Addition

Addition is the mathematical process of putting things together, that is to say joining. With the addition of two numbers, the process may be thought of moving a certain distance in the positive direction. If one considers the following equation:

$a+b = c$

The plus sign or addition symbol ( + ) marks that addition is preformed on its adjacent numerals (a and b). C is called the sum of a and b. This equation may be calculated by moving a, b whole units in the positive direction.

Computation

Taking in account the analogy from the previous section,

$3 + 4 = ?$

may be thought of as moving 3 in the positive direction by 4 units:

$3 + (1+1+1+1)$

with may be counted to achieve the answer of 7.

Properties

• Addition is commutative: $a + b = b + a$
• Addition is associative: $a+(b+c)=(a+b)+c$
• Addition has an identity element: 0,zero.
• It can be performed in terms of subtraction: $N+M==N-(-0-M)$

Estimation

Addition sums are possible to be estimated. It is done by rounding off each addend to the nearest n significant figures (where n is a whole number), and adding both of the rounded numbers.

Table of basic additions

$+$	$-\frac{1}{0}$	$-1$	$-0$	$\frac{0}{0}$	$0$	$1$	$\frac{1}{0}$
$-\frac{1}{0}$	$-\frac{1}{0}$	$-\frac{1}{0}$	$-\frac{1}{0}$	$\frac{0}{0}$	$-\frac{1}{0}$	$-\frac{1}{0}$	$\frac{0}{0}$
$-1$	$-\frac{1}{0}$	$-2$	$-1$	$\frac{0}{0}$	$-1$	$0$	$\frac{1}{0}$
$-0$	$-\frac{1}{0}$	$-1$	$-0$	$\frac{0}{0}$	$0$	$1$	$\frac{1}{0}$
$\frac{0}{0}$	$\frac{0}{0}$	$\frac{0}{0}$	$\frac{0}{0}$	$\frac{0}{0}$	$\frac{0}{0}$	$\frac{0}{0}$	$\frac{0}{0}$
$0$	$-\frac{1}{0}$	$-1$	$0$	$\frac{0}{0}$	$0$	$1$	$\frac{1}{0}$
$1$	$-\frac{1}{0}$	$0$	$1$	$\frac{0}{0}$	$1$	$2$	$\frac{1}{0}$
$\frac{1}{0}$	$\frac{0}{0}$	$\frac{1}{0}$	$\frac{1}{0}$	$\frac{0}{0}$	$\frac{1}{0}$	$\frac{1}{0}$	$\frac{0}{0}$

See also

• Multiplication
• Summation
• Series