Last week I took a LRT train at Kelana Jaya Station and disembarked at Pasar Seni Station. Immediately I got onto Go-KL free bus to KLCC. But as soon as I boarded the bus I was in the company of foreigners, Bangladeshis, a Japanese couples and a few Caucasians I must have entered a wrong bus; it was a tourist bus or it seemed and rushed out in an instant. Outside the bus I saw it was indeed the Go-KL bus.
Those foreigners really know how to travel free. I don't know why Malaysians do not take advantage of the free bus service. Come on! Malaysians, travel free as time is bad. If there is free food or free books for your kids, rush for those items. Come New Year 2014, everything is going up! Sugar,petrol, toll charges, food, entertainments. The dread GST, 6 %. You name it goes up, even corruption goes up. But one thing do not go up- your pay packet.
Tuesday, December 31, 2013
Thursday, March 28, 2013
MATHEMATICS- WHAT THEY DON'T TEACH YOU IN SCHOOL
To show you how to solve mathematical problems is to learn simple addition first. But that could bore you to death. I shall go straight to show you how to solve difficult mathematical problems first.
We begin with finding cube roots. In order to derive the cube roots we have to understand the meaning of cubes. To cube a number, say 3 we multiply 3 two times (3 x 3 x 3=27). That is 3³=27.
The cube root of 27 is derived as: ³√¯27=3. The simplest way is to use a scientific calculator by keying shift then key in √ and 27 and lastly =. The answer is 3.
In order to derive a cube root mentally I will show you a strategy that require you to memorize the cube of 1 to 9. I believe you can do this given some time. Now try memorizing these to perfection.
1³ = 1
2³ = 8
3³ = 27
4³ = 64 ,
5³ = 125
6³ = 216
7³ = 343
8³ = 512
9³ = 729
Take a closer look at the above answers of cubes from 1 to 9:-
1, 8, 27, 64, 125, 216, 343, 512, 729
You can see clearly that all the answers of cubes from 1 to 9 end with a different digit. This is how we derive the answers of cube roots from this little information. It is accurate for finding cube roots of 1 up to 1,000,000 and must be perfect cube pretty fast provided you memorize or know the cube of 1 to 9.
Let us now try a simple example. Find the cube root of 21,952 or ³√21,952.
Take a look at 21,952. We arrange the number into two parts counting from the right first three digits, i e
952 on the right part of the number 21,952 to derive the second part of our answer and 21, on the left to derive the first part of the answer.To derive the first part of the answer look at the left part of 21,952 which is 21. Where does 21 fall on the cubes table? Between 8 and 27. Since 21 is more than 8 but less than 27, the answer to the first part of our problem is the cube root of 8 which is 2. Now the second part of the answer is to look at the second part of the number 21, 952 which is 952. Take a quick look at the cube chart.The last digit of 952 is 2 which falls on 512. 512 when cube rooted is 8. So 8 forms the second and final part of the answer. Hence the answer to ³√21,952 = 28. Don't believe the answer. OK, use you calculator to multiply 28 twice.
2 8 x 28= 784 once. 784 x 28 = 21, 942 twice. Hey, Presto! Confirm ³√21,942 = 28.
Let us try a 6-digit number. ³√300,763 = ?
We follow the same procedure. We arrange the number into two parts, counting from the right first three digits, i e 763, to derive the second part of our answer and 300 on the left to derive the first part of our answer. To derive the first part of the answer look at 300 of 300,763. Where does 300 fall on the cube table? Between 216 and 343. Since 300 is more than 216 but less than 343, the answer to the first part of our problem is the cube root of 216 which is 6. Now the second part of the problem is to look at the second part of the number 300,763 which is 763. Refer to the cube chart. The last digit of 763 is 3 which falls on 343. 343 when cube rooted is 7. So 7 forms the second and final part of the answer. Hence the answer to ³ √ 300,763 = 67. Multiply 67 by itself two times gives you 300,763.
Let try another number, this time bigger number. ³√ 884,736 = ?
