Why do you need Algebra?

Answer 1

The last answer given here was just terrible, and was obviously given by someone who doesn't care about education. So let's try this again:

Though not every individual will use high-level algebra, its importance is undeniable in the sciences. Also, algebra is not a subject of arcane knowledge that will never have real-life applications. Everyone, believe it or not, has some rudimentary knowledge of the principles of algebra, and this knowledge is used to solve everyday problems. Let's look at some of the "big ideas":

1. In algebra, the natures of operations, such as the basic operations of addition, subtraction, multiplication, and division, are explained through axioms and theorems. For example, addition and multiplication are commutative and associative, meaning that, firstly, if one combines two terms with addition or multiplication, the order they were in beforehand is irrelevant, and secondly, if multiple calculations are to take place with addition or multiplication, the order in which those calculations are performed is irrelevant. In contrast, subtraction and division have neither of these properties. Also, operations that would be useful to incorporate into mathematics can be introduced with similar rules, and their relationships with other operations can be affirmed with these rules. For example, exponentiation is a shorthand for multiplication between like bases, and factorials, which are useful for finding permutations (the number of ways multiple objects may be ordered), are defined by multiplication of natural numbers.

2. Just as operations are varied, so are sets of numbers. A "set" is just a group of mathematical objects, but those objects usually share a common characteristic. For example, the set of rational numbers consists only of numbers that can be expressed as ratios of integers. It is important to know this because some theorems only work with rational numbers, as do some algorithms for finding solutions to problems. If you didn't know this, you might miscalculate the solution to a problem.

3. The third concept is introduced in pre-algebra, but it is so appealing to our "common sense" that people can realize this as children: if two quantities are equal then adding, subtracting, multiplying, and dividing them by the same quantities shouldn't change the fact that they're equal. This basic principle, by the way, enables you to solve a variety of problems involving only one unknown value. Other operations invoke the same principle, but some are less intuitive, though no less useful.

4. Lastly, algebra is all about generalizing principles that are encountered in arithmetic and higher-level subjects. In order to do this, we have to ignore quantities that are used to solve "real-life" problems. For example, if we wanted to prove that all even numbers are divisible by 2, it wouldn't help to note that 4/2 = 2 or that 14/2 = 7 or even that 66/2 = 33. This is because we cannot prove a rule that is meant to hold for, say, all real numbers merely by noting that it works for a few of them. In order to prove this, we would have to evoke the definitions of "even", "factor", "divisible", and so forth until we proved it without assuming any particular value. Some people scoff at this and consider such exercises to be useless, but something cannot be held to be true in math unless it is either proven or held to be a postulate. If things that could be proven were instead postulated, we might be concerned with whether they contradict other postulates or theorems, and if this were so, math would be inconsistent. Also, it is generally preferable to make as few assumptions as possible not only to avoid the difficulty I just mentioned but also because, frankly, it is nice to know why something is true rather than to merely assume it.

To summarize, one needs algebra not only to solve problems containing one unknown (which admittedly do crop up pretty often in the "real world"), but it is also needed to understand mathematical concepts in the absence of the "real world" context, which is especially useful for higher level math subjects. If algebra does nothing else for you (in other words, if you don't take higher math courses), it will teach you to ignore irrelevant details, which is a valuable tool in itself.