Charles Dowland Jones – is not a real character
There was a smart businessman Charles Dowland Jones. His family and close friends called him Chuck. He was not well educated but had good business sense. He lived in a small village near Toronto and often traveled around with his wife Maria. They also had a son named Harry. They wanted Harry to be educated well but there were no schools in the village. They sent him to a boarding school in Toronto.
One day, Chuck and Maria were travelling and they saw a sign for an estate sale. An old farmer had died leaving behind no one except his wife and a large parcel of land – almost five kilometers long and one kilometer wide. The farmer’s wife did not want to live there anymore. So the land had been put up for a silent auction. There were not that many people possibly because the sale was very poorly advertised. Being a smart businessman Chuck put in a bid of $50,000 in the auction. This bid was not very high and he could easily afford it.
What to do with the land?
To Chuck’s surprise, the bid was accepted. He was pleasantly surprised and was now the proud owner of this parcel of land. However, he did not know what to do with this farmland. Chuck was no farmer but he was smart. He talked around and found a real estate agent who dealt with land in that area. The agent told Chuck that he could get rich if he could develop this land into a housing project. The best thing would be to make a deal with a developer.
The agent and Chuck figured that they could make many houses on this land but about 6/10th of the land would have to be left for roads and other services. That left 4/10 of the land. He could divide this land again into 10 parts so that each part would be or 4/100 fraction of the total land.
Harry came home from boarding school
Chuck was trying to figure all this out when Harry came home. They were talking and Harry told him that he had learned about decimal points. They would be much simpler to use. Chuck was proud that his son learned something in school and excited to know what that was.
Harry: Dad, you wrote 1/10th as (1) and 1/100th as ((1)). So you started using the decimal system. We were taught that 1/10th could be written as 0.1. The point here is the decimal point and because hear appears immediately after it makes it 1/10. For 1/100, we can write 0.01 making the number 1 to be two places away from the decimal point.
Making a housing development
Using this system, I could write that 6/10th or 0.6 fraction of the land would be used for roads and services and 0.4 part of the total land will be divided into plots for individual houses. The beauty is that you can multiply and divide 0.4 by other numbers. For example, you have 5000 meters (5 kilometers) x 1000 meters (1 kilometer) which is 5,000,000 square meters of land. 5,000,000 x .4 square meters is the same as 2,000,000 square meters.
Chuck: Good son. I know that 500 square meters is a large lot for a house. So I could get 2,000,000/500 or 4000 large houses on this land.
Harry: 1/4000th part of the land is written as 2.5/10000th part. You could tell the developer that 0.6 part of the 5,000,000 square meter of the land can be used for services and 0.00025 part per house can be used for 4000 houses.
Chuck got rich
Chuck got back to the agent and they contacted a developer who said it was a lot of risk because the farmland was not yet approved for housing. If he buys this land, he would be taking a lot of risk. If approved, they will also have to work on developing the project and it could take 10 years to sell. He could pay him only a fraction of the land cost. A plot for the house when sold will be about $50,000. He will give him 0.05th fraction in cash and take all the risks.
Chuck asked Harry who figured that $50,000 times 0.05 was $2,500 per house. For 4000 houses which could be built on this land they could get 0.05 x 50,000 x 4,000 which was $10,000,000 or 200 times the $50,000 that dad had paid for it. He told dad to take the deal before the developer changed his mind.
Chuck took the deal and figured that this profit had paid for Harry’s life time of education any where he wanted.
Challenge
Tanya purchased $38.46 in groceries at a store and gave the cashier a$50 bill. The cashier gave her $1.54 in change. Tanya is angry at the cashier. What did the cashier do wrong?
Solution: Cost of the groceries = $38.46. Add the change of $1.54 returned
= $38.46+ $1.54 = $40.00. But she gave a $50 bill. The change should have been
$50.00 – $38.56 = $11.54 which is $10 more than the cashier gave her. She has every right to be angry at the cashier.
Supplementary
Ashwin (A), Bobby (B), Chris (C), Don (D) and Evert (E) each rolled two fractional dice. They decided that the sum of the two dice would decide the winner. Determine the sums and declare the winner. Convert the rolls into decimals first.
Answer: 1/6 = 0.167, 2/6 = 0.333, 3/6 = 0.5. 4/6 = 0.667, 5/6 = 0.833
Ashwin 1+ 5/6 = 1+0.833 = 1.833
Bobby 5/6 + 5/6 = 10/6, 0.833 + 0.833 = 1.666
Chris 4/6 +1/6 = 0.667 + 0.167 = 0.834
Don 4/6+3/6 = 0.667 + 0.500 = 1.167
Evert 1/3 + 1/3 = 0.333 +0.333 = 0.667
Ashwin won because 1.833 is larger than any of the other sums.
Board Games
I have made some board games. Playing one of the games will make you an expert in this area.
Click here to get to the board games for free. The games require the use of fractional dice. If you cannot buy them, use two ordinary dice and write fractions on pieces of paper with a felt pen and glue them on the dice. Have fun.
Math Stories For You 