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