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Mathematics in Working World 2
Let’s be realistic, we work to earn a living. Thus, the $$ (salary) becomes the first priority. There is a difference between gross salary and take-home salary.
The amount that your employer tells you is your gross salary. The gross salary deducts CPF and taxes (if any), then adds any overtime (OT) pay and any allowances, and the final amount is the take-home salary.
Take a simple example, the gross salary is $2000. With the assumption that you are 35 years old and below, you need to contribute 20% of your salary to CPF. Now you need your knowledge of percentage to calculate how much you need to contribute to CPF.
2000 x 20% = 400
With another assumption that there is no OT pay and other allowances, your take-home salary is
2000 – 400 = 1600
The good news is your employer contributes another 16% of your salary to CPF.
2000 x 16% = 320
400 + 320 = 720
Thus, your CPF account will have the total of $720 for the month.
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Now that you know your take-home salary, let’s go shopping. You want to buy a pair of shoes that costs $80. With GST of 7%, the cost of the shoes is
80 x 7% = 5.60
80 + 5.60 = 85.60
You need to pay $85.60 for the pair of shoes with GST included.
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All these calculations are the simplified versions that you will be using when you start working. The next time you are complaining about learning Mathematics, think about how Mathematics will help you in future and you won’t complain. Happy learning!
Mathematics in Working World 1
My ex-colleague asked me some questions on how to do her new job in a better way. To make you understand the importance of Mathematics learnt in school but at the same time to protect her working privacy, I use a simplified version of the problem that she faces.
Her company is selling packet drinks and she takes care of the inventory of the packet drinks. She already has a table to record the quantity of different flavours of the packet drinks, but she cannot get an accurate inventory sometimes. I found out the problem immediately after she told me that she used different units in the same table.
At school, we learn that we must always use the same unit for calculation. In the same operation, we cannot mix minutes and hours (different units in time). If the question gives you different units, you must change all to the same unit, preferably one that is easy to work on. It is important to use only one unit because you may get yourself confused with different units and a wrong answer.
We learn to prepare ourselves for the working world. The use of only one unit in a particular question may seem like a small matter, but you will see the problem when you are at work.
Back to my ex-colleague’s problem. Her company has loose packs, which is counted one by one, and 12 packs in a box. In the column for loose packs, she uses 1 as 1 pack. On the same table, in the column for 12 packs in a box, she uses 1 as 1 box, where 1 box has 12 packs. The units are different! If she adds 1 pack and 1 box, she does not get 2, she gets 13 packs.
The solution? As long as she uses only one unit in the same table, she should have no problem in getting the final inventory.
Why Do We Learn Percentage?
This is the second post in the “Why Do We Learn …?” series. The main purpose of this series is to show the real life application of different Mathematics concepts. In this post, we continue with the topic of buying a commodity.
Below is table showing the price of the commodity with different weights:
Weight |
Sell Out Price (S$) |
Buy Back Price (S$) |
Difference between SOP and BBP (S$) |
Difference in Percentage (%) |
1 g | 56.50 | 56.10 | 0.40 | 0.71 |
1 kg | 56300 | 56100 | 200 | 0.36 |
1 ounce | 1820 | 1750 | 70 | 3.85 |
10 ounce | 17900 | 17600 | 300 | 1.68 |
Concept 1: Money
The sell out price is the money that you pay to the bank when you buy the commodity.
The buy back price is the money that the bank pays you when you sell the commodity back to the bank.
From the table above, we can see that there is difference between the sell out price and buy back price and the buy back price is always lower than the sell out price.
Concept 2: Percentage
If we invest in a commodity, we would like to earn money, that’s common sense.
With the assumption that the price is the same as the above table when you buy and sell the commodity, which weight would you choose to make maximum profit?
The difference in price does not make a good indicator because the weight difference is big and thus the difference in price is big too. Thus, we should choose the difference in percentage as a better indicator.
We choose the smallest difference in percentage to make maximum profit. To calculate the difference in percentage for 1 g:
The price difference = 56.50 – 56.10
= 0.40
The percentage = (0.40/56.50) x 100%
= 0.71%
From the table, we know that the smallest difference in percentage is for 1 kg, 0.36% and the biggest difference in percentage is for 1 ounce, 3.85%.
If the price of the commodity has increased by 2%, investment in 1 kg has positive return while investment in 1 ounce has negative return.
In a nutshell, we can decide which weight will give you a good return by using the difference in percentage, i.e. 1 kg gives the best return among the four weights while 1 ounce gives the least return.
Disclaimer: This post is not encouraging children and / or adults to invest blindly. This is only a simple example where you can use the knowledge learnt in real life. Investment in real life is more complicated and involves more risks.
Why Do We Learn Average?
We learn different Mathematics concepts in Primary school. For Primary students, do you expect them to understand why they are learning average? Or percentage? Yes, they do not understand the reasons behind and when they face difficulties, they give up.
As parents or educators, when we are teaching the children, it would be better if we can explain the reasons behind why they are learning different Mathematics concepts and how they can apply the concepts in real life. Below is an example of buying a commodity, using different Mathematics concepts learnt at school:
Concept 1: Weight
1 kg of the commodity costs S$ 9780.00. As a small investor, you can only buy 10 g at a time. How much does 10 g of the commodity cost?
1 kg = 1000 g => S$ 9780.00
10 g => S$ 97.80
Concept 2: Average
Unfortunately, the price goes down and you wish to reduce the risk of losing more money. Thus, you buy another 10 g at S$ 96.90 and another 10 g at S$ 94.50.
The average price for 10 g = (S$ 97.80 + S$ 96.90 + S$ 94.50) / 3
= S$ 96.40
This concept is called average down in investment term, where it is commonly used for buying stock and/or commodity, such as gold, silver, etc.
Concept 3: Money
(a) At the end of the year, the price has gone up to S$ 9710.00 per kg. You are thinking if you can make money by selling all the 30 g of commodity that you have. The maintenance fee is S$ 20.00.
At the first glance, the price of S$ 97.10 per 10 g is not profitable because you first bought the 10 g at S$ 97.80. But after averaging (concept 2), you only spent averagely S$ 96.40 for 10 g.
Another factor to consider is the maintenance fees. You need to subtract the maintenance fees to get the total money won or lost:
For this example, the total money invested = S$ 96.40 x 3 = S$ 289.20
When you sell the 30 g of the commodity, you get = S$ 97.10 x 3 = S$291.30
Without considering the maintenance fees, you think that you have made S$ 2.10 from this investment. After subtracting the maintenance fees, you actually lose S$ 17.90 from this investment.
(b) After the calculation from (a), you know you are losing money, so you wait for the commodity price to go up further. After six months, the price has gone up to S$ 9920.00 per kg. The maintenance fee is S$ 20.00. You are thinking if you can make money by selling all the 30 g of commodity that you have.
The total money invested = S$ 96.40 x 3 = S$ 289.20
When you sell the 30 g of the commodity, you get = S$ 99.20 x 3 = S$297.60
Similarly, you need to subtract the maintenance fees to get the total money won or lost:
S$ 297.60 – S$ 20.00 = S$ 277.60
Again, after considering the maintenance fees, you are still lost of S$ 11.60, even though the price has gone up to S$ 9920.00 per kg.
As you can see, a simple example link three different concepts. Children will appreciate the concepts better if they can see the linkage and also the real life application.
Disclaimer: This post is not encouraging children and / or adults to invest blindly. This is only a simple example where you can use the knowledge learnt in real life. Investment in real life is more complicated and involves more risks.