## Step-by-Step Calculator

Yet despite what students may think, algebra exists to make their lives easier. Contrary to popular belief, algebra is not simply the process of substituting the numbers and operations in mathematical equations with symbols. Algebra is better thought of as a language for describing mathematical ideas. It is through algebra that we can model different phenomena and make sense of the world around us.

Still a bit puzzled as to what algebra is? The word first entered the English language in the fifteenth century and was originally used to describe the surgical procedure used for placing broken or dislocated bones back in place — which is appropriate given that algebra helps us to piece together bits of information. Aside from the fact that algebra is a prerequisite to secondary school math, algebra is also important for helping children develop their reasoning skills. It gives them a way of representing their ideas succinctly, and to work their way through math problems systematically.

Algebra comes into its own for problems that involve unknown quantities. To see what this looks like in practice, read on! How much change are they each left with? It turns out we can use a simple algebraic equation to figure this problem out quickly and easily.

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For this example, we are going to represent the change they are left with using the letter x any letter will do — x just happens to be a popular choice. The total change will, therefore, be represented by 2x because they need to divide it between themselves. There are 26 cats in the pet shop. This is two more than three times the number of dogs.

How many dogs are there in the pet shop? Alice and Bob have some candy. If Alice gives Bob a piece of candy, Bob has twice as much candy as her.

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If Bob gives Alice a piece of candy, they have the same number. How many pieces of candy do they each have? Abstract Algebra, 2nd ed. Edwards, H. Galois Theory, corrected 2nd printing. New York: Springer-Verlag, Euler, L. Elements of Algebra. Petersburg, Russia: Royal Acad. English reprint Sangwin, C. Stradbroke, England: Tarquin Pub.

Gallian, J. Contemporary Abstract Algebra, 3rd ed. Lexington, MA: D. Heath, Grove, L. New York: Academic Press, Hall, H. London: Macmillan, Harrison, M.

Herstein, I. Noncommutative Rings. Washington, DC: Math. Topics in Algebra, 2nd ed.

New York: Wiley, Jacobson, N. Basic Algebra II, 2nd ed. New York: W. Freeman, Kaplansky, I.

## Algebra -- from Wolfram MathWorld

Fields and Rings, 2nd ed. Lang, S. Undergraduate Algebra, 2nd ed. Pedersen, J.

### Mathematical Mindset Algebra

Schafer, R. An Introduction to Nonassociative Algebras. Spiegel, M. New York: McGraw-Hill, Uspensky, J. Theory of Equations. Algebra, Vol. Geometry and Algebra in Ancient Civilizations. Varadarajan, V.

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Algebra in Ancient and Modern Times. Weisstein, E.

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- Introducing Algebra.

Renze, John and Weisstein, Eric W.