Tanya and Tinku Help the Hansen Family

hansenfamily

Mister Hansen’s will

Mister Hansen, a small farmer died leaving behind 17 horses in his barn. To avoid a quarrel between his children, he had made a will.  The will read that 1/2 the fraction of all the horses should be given to his son Liam, 1/3rd fraction to his daughter Olivia and 1/9th to his daughter Ava.  Horses were not to be sold or cut up.

Little did Mr. Hansen know that he had created a situation.  Liam wanted nothing less than his share.  Half of 17 is 8 and 1/2.  He was not prepared to take 8 horses which would be less than his share.  Olivia was also adamant. 17 divided by 3 is: 5 and 2/3. She was not satisfied taking only 5 horses.  How could Ava be satisfied with only one horse when 1/9th of 17 is 1 plus 8/9.  Remember, the horses could not be cut up or sold to solve the problem. They quarreled over it all night.  Mr. Johnson, a school teacher, heard about their fight.  He thought it was a silly math problem and asked the students if anyone would be willing to help.

Tinku has to be a pretend horse

Tanya: Tinku and I will be glad to help if Tinku wants to pretend to be a horse.

Tinku: I wore a horse costume on Halloween.  I think I still have it.

Mr. Johnson:  Tanya, why are you so sure?

Tanya: I know that the lowest common multiple of 2, 3 and 9 is 18 and not 17. This made me think that the fractions 1/2 + 1/3 + 1/9  don’t add up to one.  So, the will is faulty.  Why don’t we talk to the family?  We can solve their problem.

The three of them visited the Hansen family.

Liam got his share

Liam was furious when Mr. Johnson said that the little girl Tanya could settle the matter.  Olivia and Ava smirked but asked Liam to give her a chance.

Tanya called over Tinku and told everyone that this was a pretend horse.  They had 17 horses and this pretend horse would make it 18.

Liam:  I am not going to this pretend horse but only the real ones from my father’s barn.

Tanya: You will get real horses and that too more than your share.  There were 17 horses in the will and your share was half of them. That makes it 8 and 1/2 horses.  Including the pretend horse, there are 18. You can have half of them or 9 real horses which is more than your share.

Liam: Glad to do that.  Thank you.

Olivia and Ava were happy

Tanya: Now including the pretend horse there are 9 left. Olivia your share was 1/3rd of 17 which is 5 and 2/3, you can have 6 real horses which is one third of 18.  Are you happy?

Olivia: I am glad but now I want to see how Ava gets her share.

Ava:  I see what this girl did. She showed us how silly we were.  After Liam took 9 horses and Olivia took 6, we still have two real horses plus the pretend horse.  Now she is going to say that with the pretend horse there were a total of 18 horses at the start and I can have 1/9th of them which is 2 horses.  So, the pretend horse doesn’t have to be shared.  It is just extra.

Tinku hugged Tanya and said: Thanks.  I thought I would have to go to the barn with one of them.  Let’s go home now.

Ava was confused but got the sense that they were just being silly. Liam and Olivia had no clue what Tanya had done.  Did you find out what she did?

Challenge

Mr. Ferguson told the class that there would be a test next Monday.  Because, he was teaching fractions, he decided that the value of mark for each question would be a fraction.  He cautioned the students that it would be a tough exam and challenged anyone to get a full mark of 1.  They all wrote the exam. There were 5 questions.  Q. 1 was the toughest but the questions got easier and easier afterwards. Q. 1 was worth 1/2 mark, Q. 2 was worth 1/4, Q.3 worth 1/8 and Q.4 and 5 worth 1/16. When Tanya got the marked exam back, she had all the correct answers but Tinku had missed Q.3.  What were their total marks?

Solution:  Tanya’s total mark = 1/2+1/4+ 1/8+1/16+1/16 =8/16+4/16+2/16+1/16+1/16 = 16/16 = 1.

Tinku had missed Q.3 which was worth 1/8 mark.  So his total would be1/2+1/4+ 0+1/16+1/16 =8/16+4/16+0+1/16+1/16 = 14/16 = 7/8.