There are times when we cannot remember some simple formula for a maths application.
Or we have doubts to the some maths working especially when many parameters got involved.
I ave a simple tip.
Look at the units for the numerical item.
Example:
To calculate distance travelled by a vehicle, given the speed it goes and time taken,
we look at the speed's units.
Unit: m / s
What does it tell?
Yes, it gave an indirect answer that speed = distance / time.
Thus if time is given, we are able to know that we just need to multiple speed by time in order to retain only the distance.
(m / s) x s = m (only) ==> Distance
The above allow us to use units to deduce the working (and formula).
Hence, we should not overlook the power of knowing units.
It is simply disappointing to sometimes see people missing out on writing the units for certain parameters. Maths loses its value simply by ignoring this step.
Therefore treasure this little but powerful "units".
:-)
Maths is interesting!
.
Wednesday, 25 May 2011
Monday, 14 March 2011
Watery Art using Maths Expression
Graphs are wonderful thing in the learning of maths.
Not only does it reflects visual symptom or trend in data collected, it displays, if allowed, beautiful images.
This is possible if you allow you maths juice to go free and create mathematical expressions to your fancy and view them on a graph.
Below I have created one. I visual it as water rippling through a surface (on the top view).
Hope you like this maths art of mine.
NOTE: It is created using trigonometry of circulatory expression.
Here I view a water droplet going down into the centre. It then produces ripples or waves spreading outwards in a circular manner.
Imagination ....
Maths expressing ......
:-)
.
Not only does it reflects visual symptom or trend in data collected, it displays, if allowed, beautiful images.
This is possible if you allow you maths juice to go free and create mathematical expressions to your fancy and view them on a graph.
Below I have created one. I visual it as water rippling through a surface (on the top view).
Hope you like this maths art of mine.
NOTE: It is created using trigonometry of circulatory expression.
Here I view a water droplet going down into the centre. It then produces ripples or waves spreading outwards in a circular manner.
Imagination ....
Maths expressing ......
:-)
.
Saturday, 5 March 2011
Explanation of the Elimination Method
Solving of Simultaneous equations may require one common technique called "Elimination" method.
From the name, we know that it has to eliminate or remove something from the equations.
The target is one selected variable or unknown in the mathematical equations.
However, when approaching this method, you noticed that it involved the subtraction (or addition) of equations.
The question is "Can equations be subtracted?".
And "What is the real meaning of subtracting equations?"
My answers:-
Yes, equations can of course be subtracted. Equations are like other items, e.g. apples, chairs.
The real meaning of subtracting equations is not that apparent.
The true and desired wish to subtract equations boils down to commonising a certain coefficient of a variable.
With this common coefficient, it will then be able to remove this mathematical unknown.
(It is not really the direct processing of equations, and the magical removal of variable as a result!)
We commonise the coefficient of the selected variable first before subtracting the equations in order that same items are eliminated.
Hope this clarify some doubts of new learners to simultaneous equations solvers.
Concepts have to be learned upfront without pending questions for complete understanding and smooth follow-up learning in the later stage. Seek to clarify any doubts as far as possible.
It will reduce maths anxiety and allow you to enjoy maths as a result. The reward of clearing any doubts cannot be spelled out in words but through actual working and practice with proper analysis.
I believe you support this notion.
Cheers to maths.
.
From the name, we know that it has to eliminate or remove something from the equations.
The target is one selected variable or unknown in the mathematical equations.
However, when approaching this method, you noticed that it involved the subtraction (or addition) of equations.
The question is "Can equations be subtracted?".
And "What is the real meaning of subtracting equations?"
My answers:-
Yes, equations can of course be subtracted. Equations are like other items, e.g. apples, chairs.
The real meaning of subtracting equations is not that apparent.
The true and desired wish to subtract equations boils down to commonising a certain coefficient of a variable.
With this common coefficient, it will then be able to remove this mathematical unknown.
(It is not really the direct processing of equations, and the magical removal of variable as a result!)
We commonise the coefficient of the selected variable first before subtracting the equations in order that same items are eliminated.
Hope this clarify some doubts of new learners to simultaneous equations solvers.
Concepts have to be learned upfront without pending questions for complete understanding and smooth follow-up learning in the later stage. Seek to clarify any doubts as far as possible.
It will reduce maths anxiety and allow you to enjoy maths as a result. The reward of clearing any doubts cannot be spelled out in words but through actual working and practice with proper analysis.
I believe you support this notion.
Cheers to maths.
.
Sunday, 16 January 2011
Simultaneous Equations - Decimal Numbered
In the learning of maths, questions grow challenging as one progress upwards.
One such example is the solving of simultaneous equations.
The easy type:
Solve for x and y using elimination method.
4x + 3y = 10 ---- (1)
3x + 4y = 11 ---- (2)
For the above problem can be solved easily by selecting a coefficient to be commonised.
The post of elimination method is reference here for review.
But moving on (higher) with more challenging maths question ... we may get the below.
0.4x + 0.3y = 1 ---- (A)
3x + 4y = 11 ---(B)
What should we do next?
Equation (A) may seems unusual. It is in decimal form!
But as the blog title claims "Maths Is Interesting!", we should not be worried.
This type of question is actually not new in concept or tricky as it seems.
It is there to test you understanding by being "different".
We have to remove the "catch", which is to change the decimated number to integer.
How we do it here is simply multiplying the coefficients by 10.
This makes equation (A) to be 4x + 3y = 10 (back to the original first set of simultaneous equations at the start of this post.
