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## Algebra 1

### Course: Algebra 1>Unit 1

Lesson 1: Overview and history of algebra

# The beauty of algebra

Algebra is a language that helps us understand the world around us. It's not just about numbers, it's about abstract ideas that can be applied to many areas like economics, physics, and even the fundamental structure of the universe. Created by Sal Khan.

## Want to join the conversation?

• Why in algebra do you use letters instead of numbers?
• What is the best reason for learning Algebra?
• Algebra is the fundimental language of mathematics. Mathematics is fundimentally "why things are" - as we currently understand them to be. It is a science, but it is also an artform of logic - in a sense much like any spoken language. So much of our understanding of science is based on formulae and equations.. problems, variables..

Not only does Algebra offer us the universal syntax to understanding the language(s) of mathematics, it offers us the most basic toolkits to understanding the most complicated languages, proses, and poems of science and technology itself.

It is the most basic language of science from mathematics, to quantum phyisics to economics to .. well it can even be applied to psychology. It is logic in its almost purest form - dare i say the most important language we can ever have the opportunity to teach ourselves.
• why do we have to have algebra?
• Because it will make you better at life, if only you'll use it. "The human mind has never invented a labor-saving device equal to algebra." --J. Willard Gibbs.

Algebra creates abstractions which apply to tens, hundreds, or even thousands of scenarios. In other words by solving ONE algebra problem, you are solving hundreds of "regular" problems, all at once. Sounds nice, doesn't it? For example "maximization" and "minimization" problems (both involving quadratic equations) will help you, for example, fence in the most area with the least amount of fencing material (thus saving you money).
• what jobs would i use algebra for?
• Engineer (pretty much all types of engineers), physicist, economist, accountant, architect, chemist, teacher and professor (if one teaches math), pharmacist (to add in chemicals and/or drugs to each other), and a lot of other jobs. I think I'm missing some...but i think your getting the idea?
Hope this helped. =)
• Why do you find the discount by multiplying the discount by the price?
• When you get a 30% discount on a \$20 item, that's saying that you save 30¢ for every \$1. If we were only buying a \$1 item, then we would save 30¢ in total, right?

But we're actually buying an item worth \$20. So we get to save 20 times the amount that we would save if we were only buying a \$1 item. That's because for each of the 20 dollars we save 30¢.

We could write the expression as: 30¢ + 30¢ + 30¢ + ... + 30¢ (20 times)

Or we could use multiplication...
Since 30¢ = 30% of a dollar = \$0.30, we can write the multiplication expression as: \$20 * 0.30.

That means you save \$20 * 0.30, or \$6.
• If people take Algebra so seriously, then why did they invent the calculator?
• "If people take Algebra so seriously, then why did they invent the calculator?"
well, let me ask you some questions of my own:
if people take walking so seriously, then why did they invent the car?
if people take writing so seriously, then why did they invent the typewriter?
if people take talking so seriously, then why did they invent the telephone?
if people take X so seriously, then why did they invent the Y?
The answer to all these questions are the same, Y is a tool that makes doing X easier, faster, more efficient, optimal, convenient, and so on and so forth. Just because they are tools, however, doesn't make learning X any less important. Using Algebra, we can abstract the core idea of the question and answer any question with the same basic principle in place.
• I want to become an interpreter (foreign languages are my passion!) Would I ever need to use Algebra in my day-to-day life? If I'm translating words and phrases for someone, aren't numbers universal? Why would I have to learn Algebra if I want to go into a field that deals with spoken language?

In all my years of school, nobody has ever given me an answer besides "it's required by the state." (I'm in the United States in my Junior year of High School.)
• Algebra isn't just used in jobs and careers. It can be applied to your everyday life. As an interpreter, you'll probably be making some good money. Any smart person budgets and keeps track of their money. I hope you do! Most people use Excel spreadsheets for their personal finances. A lot of algebra is used in that application.

So, don't assume you'll never have to use algebra in your day-to-day life. A lot of students complain about how "useless" it is... but don't even know they could very well be using it when they're older!
• Sal makes it seem like y = px is the answer to the universe.
So is algebra the answer to the universe?
• No, the answer to life, the universe, and everything is 42.
• Context is everything. Without the why its hard to care about what your learning.
• What is the divisibility rule for the numbers 4 and 9