## Glossary of Math Concepts

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- PEMDAS
- parenthesses, exponents, multiplication and divsion (left to right), addition and subtraction (left to right)

- Counting Consecutive Integers
- subtract smallest from largets and add one, to count integers from 13 to 31, do 31-13=18 then add one to get 19

- Exponential Growth
- if r is the ration between consecutive terms, a1 is first term, aN is nth term, and sN is the sum of the first n terms, then aN=a1*r^n-1 and Sn= A1-A1R^N / 1-R

- prime fractorization
- break up integers into factors until all the factos are prime 8=2*2*2

- LCM
- check out multiples of largest interger until you find one thats also a multiple of a smaller one

- GCF
- break down numbers into their prime factorizations and multiply all prime factors they have in common

- Multiples of 4
- if last two digits form a multiple of 4, it is a multiple of 4, ex 512, 12 is last two digits

- Divisible by 3/9
- if sum of digits are divisible by 3, its divisible by 3, if sum divisible by 9, its divisible by 9

- Reducing Fractions
- factor out and cancel all factors numerator/denominator have in common, ex 28/36, 4x7 over 4x9, 7/9

- Finding the Original Whole
- to find the original whole before a percent increase or decrease, set up an equation, ex. 15% increase over x as 1.15x

- Rate
- to solve rate problems, use units to keep things straight,

12 inches/4 hours= x inches/7 hours

- Average Speed
- Total Distance/Total Time

ex. average for 120 miles at 40mph and 120 miles at 60mph, divide 240 mph by total time of 2hrs plus 3 hours (5 hours)

48 mph

- Average of Evenly Spaced Numbers
- average the smallest and the largest, ex average of all integers from 13-77 is same as average of 13 and 77

13+77 over 2

- Finding missing number when given an average
- use the sum, ex if average 4 numbers =7, sum must be 28. if 3 other numbers are known 4th can be found

- Probability
- P=Favorable Outcomes/Total Possible Outcomes

9 shirts are white and 12 total in drawer, p of picking white =.75

- Counting The Possibilities
- if there are m ways one event can happen and n ways a second event can happen, then there are m x n ways for the 2 events to happen, ex 5 shirts and 7 pants to choose from =35 different outfits

- Adding/Subtracting Roots
- you can add and subtract radical expressions when part under radicals is the same

- Multiplying/Diving Roots
- radical 3 times radical 5 = radical 15

radical 6 divided by radical 3= radical 2

- Negative exponent and rational exponent
- 3^-2=1/3^2

if p and q are integers, and the equation is X^p/q, equation = the q root of x to the p