What is the difference between pre-algebra and algebra 1?

Answer 1

Pre-algebra essentially introduces the concept of the single variable, where one part of a binary operation (addition, subtraction, multiplication, or division) is replaced by a box. The box, in algebra, is replaced by a letter such as x or y, to denote a variable, or a, b, or c to denote constants. For example: X + 5 = 9

Pre-algebra also incorporates fractions, decimals, conversions between them, and the standard mathematical operations. In short, everything you need to build upon the concepts for algebra.

Algebra begins with single variable equations and builds up to systems of equations with multiple variables, quadratic equations, polynomials (equations of degree n), real and Irrational Numbers, the cartesian coordinate system, and on up to matrix operations involving multiple dimensions. I believe algebra pretty much stops short of Hilbert space, which has an infinite number of dimensions.

ax + by = c is a typical line equation from algebra which, in slope intercept form, is:

y = mx + b. b = the y-intercept, and m=∆y/∆x or (y2 - y1)/(x2 - x1)

ax2 + bx + c = d is a typical quadratic equation.

Polynomials would be of the form axn + bx(n-1) + ... + z = 0.

Factoring polynomials is another important concept from algebra. If you can do long division by hand you have some of the key concepts for factoring already.

Perhaps the most useful concept from algebra is ratios and proportions.