# Addition

## Addition In Algebra

In **algebra**, which is a generalization of **arithmetic**, addition is also carried out by counting. For example, to sum the expressions 5x and 6x we notice that 5x means we have five xs and 6x means we have six xs, making a total of 11 xs. Thus 5x + 6x = (5 + 6)x = 11x, which is usually established on the basis of the distributive law, an important property that the real numbers obey. In general, only like variables or powers can be added algebraically. In adding two polynomial expressions, only similar terms are combined; thus, (3x^{2} + 2x +7y + z) + (x^{3} + 3x + 4z + 2yz) = (x^{3} + 3x^{2} + 5x + 7y + 5z + 2yz).

See also Fraction, common.

## Resources

### Books

Eves, Howard Whitley. *Foundations and Fundamental Concepts of Mathematics.* NewYork: Dover, 1997.

Grahm, Alan. *Teach Yourself Basic Mathematics.* Chicago,IL: McGraw-Hill Contemporary, 2001.

Gullberg, Jan, and Peter Hilton. *Mathematics: From the Birth of Numbers.* W.W. Norton & Company, 1997.

Paulos, John Allen. *Beyond Numeracy, Ruminations of a Numbers Man.* New York: Alfred A. Knopf, 1991.

Tobey, John, and Jeffrey Slater. *Beginning Algebra.* 4th ed. NY: Prentice Hall, 1997.

Weisstein, Eric W. *The CRC Concise Encyclopedia of Mathematics.* New York: CRC Press, 1998.

J. R. Maddocks

## Additional topics

Science EncyclopediaScience & Philosophy: *1,2-dibromoethane* to *Adrenergic*Addition - Adding Natural Numbers, The Addition Algorithm, Adding Common Fractions, Adding Decimal Fractions, Adding Signed Numbers