Before this page, the reader should have read In Algebra "A Number" Doesn't Mean "Any Old Number" and should understand the idea of variable.

      Know The Invisible (Understood) Ones is also valuable to the reader because it explains the notation system used with a variable.

      This page deals mostly with expression involving only one operation, and, the first considered are those involving only one number -- unary operations.

      Before writing math expressions, one needs to know something about conjunctions and prepositions -- and, or, from, between -- as they are used in speaking and writing English. (For prepositions from an English perspective, visit http://grammar.uoregon.edu/prepositions/prepositions.html.)

      In math, as in English, AND is a signal that at least two ideas are involved. Very often these ideas also involve addition, but not always.

      In math, as in English, OF is a signal that information about 1 item is going to be stated.

      Here are expressions/equations involving of and/or and. Examine how the and indicates more than one item and how the of describes an item.

• five and seven: 5, 7
• the product of five and seven: (5)(7)
• the sum of five and seven: 5 + 7
• the product of two and a number: 2(x)
• The area of a rectangle is the product of length and width.

      Here's another important and useful feature concerning of and the prepositional phrases it begins. Prepositional phrases that begin with of may be removed from a sentence and the sentence will have the same meaning, less information, but the same meaning. Consider these examples printed in two different colors. Read the sentence first reading every word and then just reading the words in black.

• The area of a rectangle is the product of length and width.
• The square of the hypotenuse of a right triangle is equal to the sum of the squares of the two adjacent sides.

      Below is a partial list, with mathematical symbols, of operations/ functions which require information provided through an of prepositional phrase.

• the opposite of: -( )
• the absolute value of: | |
• the reciprocal of: 1/( )
• half of: ( )/2
• the square of: ( )²
• the cube of: ( )³
• the square root of: ( )

      The opposite, absolute value, square root, reciprocal are unary operations or functions -- those which are performed on one number. See how important the prepositional phrase beginning with of is in writing the math expression or equation.

      In summary,

• AND is a signal that at least two ideas are involved and very often, but not always, these ideas involve addition.
• OF is a signal that information about 1 item is going to be stated.