Treat these problems like successive percent problems.
e.g. after 2 years of 8% annual compound interest, the new amt is Principal*1.08*1.08
** Be careful of when the principal compounds versus the rate. Everytime the principal compounds, the amount increases. e.g. if you have $100 that earns 8% annual interest and compounds quarterly, then by Q3 it has compounded 6%
Percent Change = Change in value / Original Value
Sometimes I will have to plug in numbers to solve a problem, and I'll need to choose a number
The best number (aka smart number) is going to be one which is a multiple of the denominators of all fractions in the problem.
Problem: If tank #1 is 4/5 full and tank #2 is 1/2 full, and if all liquid in tank #2 is moved to tank #1, then how full is tank#1?
The smart number needed to solve this problem is 10!!
**You can ONLY pick ONE smart number per problem - NEVER PICK MORE THAN ONE SMART NUMBER!!!! You can't do this because the ratio of the two smart numbers can vary
Comparing fractions using cross-multiplication
Is 3/13 bigger or smaller than 2/9?
Sometimes I can quickly determine this (because I'm the shit...). Other times, I waste time figuring stupid stuff like this out.
So, to quickly solve, use cross-multiplication!!
3/13 ??? 2/9
9x3 ??? 13x2
27 ??? 26
3/13 > 2/9!!!!!!
Notice how important it is to avoid mixing up sides during the calculations!
When I am adding/subtracting ingredients from two different items, a mixture chart is a great way to figure out in an organized fashion what the new %'s are for each ingredient in the overall mixture.
Think of mixture charts like a simple, straightforward table. See p. 114-115 of the FDP book for examples
+ The columns show the original, change, and new (original + change = new)
+ The rows show the ingredients - e.g. alcohol, water, total solution
+ The individual cells are the volumes for each ingredient
*** Fill out what you know, then solve for unknowns!
Decimals to memorize
This will help me (a) identify solutions faster, (b) easily convert decimals to fractions so I can do math easily, (c) help me avoid careless errors. The decimals I need to know are:
+ Multiples of 1/6, Multiples of 1/7, Multiples of 1/8, Multiples of 1/9, and Multiples of 1/11