One-Line Notation

Since we are communicating via computers, there will be times when we want to write a mathematical expression on the discussion board or in an e-mail without taking the time to make an equation image and attaching or inserting it. For those times we need to be able to understand each other so we must all learn how to communicate with what I call one-line notation (since the whole expression appears on one line) as opposed to traditional notation where a single math expressions can take several lines. Many students call it online notation, which also is an adequate way to describe it since we use this notation usually only when working online. When you take traditional paper and pencil tests you can and should use the traditional notation since it is much clearer and easier to read and understand.

Here is an example: Suppose I wanted to write the expression on the right in one-line notation for the discussion board. I would write: [(x + 3)/(4 - x/(2 - y))]^2 . Now it would be up to each person reading the discussion board to translate this problem on paper back into regular notation so that he/she can follow the discussion more easily. Notice that we need extra parenthesis to indicate which parts of the expression are in the denominator and which parts are in the numerator and a carrot to indicate that the 2 is an exponent.

To help you get the hang of this, let's start out with some simple translations and then work our way up to more complicated ones.

• Use parenthesis, square brackets, or curly brackets for grouping.
• Make sure you pay attention to order of operations. For example division is a higher order of operation than addition so when you translate into one-line notation, you need parenthesis around the numerator and the denominator: (x+4)/(y+2). Do part I, 2a to see what you get when you leave out the parenthesis.
• Use sqrt(expression) for
• Use cbrt(expression) for
• Use ^ for exponents.
• Use <= for ≤
• Use >= for ≥

I	After doing all parts of I, click here to check your answers.
1.) Translate each of the following into one-line notation.
a.)	b.)	c.)	d.)
2.) Translate the following expressions that are in one-line notation into traditional notation.
a.) x+4/y+2	b.) x^(y+3)	c.) x^y+3	d.) x+4/(y+2)
II	After doing all parts of II, click here to check your answers.
1.) Translate each of the following into one-line notation.
a.)	b.)	c.)	d.)
2.) Translate the following expressions that are in one-line notation into traditional notation.
a.) (x+y/2-x)^(x^2+1)	b.) x+y/2-x^(x^2+1)	c.) (x+y/2-x)^x^2+1	d.) x+y/(2-x)^(x^2+1)
III	After doing all parts of III, click here to check your answers.
1.) Translate each of the following into one-line notation.
a.)	b.)	c.)	d.)
2.) Translate the following expressions that are in one-line notation into traditional notation.
a.) [(1/x-2)+x^(y+1)]/[3/(x-1)+x+2/x]		b.) [1/(x-2)+x^(y+1)]/[3/(x-1)+(x+2)/x]
c.) [1/x-(2+x)^(y+1)]/[3/x-(1+x+y)/x]		d.) {[1/(x-2)+x^y+1]/3/(x-1)+x+2/x}^5