addition

One of the four fundamental operations of arithmetic, denoted by the sign "+".

The numbers which are added are called summands. For example, 4 (a summand) + 3 (another summand) = 7 (sum).

Addition of fractions

Fractions can be added directly only if they have equal denominators, e.g., 3/17 + 4/17 = 7/17.

If fractions with unequal denominators are to be added they must first be brought to their least common denominator.

Addition of literal numbers

Identiaccly-named numbers can be added (and subtracted) by adding the coefficients:

2a + 3b + a + 4b = 3a + 7b

summands may be interchanged (commutative law):

a + b = b + a

With more than two summands, brackets may be inserted (associative law):

a + b + c = (a + b) + c = a + (b + c)

Addition of directed numbers

No further rule is needed for the addition of posituve numbers:

a + (+b) = a + b, 5 + (+3) = 5 + 3 = 8.

to add one negative number to another, its absolute value is subtracted:

a + (-b) = a - b, (-a) + (-b) = -(a + b);
5 + (-3) = 5 - 3 = 2, (-5) + (-3) = -(5 + 3) = -8.

Addition of powers and surds

Powers and surds must be treated like literal numbers for the purposes of addition, e.g.,

a² + 4b³ + 4c³ +4a² = 5a² + 4(b³ + c³;
3√2 + 5√3 + √2 = 4√2 + 5√3

Addition of complex numbers

In adding complex numbers the real and imaginary parts must be added separately, e.g.,

(5 + 3i) + (17 - i) = 22 + 2i.

Addition in terms of sets

The addition of positive numbers can best be defined in terms of set theory; if one considers set A to contain 4 elements, set B to contain 5 elements, then A U B (see union) contains 9 elements; i.e., 4 + 5 = 9. The addition of negative numbers is equivalent to subtraction in that a + (-b) is equivalent to a - b.

Related categories

• ALGEBRA
• ARITHMETIC

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