Caution on Mixed Number

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Fractions are a necessary part of maths.
They come in many forms; improper, proper and mixed number.


Though improper and proper forms are direct in its presentation and interpretation, mixed number form may pose a potential mistake for young learners.

Example:
   
Is this 2 + (3/4) or 2 x (3/4) ?

Caution has to be taken to stress it as 2 + (3/4).

Some students have taken it to mean 2 pieces of (3/4) !
Dangerous isn't it.

But rest assure.
If you understand the language of maths and its "grammar", all will be well and interesting.

:-)

Tips On Using Substitution

Maths entails the usage of our brain juice in solving problems. It is a good platform for stretching our imagination and creativity by using simple concepts learned to handle seemingly complex maths questions.

Let's look at a "complex" simultaneous equations maths problem, and its way of solving (suggested).

Question:

  ---- (A)

--- (B)

Solve for y and x.

How do you go about it?

Look scary, right?

But like what I said, looks can be deceiving. Use the brain to go around the issue!

Tips: The structure of the simultaneous equations looks similar to the conventional type.
(Conventional type:-
Ax + By = nn
Cx + Dy = kk      )

So what we have to do can be to simply substitute  by m, and  by h (or any variable name).

What we thus convert to is:
  ---- (A)

 --- (B)

Will this simultaneous equations be more comfortable to solve?

Hence, a simple twist to the former mathematical questions can result in a totally familiar situations where we have solve many a times.

Thus, the technique and usefulness of substitution cannot be under-estimated.

It can be powerful at times to reveal a beautiful mathematical expression for user to resolve.

Maths Is Interesting!

Treasure our brain and our thinking. 

:-)

Zippy Graphical Maths

Trigonometry is a fun topic in maths.

It generates curves more than many other topics.

By combining various trigonometrical functions, you can get interesting patterns on a graph.

Putting these functions on an algebraic expression produces even exciting diagram.

Below is one I created and an array of zips appears.

Enjoy maths.
maths is interesting!

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Math Challenge 24

Math does not purely involve writing mathematical expression .
Sometime what you need is some logically deduction base on, of course, some mathematical principles.

Below is one good example of "deduction" type of math solving.

Let start the challenge, and have some fun!

Above you will find 3 squares.

Do note that the 2 yellows are of the same area and 1 blue of area bigger than the yellow ones.

If the total area of the 3 squares are 57 sq cm, determine the area of the bigger blue square.

I believe you will enjoy this math question.

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Using Units to Deduce Maths Formula

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!

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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 ......


:-)





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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.

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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!

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