Miscellaneous Comments
Algebra always seemed dry to me in middle school, but that's because it is just like basic grammar rules which most people also find dry. Algebra is just something you need to know in order to do more interesting things with math, just as grammar needs to be understood to do more interesting things with language. Please be sure that your algebra skills are sharp. It would be silly to lose points on quizzes or exams due to an algebra error.
Order of Operations
You possibly learned the correct order of operations using a mnemonic like PEDMAS. If you do not recall the correct order or what the mnemonic stands for, please see this link.
I find that when writing expressions into calculators or computers, that students who in other contexts know the order well, still make mistakes. One context where it happens often is when using scientific notation on a calculator and rather than using the built-in button for this purpose, students choose instead to multiply some number by 10 raised to a power.
Suppose you wish to enter the value into a calculator. The correct way to do it is to type 3.65E-14, where the E is entered using the button that is labeled either "E" or "EE", or sometimes "EXP" or "10x". The bad way to enter this value is to type 3.65, then the multiplication button, then "10" and then the button that raises to a power which often looks like "^", then -14. You may wonder what the difference is. The difference is important. Using the first method the number is a single entity. Using the second method it is seen as a product of two entities: 3.65 and 10-14. This causes all sorts of errors when dividing by numbers written as scientific notation. The errors can be avoided by using parentheses, but needless parentheses are both cumbersome and ugly in computer code. The other issue is that the first method is much more efficient in terms of button presses.
Please start using the dedicated button on your calculator for scientific notation and stop using too many parentheses if you are currently in the habit of doing that.
An example of how the latter method can go wrong:
Your result should be not 1905. Please do not use any parentheses in the calculator for this calculation. They are not necessary if you use the correct button for scientific notation.
According to some quick internet search, 74% of Facebook users got the following answer incorrect: 7-1x0+3/3=?
I want you to be among the other 26%. This isn't about being smart or dumb. It isn't a puzzle. It is a test of whether you know the agreed-upon order of operations used by mathematicians world-wide. If there were other agreed-upon rules the answer would be different, but there are not and the answer is not a matter of opinion. I hope you got 8 as your answer.
Other Rules
Please also commit to memory if you haven't already done so the quadratic formula and the Pythagorean theorem. While it's not strictly algebra, you should know the law of cosines and the law of sines as well.
Division with a Slash /
All mainstream programming languages require division with the slash symbol /. In textbooks like this one and others, there are two alternatives: and In many contexts there is no difference. In some there is. For instance, if there is a sum in the denominator (or numerator) such as: versus they are very different expressions!
If they are to be equivalent expressions, then the first form requires parentheses. Without the parentheses they are very different expressions. The thing to note is that the second type of horizontal division symbol is not available in any standard programming environments. Thus, when translating an equation from a book to a computer, this must be kept in mind so that silly errors are avoided.
When using the slash symbol for division, pitfalls may be avoided by using the correct symbol for scientific notation mentioned above rather than a cumbersome multiplication of terms. In fact, most programming languages and calculators will allow entry of scientific notation by writing 5.64E-6 without any spaces to represent . When compared to 5.64*10^-6, it should be obvious that, for example:
This is true to a computer and should also be to you. Of course you can once again equate them by using parentheses on the second expression, but this makes the already cumbersome notation even worse to look at!