Contemporary state math standards emphasize that students must demonstrate an understanding of the mathematical ideas underlying the computations that have typically been the core of the elementary school math curriculum. The standards have put an increased emphasis on the study of fractions in upper elementary grades, which are the years during…

Eigenvalue is an important concept in Linear Algebra. It is well known that the eigenvectors corresponding to different eigenvalues of a square matrix are linear independent. In most of the existing textbooks, this result is proven using mathematical induction. In this note, a new proof using Vandermonde determinant is given. It is shown that this…

This paper focuses on the representation of a proper fraction "a"/"b" by a decimal number base "n" where "n" is any integer greater than 1. The scope is narrowed to look at only fractions where "a","b" are positive integers with "a" less than "b" and "b" not equal to 0 nor equal to 1. Some relationships were found between "b" and "n", which…