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Introduction to Angles: The Art of Problem Solving:

The Story of Maths : The Genius of the East /قصة الرياضيات : عبقرية الشرق
This is the untold story of the mathematics of the East, that transformed the West.
Why Math?
To put it plainly math exists in our imagination. When we practice difficult mathematics we improve our ability to utilize imagination. We live in a universe bathed in order, or at least it appears this way to us. This order takes on the form of mathematical logic in our brain. If you learn the art of math I promise your interpretation of reality will be altered and improved forever.
Placing Numbers On A Number Line
Use the number line for adding and subtracting integers:
 Add a positive integer by moving to the right on the number line
 Add a negative integer by moving to the left on the number line
 Subtract an integer by adding its opposite
Watch out! The negative of a negative is the opposite positive number. That is, for real numbers, – ( a ) = + a
Adding Fractions with Unlike Denominators
Here are the steps for adding fractions with different denominators. We will breakdown each step just like before to make sure you’ve got it.
 Build each fraction so that both denominators are equal.Remember, when adding fractions with different denominators, the denominators must be equal. So we must complete this step first.
 Rewrite each equivalent fraction using this new denominator
 Now you can add the numerators, and keep the denominator of the equivalent fractions.
 Rewrite your answer as a simplified or reduced fraction, if needed.
We know this sounds like a lot of work, and it is, but once you understand thoroughly how to find the Common Denominator or the LCD, and build equivalent fractions, everything else will start to fall into place. So, let’s take our time to do it Right!
But keep in mind, if you are doing homework, be sure to answer the problems in the form asked for in the assignment.
Adding Fractions with Different Denominators
Add 1/2 + 1/3
+
Notice that the overall size of our point of reference
(The Whole) is EXACTLY the same.
Step #1 in our rule tells us that the denominators must be equal. And the easiest way to find a common denominator is to just multiply the denominators.
So let’s do that now…
2 x 3 = 6
The Common Denominator for 1/2 and 1/3 is 6
Step #2 – Rewrite each equivalent fraction using this new denominator.
Since…
1/2 is equivalent to 3/6
And…
1/3 is equivalent to 2/6
We rewrite our equation to read…
Add: 3/6 + 2/6
Now we are ready to do Step #3 – ADD the numerators, and keep the denominator of the equivalent fractions (which is 6).
So, we end up with…
3/6 + 2/6 = (3 + 2 )/6 = 5/6
+
=
Finally, Step #4 – Rewrite your answer as a simplified or reduced fraction, if needed.
In our example, the answer (5/6) is already in its simplest form. So, no further action is required!
That’s It!
A quick and easy way to add fractions with different denominators.
The Fundamental Theorem of Arithmetic
The Basic Idea is that any integer above 1 is either a Prime Number, or can be made by multiplying Prime Numbers together.