Formulas/Process

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Author:
JanineG14
ID:
81553
Filename:
Formulas/Process
Updated:
2011-06-17 00:31:14
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Formulas
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Description:
Formulas/Process to Memorize
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  1. LCM (Least Common Multiple/Factor) Steps:
    • 1) Determine the prime #s
    • 2) Take each prime factor to the highest power it appears.
    • 3) Multiply together the results of the primes to their highes power
  2. Universal Divisibility Strategy:
    Simply subtract easy to identify multiples of that # until you recognize a factor or non-factor, or 0.

    ex. 952 divisible by 7?

    • 952 - 700 = 252 ->
    • 252 - 210 = 42 ->
    • 42-42 = 0 (thus yes, divisible by 7)
  3. Divisibility rule 3:
    # is divisible by 3 if the sum of the digits is a multiple of 3
  4. Divisibility rule 4:
    # is divisible by 4 if last two digits together is divisible by 4. Ex: 724
  5. Divisiblity rule 6:
    # is divisible by 6 if even AND sum of digits divisible by 3
  6. Divisibility rule 9:
    # is divisible by 9 if sum of digits is a multiple of 9
  7. Divisibility rule 11:
    # is divisible by 11 if difference b/w sums of alternate digits is divisible by 11

    • ex: 4,983 divisible by 11?
    • 4+8 = 12
    • 9+3 = 12
    • 12-12 (diff b/w sums) = 0

    Thus yes 4,983 is divisible by 11
  8. Prime factors vs. Unique Factors:
    How many prime factors does 20 have?
  9. Prime factors vs. Unique Factors:
    How many unique factors does 20 have?
    Figure out factors working from greatest to least (outside -> in pairs)

    20, 10, 5, 4, 2, 1

    Unique factors = 6
  10. Comparing Fractions:
    A vs C
    B vs D
    • AD vs BC
    • BD vs BD

    Multiply denominators for common denominator, then cross multiply numerators
  11. Comparing Fractions - which is greater?
    3 vs 11
    7 vs 25

    best way?
    Since denominators will be the same, just skip calc & compare numerators after cross multiply.

    • 3x25=75 -------- 7x11=77
    • 75 or 77 greater? 77 so... 11/25 greater
  12. What is the distance/rate or Work/Rate formula?
    D=RT or W=RT
  13. What is the "trick" to calculating rate?
    Rate is the inverse of time (only when talking about a full job).

    ex. T = 6hrs, R = 1/6th per hour
  14. What are the 5 important steps to rates?
    • 1) Always convert time to rates
    • 2) Rates are additive
    • 3) Once you have the necessary rate, plug in the info to W=RT to solve.
    • 4) When conditions change, reset equations & solve with multiple equations (not one)
    • 5) Recognize if the rate is the same, then time used is proportional to # of workers. More workers = less time & vice versa.
  15. % of =
    % of = (part/whole) x 100
  16. Ex: 15/30 x 100 = 50%
  17. % Change =
    % Change = (New value - Orig Value)/ Orig Value x 100
  18. Greatest common factor/steps?
    • 1) Factor out the #s into primes
    • 2) Pick the prime #s out that they both share (only)
    • 3) Multiply those prime #s together (only once for ea. #).
  19. What's this definition for..."The smallest non-zero # that is a multiple of two or more #s"
    LCM (least common multiple)
  20. What's this definition for... "The largest # that divides evenly into each of a given set of #s"
    GCF (Greatest common factor or divisor)

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