Guessing, for Pólya, is an important way of getting an initial handle on a mathematical problem. An argument can be made to place guessing in any one of the first three steps of the four-step approach to problem solving as described in "How to Solve It" (Pólya 1945). It could be a part of understanding the problem, devising a plan, or…

By the time they reach middle school, all students have been taught to add fractions. However, not all have "learned" to add fractions. The common mistake in adding fractions is to report that a/b + c/d is equal to (a + c)/(b + d). It is certainly necessary to correct this mistake when a student makes it. However, this occasion also…

Presents an activity on fractions and explains how students obtain different fractions having different patterns when they are represented by their decimal expansions. (ASK)

Rules for determining the number of initial zeros and the period of a repeating decimal are stated and proved. (SD)

Patterns that appear in the repeating digits of a decimal are used to help convince students that any infinite repeating decimal can be written in the form of a rational number. (JT)

The application of the Hamilton method for apportioning seats in the United States House of Representatives is presented based on the 1980 census. It is felt that this method is preferable to the equal proportion method currently used if for no other reason than the greater appearance of fairness. (MP)

Interesting mathematical questions that require computations involving fractions, percentages, and decimals are presented. The material is designed for students in the middle school grades, but many of the ideas could be used with higher or lower level pupils. (MP)

Discusses the characteristics of repeating decimals to facilitate the translation of repeating decimals to fractions. Describes the algebraic and arithmetic methods for converting the repeating decimal. Illustrates arithmetic operations for n-digit integer. Eight references are listed. (YP)

This discussion of cyclic patterns that appear in repeating decimals includes the use of the calculator in discovering the patterns. (MP)

Repeating decimals are used as a source for geometric patterns. Ways for generating patterns focus on dividing a circle into certain numbers of equal parts and interpreting the decimal expansions of certain fractions in terms of connecting sequences of points. Suggestions for possible expansions are given. (MP)

This article first classifies fractions according to whether their decimal expansions terminate or repeat, and then considers the corresponding classification when the expansion is made in the base "s" numeration system. (MM)