.
Father: How many marks did you get for your math test?
Son: I obtained 100 marks!
Father: Great! You have done me proud. You deserve an ice-cream.
Son: Thanks Dad!
Son to brother: Actually my math test is over a total of 200 marks. I almost failed the test! Luckily dad did not master percentage, otherwise I would not get my free ice-cream.
(To understand percentage, click this link).
..
Tuesday, 23 June 2009
Tuesday, 16 June 2009
What is Percentage?
'
Many people do understand what percentage is about.
If you see a sales offer with 50% discount, you will know that it is cheaper by half.
If the offer is with 40% less, you will also realise that is a good deal since it is almost half the original price.
But what is this percentage in detail?
A mark of 4 / 5 is reflected as a fraction.
A learned maths person will understand that it is (4 /5) x 100 = 80%
If you tell a student that he achieved 50 marks. Is that enough?
The information will not be enough as the total score is not known (unless using the default told before hand).
Thus a mark of 50 upon 50, and a mark of 50 upon 100 means different story altogether.
I believe you will agree totally!
A percentage will always reflect better information since 80% means 80 / 100.
The base of 100 is taken as the default.
The actual base number is immaterial in this matter.
An information of 50 marks compared to 50% showed the power of using percentage.
For absolute marks, you need to tell the total marks to form a complete message.
Using percentage, the fraction part of the calculation can be ignored.
Percentage and fraction are related. But percentage used a common base number (100) to commonise the value.
For comparison sake, percentage, thus stand a more proper way to tell the result.
Example:
Is it easy to tell the closeness between 49 / 56 and 46 / 56,
or is it easier to tell between 78% and 81% ?
The answer is obvious, I hope.
Maths is interesting, and mastering simple concept makes maths learning even more interesting.
Happy learning.
Cheers! :D
Many people do understand what percentage is about.
If you see a sales offer with 50% discount, you will know that it is cheaper by half.
If the offer is with 40% less, you will also realise that is a good deal since it is almost half the original price.
But what is this percentage in detail?
A mark of 4 / 5 is reflected as a fraction.
A learned maths person will understand that it is (4 /5) x 100 = 80%
If you tell a student that he achieved 50 marks. Is that enough?
The information will not be enough as the total score is not known (unless using the default told before hand).
Thus a mark of 50 upon 50, and a mark of 50 upon 100 means different story altogether.
I believe you will agree totally!
A percentage will always reflect better information since 80% means 80 / 100.
The base of 100 is taken as the default.
The actual base number is immaterial in this matter.
An information of 50 marks compared to 50% showed the power of using percentage.
For absolute marks, you need to tell the total marks to form a complete message.
Using percentage, the fraction part of the calculation can be ignored.
Percentage and fraction are related. But percentage used a common base number (100) to commonise the value.
For comparison sake, percentage, thus stand a more proper way to tell the result.
Example:
Is it easy to tell the closeness between 49 / 56 and 46 / 56,
or is it easier to tell between 78% and 81% ?
The answer is obvious, I hope.
Maths is interesting, and mastering simple concept makes maths learning even more interesting.
Happy learning.
Cheers! :D
Monday, 8 June 2009
Meaning of Minus
'
To the ignorant, a "-" or minus is a strange symbol.
Is this more so when it is expressed as "-6", "-5 km", "-$3", etc.
What is then the true meaning of this "minus" sign?
Answer: It indicates a reversal of action of intention.
Maths is a useful tool to help explain this concept.
Example:
When a car moves forward by 5 km, it moves +5 km. ( By default, no sign means positive)
When it reverses by 5 km, it moves -5 km. The direction of movement reverses!
When a person gain $3, he has +$3 in his pocket.
When he loses $3, he has -$3.
From the 2 examples above, you can see that the "minus" sign is a reversal to the default.
If you "reverse" and then "reverse" again, you find yourself in the positive direction.
(-1) x (-1) = + 1
If you reverse 5 times, 5 x (-1) = -5 . You are facing the reverse to the default starting direction.
Now take note of this coming information.
If you reverse the car by 5m and another 5m, you reversed in total (-5) + (-5) = -10m.
If you reverse the car by 5m, followed by changing the direction and moving by another 5m, you moved (-5) + (+5) = 0m.
(Reverse direction followed by forward direction).
Does all these "reversing" cause a daze in you?
Do not despair.
Message is "When there is a reversal, put a minus in front of the number". Simply that!
I owe you $5 ==> -$5.
I gained $5 but lost $3 ==> + $5 + (- $3) = $2 (Action followed by another using "+").
Understand?
Hope this post on minus sign reduces your anxiety about this little maths symbol.
Cheers :-)
.
To the ignorant, a "-" or minus is a strange symbol.
Is this more so when it is expressed as "-6", "-5 km", "-$3", etc.
