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### Course: Algebra basics > Unit 2

Lesson 3: Writing algebraic expressions# Writing expressions with variables

To write simple algebraic expressions from mathematical statements, you can follow this procedure: 1. Identify the key terms in the written statement (e.g. "sum," "product," "quantity"). 2. Break the statement down into its component parts. 3. Translate each part into algebraic form, using the appropriate symbols and operations.
4. Simplify the expression if needed. Created by Sal Khan.

## Want to join the conversation?

- whats a quanity(50 votes)
- Exactly.It can be a negative number to infinity,a positive number to infinity and zero.In fact, ANY number is a quantity.(29 votes)

- When there's a problem with division, how do you know what's the numerator and what's the denominator?(9 votes)
- Here the number above the fraction bar is the numerator, and the one below the fraction bar is the denominator. A numerator represents the number of parts out of the whole, which is the denominator. did that help(7 votes)

- What is a quotient?(8 votes)
- Quotient is the result of division.

So, if you are asked to "find the quotient of a number and 6" you would do "x/6".

Hope this helps.(18 votes)

- Why does it change from 1x to x(6 votes)
- "1x" and "x" mean the same thing. It is common practice to not write in the coefficient of 1.(7 votes)

- When it says, "Eight less than the product of 2 and the letter x" how do you know if you have to put the -8 before or after the 2x?(5 votes)
- The problem says eight
*less than*, which suggests subtraction is needed. Subtraction, unlike addition, is not communative, meaning 3-4 will not equal 4-3 (but for addition 3+4 will equal 4+3), so since it's 8 less than 2x it will be 2x - 8. Hope I helped, let me know if there's anything you need to clarify :)(6 votes)

- i kinda dont get this(5 votes)
- This is where English and Math come together. You need to translate the words into math symbols. The challenge is that in English, we have multiple ways of saying the same thing. If you do an internet search on "translating words to math symbols", you can find some good tables with English words / phrases and what they become in math.

Note: This is a critical skill set that enables you to apply math to real life situations. It also helps you solve word problems, which get more challenging as you progress thru higher level math classes.(5 votes)

- When there's a problem with total, what do you do?(5 votes)
- save the planet I guess 😂(0 votes)

- what is a quantity(1 vote)
- If I have 5 apples, then the quantity of apples is 5.(9 votes)

- I swear is it just me or once you start getting on to the complex stuff and you master that the more easier stuff looks even more harder ( basically why does the easy stuff from math look extra harder now )(2 votes)
- Because you have to start thinking more abstractly the more difficult the math becomes. For instance, take the equation 7 - 9 =-2. The answer is nonsensical without algebra. You can’t come home from the store with -2 bananas. Likewise, many things in algebra are nonsensical that are not in calculus. And so on and so on. Once you’ve trained your mind to think that way though, you have to kind of stick with it, because logical does not mean intuitive. There’s nothing intuitive about bringing home -2 bananas. It requires not just understanding the framework, but thinking in a framework that is very abstract, and it gets more difficult the higher the math you learn. Simple equations get more difficult because you understand their abstract nature. Thus, for instance, why it is a well-known joke that a topologist can’t tell the difference between a donut and a coffee cup, because abstractly, to them, they are the same, even though intuitively, even a young child can tell the difference between a donut and a coffee cup. Just like a young child can tell you that you can’t come home from the store with less than zero bananas.(6 votes)

- I have a question to this problem:

A zoo has two fewer elephants than zebras and five times more monkeys than elephants. The total number of elephants, monkeys, and zebras is 30.

The expression is z + (z-2) + 5(z-2) = 30.

I dont know why for the part where it says "five times more monkeys than elephants," i do know that five times is distributive property but i dont know why its z-2 when it says five times more monkey than elephants.

Im sorry for asking you this i just need help on this with my homework. Thank you.(2 votes)- In your equation, z=number of zebras.

There are 2 fewer elephants than zebras gives you that elephants = z-2

5 times more monkeys than elephants means the number of monkeys is 5 (number of elephants) = 5(z-2)

Hope this helps.(4 votes)

## Video transcript

What I want to do
in this video is write the algebraic expressions
that represent the same thing that these statements
are saying. So this first statement, they
say the sum of negative 7 and the quantity 8 times x. So the sum-- so we're going
to have an addition here-- of negative 7 and the
quantity 8 times x. So the quantity 8 times
x, well, that's just 8x. So I can just write
8x over there. So it is negative 7 plus 8x. Or you could view this
as the sum of negative 7 and the quantity 8 times x. Let's do the next one. Take the quantity negative
3 times x and then add 1. So the quantity
negative 3 times x, we can write that
as negative 3x. And then we need
to add 1 to that. So that's going to be plus 1. Now this one. Negative 6 plus--
so we can write negative 6 plus something-- the
product of negative 1 and x. So the product of
negative 1 and x, that's just going to
be negative 1x, which is the same thing as negative x. So we can write this as
negative 6 plus negative x. Or we can just
write this-- this is the exact same thing
as negative 6 minus x. And we are done.