Form and Value
Two mathematical expressions may take different form and yet have the same value. For example, 
and 2 look different but are the same number. Likewise, the number 1 can be expressed as 30 or 
.
In the decimal system, for example, the fraction ½ is also express as 0.5. The word "fraction" refers to the form of a number. The form of 
is a fraction, but its value is 4, which is an integer. Similarly, 2 ½ has the form of a mixed fraction, but it can be expressed as the fraction 
, or the decimal number 2.5.
Algebraic expressions also have form and value. The value of 3(x + 2) and 3x + 6 is the same, but 3(x + 2) is in the monomial form, and 3x + 6 is in the binomial form. Numbers can be also written using both monomial and binomial form.
In monomial form, even numbers are expressed as 2x for x = 1, 2, 3,… generating all even numbers 2, 4, 6,…. In binomial form, even numbersare expressed as 2x + 2 for x = 0, 1, 2,…, which again generates all the even numbers 2, 4, 6,….
Bibliography
Amdahl, Kenn, and Jim Loats. Algebra Unplugged. Broomfield, CO: Clearwater Publishing Co., 1995.
Miller, Charles D., Vern E. Heeren, and E. John Hornsby, Jr. Mathematical Ideas, 9th ed. Boston: Addison-Wesley, 2001.
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