We follow the same procedure:- We again arrange the number into two parts, counting from the right first three digits, i e 736, on the right to derive the second part of our answer and 884 on the left to derive the first part of our answer. Where does 884, to derive the first part of our answer fall on the cube table? 884 falls outside 729 which is more than 729 but less than 1000. So the first part of our answer cannot be the cube root of 1000. It must be the cube root of 729 which is 9, giving us the first part of the answer. To derive the second part of our answer is to follow the same procedure for the second part. Look at 736, the second part of the given number. The last digit of 736 is 6. Again take a quick look at the cube chart. The last digit of 736 is 6 which falls on 216. 216 when cube rooted is 6. So 6 forms the second part of the answer. Hence the answer to ³√ 884,736 = 96.
I shall post multiplication of big numbers if you are interested.
98 x 98 = ? I can give you the answer instantly. Reply me if you are interested by posting on the comments column.
We begin with finding cube roots. In order to derive the cube roots we have to understand the meaning of cubes. To cube a number, say 3 we multiply 3 two times (3 x 3 x 3=27). That is 3³=27.
The cube root of 27 is derived as: ³√¯27=3. The simplest way is to use a scientific calculator by keying shift then key in √ and 27 and lastly =. The answer is 3.
In order to derive a cube root mentally I will show you a strategy that require you to memorize the cube of 1 to 9. I believe you can do this given some time. Now try memorizing these to perfection.
1³ = 1
2³ = 8
3³ = 27
4³ = 64 ,
5³ = 125
6³ = 216
7³ = 343
8³ = 512
9³ = 729
Take a closer look at the above answers of cubes from 1 to 9:-
1, 8, 27, 64, 125, 216, 343, 512, 729
You can see clearly that all the answers of cubes from 1 to 9 end with a different digit. This is how we derive the answers of cube roots from this little information. It is accurate for finding cube roots of 1 up to 1,000,000 and must be perfect cube pretty fast provided you memorize or know the cube of 1 to 9.
Let us now try a simple example. Find the cube root of 21,952 or ³√21,952.
Take a look at 21,952. We arrange the number into two parts counting from the right first three digits, i e
952 on the right part of the number 21,952 to derive the second part of our answer and 21, on the left to derive the first part of the answer.To derive the first part of the answer look at the left part of 21,952 which is 21. Where does 21 fall on the cubes table? Between 8 and 27. Since 21 is more than 8 but less than 27, the answer to the first part of our problem is the cube root of 8 which is 2. Now the second part of the answer is to look at the second part of the number 21, 952 which is 952. Take a quick look at the cube chart.The last digit of 952 is 2 which falls on 512. 512 when cube rooted is 8. So 8 forms the second and final part of the answer. Hence the answer to ³√21,952 = 28. Don't believe the answer. OK, use you calculator to multiply 28 twice.
2 8 x 28= 784 once. 784 x 28 = 21, 942 twice. Hey, Presto! Confirm ³√21,942 = 28.
Let us try a 6-digit number. ³√300,763 = ?
We follow the same procedure. We arrange the number into two parts, counting from the right first three digits, i e 763, to derive the second part of our answer and 300 on the left to derive the first part of our answer. To derive the first part of the answer look at 300 of 300,763. Where does 300 fall on the cube table? Between 216 and 343. Since 300 is more than 216 but less than 343, the answer to the first part of our problem is the cube root of 216 which is 6. Now the second part of the problem is to look at the second part of the number 300,763 which is 763. Refer to the cube chart. The last digit of 763 is 3 which falls on 343. 343 when cube rooted is 7. So 7 forms the second and final part of the answer. Hence the answer to ³ √ 300,763 = 67. Multiply 67 by itself two times gives you 300,763.
Let try another number, this time bigger number. ³√ 884,736 = ?
We follow the same procedure:- We again arrange the number into two parts, counting from the right first three digits, i e 736, on the right to derive the second part of our answer and 884 on the left to derive the first part of our answer. Where does 884, to derive the first part of our answer fall on the cube table? 884 falls outside 729 which is more than 729 but less than 1000. So the first part of our answer cannot be the cube root of 1000. It must be the cube root of 729 which is 9, giving us the first part of the answer. To derive the second part of our answer is to follow the same procedure for the second part. Look at 736, the second part of the given number. The last digit of 736 is 6. Again take a quick look at the cube chart. The last digit of 736 is 6 which falls on 216. 216 when cube rooted is 6. So 6 forms the second part of the answer. Hence the answer to ³√ 884,736 = 96.
I shall post multiplication of big numbers if you are interested.
98 x 98 = ? I can give you the answer instantly. Reply me if you are interested by posting on the comments column.
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