ALGEBRA IS A METHOD OF WRITTEN CALCULATIONS that help us reason about numbers.
At the very outset, the student should realize that algebra is a skill. And like any skill -- driving a car,
baking cookies, playing the guitar -- it requires practice. A lot of practice. Written practice.
That said, let us begin.The first thing to note is that in algebra we use letters as well as numbers.
But the letters represent numbers. and the rules of algebra correspond to the rules of arithmetic, but
we write those rules using letters.
At the very outset, the student should realize that algebra is a skill. And like any skill -- driving a car,
baking cookies, playing the guitar -- it requires practice. A lot of practice. Written practice.
That said, let us begin.The first thing to note is that in algebra we use letters as well as numbers.
But the letters represent numbers. and the rules of algebra correspond to the rules of arithmetic, but
we write those rules using letters.
For example, we know in arithmetic that the order in which we add two numbers does not matter.
7 + 3 = 3 + 7.
In algebra, we express that as the rule:
a + b = b + a.
Letter a simply means the first number -- whatever it might be. Letter b means the second number. We use letters because we mean that the rule will be true for any numbers. In algebra, we imitate with letters what we could write with numbers.
(The symbols for numbers, after all, are nothing but written marks. And so are letters.)
(The symbols for numbers, after all, are nothing but written marks. And so are letters.)
The numbers are the numerical symbols, while the letters are called literal symbols.
