with two decimal places?”
The goats went into a huddle but eventually came out and said,
“ It is clear to see.”
“That the answer is.”
“0.66428571428 but someone unable to understand a number more than two decimal places would not comprehend this so…”
“We need to round it!” said all three goats in unison.
“What's that?” said Divisio.
“Well, 5 and above go up, and 4 and below go down.”
“So looking at all those digits, the answer you need is 0.66!” Explained the goats.
“You are indeed wise said Divisio.
“Very wise!” reminded one of the goats.
Divisio hurried home and on his arrival in Decimallia he announced to all the people.
“I have an answer that will work for all!”. “I was right. Indeed, there are more than two digits after the decimal point, and there is also a reasonable way that we can know the answer using your restriction to two decimal places. The way was shown to me by some wise goats.”
“Were they very wise ?” said one of the townsfolk.
“It doesn't matter.” snapped Divisio. “All you need to know is that the answer is ….”.
“Yes ….” cried the gathered crowd.
“0.66” said Divisio.
“Are you sure” said a small child.
“Yes.” replied Divisio.
The clock struck twelve and all was well.
By Mikey
ESTIMATING with brownies
Once there were two best friends, 2561 and 3126, who were doing their homework about friends. One of the tasks was:
In 10 seconds, add together your numbers.
2561 and 3126 were puzzled until the crazy 102,943 old half-deaf lady came knocking on the door giving out brownies. Since they were the closest to the door, it was 3126’s job to answer the door.
“What you kids up too?” said the crazy lady.
“Oh, just some homework.” replied 3126. “It’s about friends and we’re trying to figure out how we could add our numbers together in 10 seconds.”
“Ohhh, that was good fun.” said the half-death lady who probably didn’t hear a word 3126 said under her mumbling. “Well, I came to give you some brownies that I made for the neighbourhood.” babbled 102,943. “Now,now, how many houses are there here in Seaside Passage?”
“I think about 10” said 3126.
“Ok then. I have 64 brownies so how many should each house get?” asked the old grandma.
“Umm.. just wait a second while I get some paper.” 2561 told her.
“No no no, 2561, I’m not waiting that long. You need to ESTIMATE.” said 102,943, a little too loudly.
Then, from behind the girls, they heard 3126’s dad calling “Yes girls, you need to start estimating simple sums.”
“But how do you estimate?” asked 2561.
“Good question.” said 3126’s mum joining the conversation. “You just round the numbers to something easy then you do the calculation. It’s much easier and faster for simple things.”
“Ohhh. So I just round 64 to 60 then divide it by ten? That makes it much more easier.” said 3126 after thinking through it first.
“Yes dear girl, you must know know to estimate. You might need it in emergencies” warned the old grandma from next door snapping out of her daydream.
“Now girls, I was looking over your homework so what’s 2561 plus 3126?” said the dad starting to count from 10.
“So, 2561 rounded to the nearest 1000 is 3000,” said 3126 listening carefully to the time - 8 more seconds.
“And 3126 rounded is 3000 so 3000 plus 3000 is…” added 2561 with 5 second to go.
“6000!” cried both girls at the same time with 3 seconds left.
“We did it!” laughed 3126. “Thanks 104,943, mum and dad.”
And the best friends completed their homework and ate warm brownies from the half-deaf old lady from next door while watching their new favourite movie, ESTIMATING with brownies by granny 102,943.
By Sena
½ * ¼
Once upon a time there was a family called one-half and one-quarter they hated each other and always fight with just a little things. One day the king of Fractions ⅛ died and was finding a new king ½ and ¼ both wanted to be the king so they fought again. One day the lawyer told them that the the new king still needs to be the number ⅛, then ⅗ said to ½ if you times your-self with ¼ you can be the king. So they timesed the numerator which made 1 next they timesed the denominator which made 8 they putted them together which made ⅛. They became the new king of the fraction land!!
By Lisa
No comments:
Post a Comment
Thank you so much for your comment. We really do appreciate it!