What is then the true meaning of this "minus" sign?
Answer: It indicates a reversal of action of intention.
Maths is a useful tool to help explain this concept.
Example:
When a car moves forward by 5 km, it moves +5 km. ( By default, no sign means positive)
When it reverses by 5 km, it moves -5 km. The direction of movement reverses!
When a person gain $3, he has +$3 in his pocket.
When he loses $3, he has -$3.
From the 2 examples above, you can see that the "minus" sign is a reversal to the default.
If you "reverse" and then "reverse" again, you find yourself in the positive direction.
(-1) x (-1) = + 1
If you reverse 5 times, 5 x (-1) = -5 . You are facing the reverse to the default starting direction.
Now take note of this coming information.
If you reverse the car by 5m and another 5m, you reversed in total (-5) + (-5) = -10m.
If you reverse the car by 5m, followed by changing the direction and moving by another 5m, you moved (-5) + (+5) = 0m.
(Reverse direction followed by forward direction).
Does all these "reversing" cause a daze in you?
Do not despair.
Message is "When there is a reversal, put a minus in front of the number". Simply that!
I owe you $5 ==> -$5.
I gained $5 but lost $3 ==> + $5 + (- $3) = $2 (Action followed by another using "+").
Understand?
Hope this post on minus sign reduces your anxiety about this little maths symbol.
Cheers :-)
.
Sunday, 31 May 2009
Power Law of Logarithm Explained
Logarithm study has a few formulae that are important and key to solving math questions.
By remembering them , you will be in line to solve logarithmic problems and, maybe, fast too.
However, what if you forget them?
Does it mean that you are not able to solve the question regardless of speed?
Do not despair.
As long as you are able to manage the 2 basic laws in logarithm, you are safe.
The product law and the quotient law are must for any students.
Why do I say that?
Let us take the Power Law and do a review.
n log x = log X n
Why is it so? What if you forget this law? Any problem?
These are the very queries any new learners exposed to logarithm will ask.
First allow me to go through the product law of logarithm.
log (XY) = log X + log Y
meaning, 4 log Y = log Y4.
You see that you did not utilise the Power Law here,and yet is able to form this formula!
Amazing isn't it.
What is the message here?
The message is that, when you have the basic understanding in logarithmic principles, you will be able to twist and turn any given problems to come out a solution.
You had used the basic product law to discover this unique Power Law.
It is similar to other laws and also can be expanded to cover other maths topics too.
Do enjoy maths.
Do discover more exciting twists it presents wwith a bit of thinking.
Happy learning :-)
.
By remembering them , you will be in line to solve logarithmic problems and, maybe, fast too.
However, what if you forget them?
Does it mean that you are not able to solve the question regardless of speed?
Do not despair.
As long as you are able to manage the 2 basic laws in logarithm, you are safe.
The product law and the quotient law are must for any students.
Why do I say that?
Let us take the Power Law and do a review.
n log x = log X n
Why is it so? What if you forget this law? Any problem?
These are the very queries any new learners exposed to logarithm will ask.
First allow me to go through the product law of logarithm.
log (XY) = log X + log Y
Here you see that the product of "X" and "Y" in logarithmic operation, becomes a "sum"of the individual logarithms.
4 log Y = log Y + log Y + log Y + log Y (adding up 4 of the log Y)
Using product law, you know that these 4 terms can be combined to log (Y x Y x Y x Y).
log (Y x Y x Y x Y) = log Y4
Now, you see, through the product law, you are able to equate the 4 log Y into log Y4 ,meaning, 4 log Y = log Y4.
You see that you did not utilise the Power Law here,and yet is able to form this formula!
Amazing isn't it.
What is the message here?
The message is that, when you have the basic understanding in logarithmic principles, you will be able to twist and turn any given problems to come out a solution.
You had used the basic product law to discover this unique Power Law.
It is similar to other laws and also can be expanded to cover other maths topics too.
Do enjoy maths.
Do discover more exciting twists it presents wwith a bit of thinking.
Happy learning :-)
.
Saturday, 9 May 2009
Learning Math Topics in Isolation
Learning encompasses linking with other area and related topics.
Learning thing with disregard for other is alright for the sake of triggering the mind. But does it benefits more if linked to others?
Does indices related to quadratic equation?
Does multiplication relates to addition?
Does complex number relates to algebra?
All the above questions are common in the mind of a math learners.
If you do not have these questions along the learning phase, something is very wrong.
Learning math in isolation is similar to living in an isolated island all by yourself.
You do not know what is happening in the world.
You do not know if there is famine somewhere, or swine flu going round, or a plane crash near you.
Math has to be done with linkage to many other mathematical topics. It cannot be done in isolation.