The above example serves to illustrate the simplicity of changing numbers to suit the condition for easy solving. (Other questions may be multiply by another decimal number, or integer).
Just have a clear mind and a confidence attitude will be enough to allow you to solve most of the maths questions.
Try it and you will believe what I say (or write).
Maths is interesting!
.
One such example is the solving of simultaneous equations.
The easy type:
Solve for x and y using elimination method.
4x + 3y = 10 ---- (1)
3x + 4y = 11 ---- (2)
For the above problem can be solved easily by selecting a coefficient to be commonised.
The post of elimination method is reference here for review.
But moving on (higher) with more challenging maths question ... we may get the below.
0.4x + 0.3y = 1 ---- (A)
3x + 4y = 11 ---(B)
What should we do next?
Equation (A) may seems unusual. It is in decimal form!
But as the blog title claims "Maths Is Interesting!", we should not be worried.
This type of question is actually not new in concept or tricky as it seems.
It is there to test you understanding by being "different".
We have to remove the "catch", which is to change the decimated number to integer.
How we do it here is simply multiplying the coefficients by 10.
This makes equation (A) to be 4x + 3y = 10 (back to the original first set of simultaneous equations at the start of this post.
The above example serves to illustrate the simplicity of changing numbers to suit the condition for easy solving. (Other questions may be multiply by another decimal number, or integer).
Just have a clear mind and a confidence attitude will be enough to allow you to solve most of the maths questions.
Try it and you will believe what I say (or write).
Maths is interesting!
.
Wednesday, 8 December 2010
Decimal Number Simplification
.
Algebraic expressions and equations normally come in integer or fraction form.
Examples:
1) 4x - 3 = x
2) (3/4)x - 3x = 1/(3x)
Simplification of the above examples will not pose much of a problem except maybe in the challenge of bringing the numbers and unknowns over the "equal" sign.
But algebraic equations can come in decimal form too.
Example:
0.3(0.2x - 1) = 0.1x
How do we go about solving the above "decimated" algebraic equation easily?
A simple trick that I can think of (or maybe too simply a technique to call it 'trick").
What I would do is to multiply the expression on both sides by 10.
The idea is to bring the decimal number into the integer range.
BUT do note that the expression on the left side has two decimal numbers.
As such I would have to "x 10" twice.
This means that there is a "x 100" on the left and right side.
The new equation will thus be:
3 (2x - 10) = 10 x
==> 6x - 30 = 10x
==> -30 = 10x - 6x = 4x
==> x = -30 / 4 = -7.5
Conclusion:
Decimal can be seen to be intimidating when in the decimal form. However, it can be elevated to the familiar integer form through simple multiplication.
However, do take note of how many decimal number has been multiplied.
Left and right sides of the equation has to have the same number of multiplication (or division) to stay equal and valid.
Maths is not that frightening.
It can be interesting, if the method to "attack" it is properly done.
:-)
Algebraic expressions and equations normally come in integer or fraction form.
Examples:
1) 4x - 3 = x
2) (3/4)x - 3x = 1/(3x)
Simplification of the above examples will not pose much of a problem except maybe in the challenge of bringing the numbers and unknowns over the "equal" sign.
But algebraic equations can come in decimal form too.
Example:
0.3(0.2x - 1) = 0.1x
How do we go about solving the above "decimated" algebraic equation easily?
A simple trick that I can think of (or maybe too simply a technique to call it 'trick").
What I would do is to multiply the expression on both sides by 10.
The idea is to bring the decimal number into the integer range.
BUT do note that the expression on the left side has two decimal numbers.
As such I would have to "x 10" twice.
This means that there is a "x 100" on the left and right side.
The new equation will thus be:
3 (2x - 10) = 10 x
==> 6x - 30 = 10x
==> -30 = 10x - 6x = 4x
==> x = -30 / 4 = -7.5
Conclusion:
Decimal can be seen to be intimidating when in the decimal form. However, it can be elevated to the familiar integer form through simple multiplication.
However, do take note of how many decimal number has been multiplied.
Left and right sides of the equation has to have the same number of multiplication (or division) to stay equal and valid.
Maths is not that frightening.
It can be interesting, if the method to "attack" it is properly done.
:-)
Monday, 22 November 2010
Basic Decimal Conversion
`
Every thing falls back to basic.
If the fundamentals are weak, any maths learners will have a hard time moving forward in their maths learning journey.
Let me quote an example.
How do we change 4.75 to fraction.
We can use 475 / 100 and reduce it through long division. This will give 4 and 3/4.
However, if we know that 4.75 is actually consisting of 4 add to 0.75, the conversion will be simpler.
4 and 0.75 means 4 + (3/4) which leads directly to 4 whole and 3/4. Same as answer of above.
(NOTE: 0.75 is a quarter which equates to 3/4).
Simple isn't it?
Maths is interesting.
:-)
Every thing falls back to basic.
If the fundamentals are weak, any maths learners will have a hard time moving forward in their maths learning journey.
Let me quote an example.
How do we change 4.75 to fraction.
We can use 475 / 100 and reduce it through long division. This will give 4 and 3/4.
However, if we know that 4.75 is actually consisting of 4 add to 0.75, the conversion will be simpler.
4 and 0.75 means 4 + (3/4) which leads directly to 4 whole and 3/4. Same as answer of above.
(NOTE: 0.75 is a quarter which equates to 3/4).
Simple isn't it?
Maths is interesting.
:-)
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