It was said, the language of science is mathematics, and the grammar of mathematics is algebra. The word algebra comes from the Arabic al-jabr, in German “reunification of parts” or “simplification”. Without algebra, part of our scientific and technical progress would not have been possible. Algebra is like a tunnel through a mountain – a shortcut. As long as we only calculate with natural numbers or with fractions from them, knows z. B. With 1/7 or with 0,34 = 34/100, that's how long we do arithmetic. In algebra, letters are also used for arithmetic. We can z. B. to say, a box of nuts is equal to a. Than are 5 Boxes of nuts = 5a or 7a = 7 Boxes of nuts. If we 5 Boxes of nuts and 7 Want to add boxes of nuts, so we write
5a + 7a = 12a.
That is also correct then, when we say, a be a sack of potatoes or a be 3 Apples. 5a is an abbreviation for 5 · a. Mathematicians want to write as little as possible and therefore do without the mark, because letters and letters cannot be confused with numbers! so ab is the same as a times b: ab = a · b.
If you have several numbers in a row, you must of course not leave out the multiplication symbol, because 5 · 3 means something other than 53:
5 · 3≠53.
The sign * is the mathematical abbreviation for "not equal".
When you multiply two numbers together, so it is the same, whether one for example 3 · 4 or 4 · 3 calculates. It doesn't matter, what numbers you take together: the order of the factors does not matter. In the language of algebra this is called
a b = b a (amal b is equal to b times a).
But also the tasks, which seem quite complicated in natural language, can be easily surveyed in algebraic notation. The question: "What is the number, their around 1 diminished threefold, added to their double, 9 results?“Is algebraically simple:
2x + 3x – 1 =9.
The letter x is used for the unknown number, In this equation one could (You can easily find the number you are looking for by trying. The equation can be transformed with a simple mathematical procedure, that the solution arises by itself:
2x + 3x —1 =9
5x — 1 =9
5x — 1 + 1= 9 + 1
5x = 10
x = 2
So the number we are looking for is called 2.
The difference between arithmetic and algebra, however, is not just that, that in algebra one calculates not only with numbers but also with letters. In addition to the basic arithmetic operations a + b, a – b, a – b and a : b one still uses powers and roots, and except with the numbers, which are greater than 0 are (called positive numbers) is also with 0 and calculated with the so-called negative numbers. You write these negative numbers with a minus sign in front of the number, also -3 or -6:
4 — 6 = —2.