Math is a tool that solves real-life problems. With mastery of various mathematical concept and relation among them, you will be better prepare to solve more problems.
Many a time, you will come across students who just study topical math without knowing that they can apply what have been taught to them previously.
They start fresh when a new topic is introduced.
Algebra is different from complex number.
The addition in complex number is done differently from that done in algebra. That's what they assumed, since the heading is different!
Interesting learning ways, right?
That is human nature, to be frank. Only when you are told, sometimes, otherwise you will not know it. Adults learn through experience that this assumption is pulling you down.
The ability to link many things together is a very beneficial skill to permanently internalise.
This does not point to math alone. Others apply.
Math can be tough if learned using an improper learning method.
One good technique is the linking technique where you will see yourself happily doing math, being able to apply and solve questions using previous and current taught concepts.
It motivates you.
This is the STARTING point if you are unaware. This is the point where it decides whether you can sustain math learning.
Learn wide and later deep into math. But start with the correct footing. Link as much to previous as possible. It will be a sure way to happy math doing.
:-) I like math!
.
Learning thing with disregard for other is alright for the sake of triggering the mind. But does it benefits more if linked to others?
Does indices related to quadratic equation?
Does multiplication relates to addition?
Does complex number relates to algebra?
All the above questions are common in the mind of a math learners.
If you do not have these questions along the learning phase, something is very wrong.
Learning math in isolation is similar to living in an isolated island all by yourself.
You do not know what is happening in the world.
You do not know if there is famine somewhere, or swine flu going round, or a plane crash near you.
Math has to be done with linkage to many other mathematical topics. It cannot be done in isolation.
Math is a tool that solves real-life problems. With mastery of various mathematical concept and relation among them, you will be better prepare to solve more problems.
Many a time, you will come across students who just study topical math without knowing that they can apply what have been taught to them previously.
They start fresh when a new topic is introduced.
Algebra is different from complex number.
The addition in complex number is done differently from that done in algebra. That's what they assumed, since the heading is different!
Interesting learning ways, right?
That is human nature, to be frank. Only when you are told, sometimes, otherwise you will not know it. Adults learn through experience that this assumption is pulling you down.
The ability to link many things together is a very beneficial skill to permanently internalise.
This does not point to math alone. Others apply.
Math can be tough if learned using an improper learning method.
One good technique is the linking technique where you will see yourself happily doing math, being able to apply and solve questions using previous and current taught concepts.
It motivates you.
This is the STARTING point if you are unaware. This is the point where it decides whether you can sustain math learning.
Learn wide and later deep into math. But start with the correct footing. Link as much to previous as possible. It will be a sure way to happy math doing.
:-) I like math!
.
Saturday, 2 May 2009
Counting Down With Base Eight
'
Counting up is an easy task for anyone, even when the base is not ten.
You may refer to this link for counting (up) with base 8.
However, counting down may be slightly harder than normal, especially when dealing with another number base other than 10.
Let's try with base 8 for a start.
10
03 -
----
??
---
Here a count down of 3 from 10 is needed.
How do you go about it?
Thinking of the way base 10 subtraction was dealt with, this is similar.
After all maths is the same. It is the technique that is important.
When you encounter a " bring back" from the upper (rightmost) digit to the lower leftmost digit, you will, for base 10, add a 10 to the "ones" digit.
Here, with base 8, you will do likewise, except that now it is adding the number 8 to the leftmost digit.
Thus, 0 + 8 = 8.
And 8 - 3 = 5.
10
03 -
----
05 (Answer in base 8).
---
There is nothing difficult if you look at the technique or concept in counting up or down.
Maths is just playing with methods to resolve numerical issues.
The above is a good example. Hope you agree?
Have fun counting in other number base.
Cheers!
.
Counting up is an easy task for anyone, even when the base is not ten.
You may refer to this link for counting (up) with base 8.
However, counting down may be slightly harder than normal, especially when dealing with another number base other than 10.
Let's try with base 8 for a start.
10
03 -
----
??
---
Here a count down of 3 from 10 is needed.
How do you go about it?
Thinking of the way base 10 subtraction was dealt with, this is similar.
After all maths is the same. It is the technique that is important.
When you encounter a " bring back" from the upper (rightmost) digit to the lower leftmost digit, you will, for base 10, add a 10 to the "ones" digit.
Here, with base 8, you will do likewise, except that now it is adding the number 8 to the leftmost digit.
Thus, 0 + 8 = 8.
And 8 - 3 = 5.
10
03 -
----
05 (Answer in base 8).
---
There is nothing difficult if you look at the technique or concept in counting up or down.
Maths is just playing with methods to resolve numerical issues.
The above is a good example. Hope you agree?
Have fun counting in other number base.
Cheers!
.
Subscribe to:
Posts (Atom)
+copy.jpg)
Posts
