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| Number line -2, -1, 0, 1, 2, 3 |
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| all numbers except decimals that don't repeat or don't terminate like pie |
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| pie etc sqr 2, decimals that don't end and don't have a pattern |
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| Commutative Property of Addition |
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When adding any 2 or more numbers,
3 + 4 = 4 + 3
7 = 7 |
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| Associative Property of Addition |
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When adding 3 or more numbers, (3 + 4) + 5 3 + (4 + 5)
7 + 5 = 12 3 + 9 = 12
• Associative |
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| Commutative Property of Multiplication |
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Definition
When multiplying any 2 or more numbers, changing the order does not change the
product. 3 · 4 = 4 · 3
12 = 12 |
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| Associative Property of Multiplication |
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When multiplying any 3 numbers, changing the grouping does not change the product.
(3 · 4)5 3(4 · 5)
12 · 5 = 60 3 · 20 = 60 |
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| distributive property of multiplication |
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Distribute it out of the parenthesis to multi 3(2 + 7 - 5) = 3(2) + 3(7) + (3)(-5)
3(4) = 6 + 21 - 15
12 = 12 |
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| Multiplicative inverse property |
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Definition
If you multiply two numbers and the product is 1,
4 × 1/4 = 1
1/4 is also the multiplicative inverse of 4 because 1/4 × 4 = 1 |
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| Multiplicative Identity Property: |
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| Most 1st place votes wins |
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| 3 candidates,each 1st place vote is worth 3 points, 2-2 3-1 then add up total points, candidate with the most points wins |
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| Plurality with ellimantion |
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| Remove the lowest vote getter and move everyone up a spot to count the votes. Keep doing this by rounds until there are only 2 choices left. |
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Set every candidate up in a pair with every other candidate. 1 point is awarded in each round that they beat that person (.5 for ties)
Total points for each candidate to find winner |
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| divide by 2, if that does not work move up and keep trying until no longer divisible. |
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the largest whole number that's a divisor (factor) of both of them.
Use factor tree then take the largest number found in both trees. |
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| Factor tree, then take the largest exponent version of every number and multiply all of those numbers. |
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| Compared to every other candidate and preferred he wins. |
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| Wins, then in a revote only changes happen to favor the candidate then they should win again |
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| Wins, then a recount, one or more other candidates are removed, it should not effect the outcome. |
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| Fairness by election type, Plurality |
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| majority, Monotonicity, may meet Irrelevant sometimes |
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| Fairness by election type: Borda Count |
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| Monotonicity, mabey on all others |
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| Fairness by election type: Pairwise |
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| Majority, head-to-head, monotonicity, maybe Irrelevant |
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| Fairness by election type:Plurality with Elimination |
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| Majority always, maybe the others |
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| Arrow's Impossibility Theorom |
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| Basically mathematically impossible to satisfy all 4 fairness criteria |
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| Ends in 0 or an even number |
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| add up the numbers...if that new number is divisible by 3 |
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| last two numbers are like 524 is because 24 can be divided by 4 |
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| if you can divide by both 2 and 3 then yes |
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| Last three digits are a number that is divisible by 8 example 123,960, 960/8=120 |
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| add last three digits and divide by 9 |
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| add the odds places, then add the evens places then subtract those two numbers. Then divide that new number by 11 to check it |
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