Learning About Addition

By Author: Pierce Brosnan
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Introduction of learning about addition :

Addition is a mathematical operation that represents combining collections of objects together into a larger collection. It is signified by the plus sign (+).

For example, in the above picture on the right, there are 1 + 4 apples—meaning one apple and four other apples—which is the same as five apples. Therefore, 1 + 4 = 5. Besides counts of fruit, addition can also represent combining other physical and abstract quantities using different kinds of numbers: negative numbers, fractions, irrational numbers, vectors, decimals and more. This is how we have to learn addition learning.

Learning of addition properties:

I) Positive number addition:

Positive integers are whole numbers greater than zero. Example: 2 + 3, 2 + 9, 20 + 45 + 23…etc. Example: 2 + 3 = 5, 3 + 7 = 10

II) Negative number addition:

The addition is done for negative numbers. Example: -19, -38, -458, -594, and 6558…etc. Negative numbers indicated by the minus sign (-). Example: (-2) + 3= 1, 3 + (-5) = -2.

Adding Integers Rules:

Rule 1: The ...
... sum of two positive integers is always positive integer.

Rule 2: To add a positive and a negative integer

1) Find the absolute value of each integer.

2) Subtract the small number from the larger number you get in Step 1.

3) The answer from Step 2 takes the sign of the integer with the greater absolute value.

Properties for adding numbers:

The properties are,

Identity property: 0+c=c+0=c
Example: 41+0=0+41=41.

Community property: a+b=b+a
Example: 200+16=16+200.

Associative property: (a+b)+c=a+(b+c)
Example: (5+24)+7=5+(24+7)=36.

Inverse property: c+(-c)=0
Example: 7+(-7)=0

Examples for learning about addition:

Example 1: 705 + 922 = 1627

Example 2: 4694 + 5887 + 6559 = 17140

Example 3: 4633+ 565 + 879 + 1336 = 7413

Example 4: Find two consecutive integers whose sum is equal 127.

Solution:

Let x and x+1 be the two numbers. Use the fact that their sum is equal to 127 to write the equation

x + (x + 1) = 127

2x +1 = 127

Solve for x to obtain

x = 63

The two numbers are

x = 63 and x + 1 = 64

Problem 5: Find three consecutive integers whose sum is equal to 888

Solution:

Let the three numbers be x, x+1 and x+2. Their sum is equal to 888, hence

x + (x + 1) + (x + 2) = 888

Solve for x and find the three numbers

x = 295, x + 1 = 296 and x + 2 = 297

Adding decimals

3.25

(+) 2.34

5.59

Right angles are fundamental in Euclid's Elements. They are defined in Book 1, definition 10, which also defines perpendicular lines. Euclid uses right angles in definitions 11 and 12 to define acute angles (those smaller than a right angle) and obtuse angles (those greater than a right angle).Two angles are called complementary if their sum is a right angle.

Book 1 Postulate 4 states that all right angles are equal, which allows Euclid to use a right angle as a unit with which to measure other angles. Euclid's commentator Proclus gave a proof of this postulate using the previous postulates, but it may be argued that this proof makes use of some hidden assumptions. Saccheri gave a proof as well but using a more explicit assumtion. In Hilbert's axiomatization of geometry this statement is given as a theorem, but only after much groundwork. One may argue that, even if postulate 4 can be proven from the preceding ones, in the order that Euclid presents his material it is necessary to include it since without it postulate 5, which uses the right angle as a unit of measure, makes no sense.

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