Superior of partial fraction

What is complex fraction?
Complex fraction is a fraction whereby its numerator or denominator or both consists of fractions.

Partial fraction helps us to solve some problematic question involve complex fractions.

No worries!

There are always patterns in Mathematics.

You may observe and deduce formula from it.

Please download and learn from the exercise - solution below.

Partial Fraction

Advanced book 1 - Accessment

Dear all, here is the wrap up for advanced book 1.

It consists of interesting concept like HCF, LCM, Prime Factors, Divisibility, Complex Fraction, Partial Fraction.

Please get the solution for the accesment .
Answer Advanced Accessment 1

Complex fraction

What is fraction?

Imagining you have one whole cake and you need to share the cake among you and your friends.

Here come the problems, to be fair, we should share the cake equally.

I cut the cake equally to eight pieces and share it with 7 of my friends.

Each of us getting 1/8 of the whole cake.

When one of my friend - Lily is sick and refuse to eat the cake. She cake the cake to me.

Then I get 2 / 8 of the whole cake. By simplification, I get 1 / 4 of the whole cake.

When it comes to include operation in fraction, it follows BODMAS rule as whole number.

What is BODMAS ? BODMAS is the precedence rule when we are solving equation. 

B - Bracket

O - Power of / root

D / M - Division / Multiplication (from left to right)

A / S - Addition / Subtraction (from left to right)

So, when there is a equation, we need to solve all those grouped in one bracket, then follow by power of / root of a number , then division / multiplication (left to right because they are in same level of precedence), then addition / subtraction (left to right because they are in same level of precedence as well).

Fraction have numerator / denumenator. 

Remember, division bar / can be treated as division as well.

What is complex fraction ?

Complex fraction is a fraction where numerator or denumenator is also a fraction.

No worry, solving a complex fraction is nothing much more difficult than fraction.

First, simplify the complex fraction to simpler form before doing + / -

You have to treat division bar as division. 

When you divide a fraction a by another fraction b, you may just change to multiplication by reversing numerator and denumerator of fraction b.

You should need to change the fraction to similar denumerator before doing + / -.

In short, please do refer to the notes below for extra explaination.

Complex fraction

Revision Intermediate Level book 1 - 8

After a quite a long and challenging journey, we finally finish the training on Intermediate level book 1 to book 8.

What a relieve huh ?

Along the training, we have go through concept or theory related to Euler Path, Counting, Shortest Path Distance, Gauss Theorem, Tricks in calculation, Logical Thinking Skills, Speed, Marvels of Triangle and etc. Sorry that I could not list down all one by one.

Please refer to the attachment below for revision exercise (answer provided).

Revision Intermediate level Book 1 - 8

I also do provide the python code to solve question 28 - How many times a digits appear in a range of number. If you may use the code to check your answer.

Check the number of occurence of a digit in a range of number

Loops

What is loops ?
What loops do ?

Please do imagine you need go bicycle for 7 days.
There is a loop of 7 iterations, and your statement / activity should be cycling.

Keep it simple.
Loop help us to do job repeatedly in one block of codes.

There are several types of loops. For instance, there are for loop, while loop, do while loop and etc.

The basic / simple loop should be for loop.
You may ask your program to do the loop for how many times using "for" keywords.

Example : you may print number 0 to 4 using the statement below
for ind in range(5) : 
      print (ind)

On the other hand, a while loop will execute the block of codes / statement while / when some condition is fulfilled.

Example : the while loop print "It is true" as long as the condition is true.
Please be reminded that the condition must be true initially, else the while loop will not be executed.
Please be aware that u must have stopping criteria : assign the condition to false in the while loop.
Else you will be having an infinity loop and hit runtime error. (since you never tell the program when should it stops)

condition is true initially
while condition is true : 
       print("It is true")
       if  something happend :
              condition is false

Please do refer to the link below for further details:
Loop

Dictionary

The problems in this set are designed to be more accessible to beginning coders. As a learning aid, walkthroughs discussing how to solve the problems in this set are available by clicking on this link. On completion of this problem set, students should have experience at using arrays to store, search through, and manipulate large data sets.

Dictionary

Input File: dictin.txt
Output File: dictout.txt
Time Limit: 1 second

Integerland and Wholenumberland are alike in many ways: similar culture, similar traditions - they even share the same national dress (the parenthetic pyjamas). Yet despite this, the two nations have never gotten along well. It is widely believed that this is because of their greatest differences - their language. A sentence that sounds perfectly intelligible on one side of the border is complete gibberish on the other side.

For example, if an Integerlander wanted to find out the time, she would ask, "140 2 87 2 3?". On the other hand, a Wholenumberlander would ask "19 71 555 71 556?". As you can see, these languages are very distinctive. It would be impossible to mistake one for the other.

This year's regional trade talks are to be held in Australia. You have been appointed the official translator for the proceedings. Using your trusty Integerlandese-Wholenumberlandese dictionary and your rusty laptop, you must be able to fluently translate from one language to another.

Input

The first line will consist of two integers d and w, separated by a space. You are guaranteed that 0 <= d, w <= 1,000.

The following d lines will each describe an entry in your bilingual dictionary. Each of these lines contains two integers separated by a space: a word in Integerlandese, and its Wholenumberlandese counterpart. All integers will be between -2,000,000,000 and 2,000,000,000 inclusive. You are guaranteed that no Integerlandese word will appear more than once in the dictionary.

The following w lines will each contain a single word in Integerlandese for you to translate.

Output

For each Integerland word you are asked to translate, you must print out a single line containing the corresponding Wholenumberland word. If there is no translation in your dictionary, you should print "C?" for that line.

Please do get the solution by the link below: 

Dictionary solution

Python Operator

What coding can do?
What coding can help?
How python help us in coding ?

Python Operator is one of those basic but "powerful" problem solving tools.
We may use it to do arithmetic operation like solving our daily Mathematics questions.
We can't deny how powerful is it when it combine with other operators like Assignment operators, Comparison operators, Logical operators, Identity operators, Membership operators and bitwise operator.

Assignment operators, we can guess what it does by its name. Simpy - it do assignment.
Wait a second! What is assignment ?
Remember = means assignment and == means equal in python.
Some  may scratch his or her head when it come to here.
Kind of confusing, huh?
Lets say we have a variable name box, and we put RM 10 into it.
Simply the equation will be as follows:
box = 10 (This is called assignment)

But, is box equal to 10 ? No! box is a container to keep the money.

Then what == do ?
We use == when we need to do comparison, which will be discussed in Comparison Operators.

If my mother give me 3 ringgit more, then i should have:
box = 10
box = box + 3 (total money I got at the moment) (= 13)
This equation is  kind of too long, it could be abbreviated as :
box += 3

Simply, x-=3 means x = x - 3
x * = 2 means x = x*2

You may explore more in the notes provided in the link below.

Okay! Now, we may continue to Comparison operator.
For instance, I would like to check if I got RM 10 in my box.
I use box == 10 (it return true if I got RM 10 else return false)
I had RM 13 now, so the equation will return false.
Obviously, box == 13 will return true.

It could be a super long story if I continue the other operator here.
You may explore more from the link below.
Please do try the humble and simple question provided in the notes as exercise.

Practise Makes Perfect!

Week3 - Python operator