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### Course: Algebra 1>Unit 1

Lesson 1: Overview and history of algebra

# Why all the letters in algebra?

In algebra, we often want to work with general concepts instead of specific numbers. Using letters allows us to represent quantities that could change or that we don't know the value of yet. Letters can also be used to generalize formulas or equations. Created by Sal Khan.

## Want to join the conversation?

• At , Sal mentions the convention of using letters comes from history. Where in history did the convention of letters come from, and how did x and y become so popular (especially with the coordinate plane?)
• There's a short TED talk about why x became the standard letter representing an unknown: http://www.youtube.com/watch?v=YX_OxBfsvbk. In short it is the English (or Latin) version of the Greek letter χ (chi), which was the first letter of the transliteration of the Arabic word for 'something', which was used in the original algebra texts.

Since x was commonly used for one unknown, it made sense to use y as a second, and z as a third unknown.
• At , Can we use any symbol (ë, æ, ´¬ or ¤) represent an unknown number?
• I think that's a yes, since Mr. Khan says you could use a smiley face.
• why do we need to have letters
why can't they just give it to us?

EDIT: Well, I actually meant to ask what's the use of a variable and how is it used in real life.
• Because the letters are for when you don't know something - in real life, say you wanted to know how much it cost to drive your car somewhere, and you knew that gas was \$5 a gallon, and that your car got 60 miles to the gallon. With that knowledge you can write an equation with x equalling how many miles you drive, and you can use that equation again and again to figure out how much it would cost you to go different distances.

If you didn't have the x in there, you would have to create the equation each time with a different distance.
• Why do we have hard hard math
• 1. Just because it's hard for you doesn't mean it's hard for everyone.
2. Maths the language of the universe, and the laws of the universe don't have to be simple to understand for them to be true.
• Imagine you are a person who doesn't know any languages that use the Latin alphabet letters (ex. a, b, c). Do you do algebra with letters from the Latin alphabet, or do you do algebra with letters from your own non-Latin based language?
• Well, it would seem to make sense if any culture who doesn't know the English language and/or alphabet to use their own symbols or calligraphy.
• Why was Jesse Roe in this video if Sal was going to do all the talking anyway? :)
• Fun right
• This would be really helpful for some students. While I was a student my teachers didn't really want to answer that question. why? because he thought this was easy. But I was first doing this stuff. I needed answers.
• While Sal was explaining the second reason to why we use letters(), he wrote and used the equation y = x + 1 . But did he actually mean to use y = y + 1 ? The examples he gave were 3 -> 4 , 5 -> 6 , 7.1 -> 8.1 . So the pattern here is whatever you give, I'll give that amount +1 . So wouldn't the correct equation be y = y + 1 ? Or am I just confusing this with coding(variable declaration). (I am an active coder)
• Vote this answer if you watched the video
• how does it work it seams complicated how would you describe it
• I had the same reaction and would have preferred simpler examples.
Sal actually does do something like I do briefly in the next video.
You are probably familiar with problems like this.
4 + 3 = _
In Algebra we might write it like this and ask the value of a instead of what number goes in the blank.
a = 4 + 3.
If you think that just makes it harder, I can't disagree.
Even this might seem simple.
7 = 4 + _

While this seems harder.
7 = 4 + a
This seems easy.
3 x 5 = _
This seems harder.
a = 3 x 5
Even this may seem easy.
15 = 3 x _

This may seem harder (especially without the multiplication symbol).
3a = 15
3 x __ - 4 = 5
This kind of problem is where variables might start to make sense.
3a - 4 = 5
You may still be able to solve the problem easily because the numbers are small and the answer is an integer.
Consider this problem.
Tom needs \$47 more to buy a pair of shoes he wants,
He has a chance to earn some money painting a fence.
He figures the job will take 4 hours and the paint will cost \$20.
If he is right, what is the least hourly rate he can charge to earn the money he needs.
You might be able to figure this out without using Algebra (and a variable) but it won't be easier.