( 1 ) One times one equals one.
( 2 ) One divided by one equals one.
These two concepts can get anyone off the ground and on their way to mastering intro. chemistry and/or physics.
The following numbers are equivalent to the number 1 : ( 2 divided by 2 = 1 ), ( 7 divided by 7 = 1 ), ( 2543 divided by 2543 = 1 ), and ( XYZ divided by XYZ = 1 ). The notation for ” divided by ” is a slash. Therefore, from here on out, ( XYZ divided by XYZ ) = ( XYZ / XYZ ).
Therefore, if 2 times 1 = 2, what is 2 times ( XYZ / XYZ ) ? The shorthand way of writing 2 times 1 is to use parentheses. 2 times 1 = ( 2 )( 1 ) = 2. Therefore, ( 2 )( XYZ / XYZ ) = 2, because ( XYZ / XYZ ) = 1.
KEY: If the top and bottom of a fraction represent the same quantity of something, then the expression represents the number 1. For example, there are 60 seconds in 1 minute, therefore, 60 seconds = 1 minute. Therefore, ( 60 seconds / 1 minute ) = 1 Similarly, ( 1 minute / 60 seconds ) = 1.
HERE IS THE MOST IMPORTANT CONCEPT TO MASTER BEFORE TAKING AN INTRO CHEMISTRY CLASS. Both of the above ratios give the number 1, but which would be the most appropriate to use in a given situation?
Example: How many seconds transpire in a two hour time period? Well, always start with what is given, or known, then use it to find the unknown. Multiply 2 hours by some conversion factor equal to one in order to get the correct answer.
Key: As you move to the right, always put what is at the top of one expression into the bottom of the next. It will become apparent why this is done so shortly. Visually follow the ” zig-zagging ” pattern that follows. ( 2 hours )( 60 minutes / 1 hour )( 60 seconds / 1 minute ) = ( 2 )( 1 )( 1 ) = 7200 seconds. Look again at the beginning of the equation. We started with ” 2 hours “, so ” hours should be at the bottom of the following fraction, and minutes at the top. Minutes are then written on the bottom of the following fraction, and seconds on the top.
Look very carefully at the next note.
HERE IS THE WRONG ANSWER : ( 2 hours )( 1 hour / 60 minutes )( 60 seconds / 1 minute ). This expression is wrong because the second term ( 1 hour / 60 minutes ) should have been arranged as ( 60 minutes / 1 hour ). The reason is as follows.
( hours )( minutes / hour )( seconds / minute ) can be rearranged to get ( hour / hour )( minute / minute )( second ) by moving the denominators ( bottoms of ratios ) around. Practice doing so visually. Since ( hour / hour ) = 1, and ( minute / minute ) = 1, the above equation reduces to ( 1 )( 1 )( seconds) = seconds. This and only this will give the desired outcome we want ( How many seconds are in 2 hours ).
RENAISSANCE PHYSICS 