MATH IS HARD?

MATH IS HARD?

Why do some students find math is hard?  Because knowing math means knowing a lot of stuff.

First of all, there are many numbers in math that you need to know by heart. There's 0, there's 1, there's 2, there's 3, and on and on and on till you learn that there's also the number 1,000,000,000.  So now you have a trillion things to know.  That is you have a trillion and one numbers to know: all the numbers from 0 to 1,000,000,000.  

Luckily, mathematicians have made it easier for students to know all these numbers without having to learn each one of them or even to say or write each one of them.  What is this thing that makes it easy to know all these 1,000,000,001 numbers?  The key to knowing all of them is that each number following another is only 1 more than the previous number.  For example:

1 = 0 + 1.

2 = 1 + 1.

3 = 2 + 1.

4 = 3 + 1.

5 = 4 + 1.

Do you see the pattern?  Each succeeding number is 1 more than the previous number.  So that means that 1,000,000,000 is this:

1,000,000,000 = 999,999,999 + 1.

So knowing only one thing makes you learn a trillion things.  And you can learn these trillion things in only 10 minutes, 1 hour, or 10 hours depending on how much fun you are having in learning a trillion things.

What about the rest of math?  Math is all about patterns.  Knowing one pattern can make you learn 10, 100, 1000, 10000 or a trillion things all at once, I mean, 10 minutes, 1 hour, or 10 hours.

Have fun discovering and exploring mathematics!

John

The Basic Operations On Numbers

THE BASIC OPERATIONS ON NUMBERS

There are two (2) basic operations on numbers.  They are ADDITION (+) and SUBTRACTION (-).  All other operations on numbers are different versions of addition or subtraction.

Also, if one is to do a deep analysis on numbers, à la NUMBER THEORY, there is only one operation on numbers -- addition.  Because, one can always add NEGATIVE NUMBERS and get the same results in addition as one would in subtraction.  But for the sake of clarity and brevity, we will say there are two basic operations on numbers.

The following exploration discusses the variations of HOW TO ADD NUMBERS.

HOW TO ADD WHOLE NUMBERS

Whole numbers starts with 0 followed by 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, et cetera, excluding INFINITY.

Given: 1 + 2

The SYMBOL + means to ADD THE NUMBERS.

So we have 1 + 2 = 3.

The symbol = means IS EXACTLY EQUAL TO.

Summary:  When adding whole numbers, you just add the QUANTITIES the numbers represent and combine them into one number.

HOW TO ADD INTEGERS
Integers starts with the lowest integer next to the lowest infinity followed sequentially by the next higher integer, and so forth, with the middle integer being zero (0), and continuing on up to the highest integer next to the highest infinity.

Given: 1 + (-2)

The symbol “(“, OPEN PARENTHESIS, and “)”, CLOSED PARENTHESIS, means the enclosed number or EXPRESSION should be solved or evaluated first.

We will solve the GIVEN step by step.

Step 1: Write given.

1 + (-2) =

Step 2: Rewrite the given so that it is easily solvable or readable.  We use the COMMUTATIVE PROPERTY OR RULE OF ADDITION.

1 + (-2) = (-2) + 1

Step 3: Solve the number or expression inside the parentheses.

(-2) + 1 = -2 + 1

Step 4: Solve the easily solvable, readable, or simplified expression, or simplify it further.  We will simplify this expression further for those who wanted to simplify it further.  We will use the DISTRIBUTIVE PROPERTY OF MULTIPLICATION on -2, negative two.

-2 + 1 = (-1) (1 + 1) + 1

Step 5: Simplify the whole expression.  We continue using the distributive property of multiplication.

(-1) (1 + 1) + 1 = (-1) + (-1) + 1

Step 6: Simplify the whole expression.  Using the INVERSE PROPERTY OF ADDITION, we add up numbers that add up to zeroes (0).

(-1) + (-1) + 1 = (-1) + 0

Step 7: Simplify the whole expression. We will use the IDENTITY PROPERTY OF ADDITION.

(-1) + 0 = (-1)

Step 8: Simplify the expression and write the final answer.  We solve the expression inside the parentheses simply by releasing the parentheses because the expression is already in its most simplified form.

(-1) = -1

Given: 1 + (-2)

Answer: -1

Summary: When adding integers, knowledge and understanding of the commutative, ASSOCIATIVE, distributive, inverse, and identity properties of addition and multiplication will make you truly understand the dynamics and complexities involved in the simple process of adding integers.

Have fun learning!

John