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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
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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)
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Divisibility rule 3:
# is divisible by 3 if the sum of the digits is a multiple of 3
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Divisibility rule 4:
# is divisible by 4 if last two digits together is divisible by 4. Ex: 724
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Divisiblity rule 6:
# is divisible by 6 if even AND sum of digits divisible by 3
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Divisibility rule 9:
# is divisible by 9 if sum of digits is a multiple of 9
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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
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Prime factors vs. Unique Factors:
How many prime factors does 20 have?
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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
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Comparing Fractions:
A vs C
B vs D
Multiply denominators for common denominator, then cross multiply numerators
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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
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What is the distance/rate or Work/Rate formula?
D=RT or W=RT
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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
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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.
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% of =
% of = (part/whole) x 100
Ex: 15/30 x 100 = 50%
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% Change =
% Change = (New value - Orig Value)/ Orig Value x 100
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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. #).
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What's this definition for..."The smallest non-zero # that is a multiple of two or more #s"
LCM (least common multiple)
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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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