Who Can Explain Why This *Always* Works?

Discussion in 'General discussions' started by bookslover, Apr 18, 2017.

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  1. bookslover

    bookslover Puritan Board Post-Graduate

    1. Pick a number

    2. Double it

    3. Add 6

    4. Divide it in half

    5. Take away the number you started with

    6. Your answer is 3

    Works every time, but I don't know why.
     
  2. Taylor Sexton

    Taylor Sexton Puritan Board Freshman

    Visualize the steps this way, paying particular attention to Step 4, which I do the math using the distributive property...

    1) 5

    2) 10

    3) 10 + 6 (=16)

    4) (10 +6)/2 = (5 + 3) (= 8)

    5) 8 - 5 = 3

    Essentially, this is just a really complicated way of dividing 6 by 2. Take away all the "+ 6" out of this equation, and you simply have a math problem that always equals zero. In other words, there is nothing special about "+ 6"; the same could be done with any number. Substitute "7" for "6" and the answer would always be 3.5.
     
  3. Ask Mr. Religion

    Ask Mr. Religion Flatly Unflappable Staff Member

    What Taylor said, in algebraic terms:

    x
    2x
    2x+6
    (2x+6)/2=x+3
    x+3−x=3

    Q.E.D.
     
  4. Ask Mr. Religion

    Ask Mr. Religion Flatly Unflappable Staff Member

    Playing with numbers (a nice home-schooling activity):

    1 x 8 + 1 = 9
    12 x 8 + 2 = 98
    123 x 8 + 3 = 987
    1234 x 8 + 4 = 9876
    12345 x 8 + 5 = 98765
    123456 x 8 + 6 = 987654
    1234567 x 8 + 7 = 9876543
    12345678 x 8 + 8 = 98765432
    123456789 x 8 + 9 = 987654321

    1 x 9 + 2 = 11
    12 x 9 + 3 = 111
    123 x 9 + 4 = 1111
    1234 x 9 + 5 = 11111
    12345 x 9 + 6 = 111111
    123456 x 9 + 7 = 1111111
    1234567 x 9 + 8 = 11111111
    12345678 x 9 + 9 = 111111111
    123456789 x 9 +10= 1111111111

    9 x 9 + 7 = 88
    98 x 9 + 6 = 888
    987 x 9+ 5 = 8888
    9876 x 9 + 4 = 88888
    98765 x 9 + 3 = 888888
    987654 x 9 + 2 = 8888888
    9876543 x 9 + 1 = 88888888
    98765432 x 9 + 0 = 888888888

    Observe this symmetry:

    1 x 1 = 1
    11 x 11 = 121
    111 x 111 = 12321
    1111 x 1111 = 1234321
    11111 x 11111 = 123454321
    111111 x 111111 = 12345654321
    1111111 x 1111111 = 1234567654321
    11111111 x 11111111 = 123456787654321
    111111111 x 111111111 = 12345678987654321


    Next, let's see what else we can do with numbers...

    From a strictly mathematical viewpoint: What Equals 100%?

    What does it mean to give MORE than 100%?

    Ever wonder about those people who say they are giving more than 100%? We have all been in situations where someone wants you to...

    Give over 100%.

    How about achieving 101%?

    What equals 100% in life?

    Can mathematics help us answer this question?

    If:

    A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

    is represented as:

    1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

    Then:

    H-A-R-D-W-O-R- K

    8+1+18+4+23+15+18+11 = 98%

    And:

    K-N-O-W-L-E-D-G-E

    11+14+15+23+12+5+4+7+5 = 96%

    But:

    A-T-T-I-T-U-D-E

    1+20+20+9+20+21+4+5 = 100%


    But, hold on now, brothers and sisters, look how far the love of God will take you:

    L-O-V-E- O-F- G-O-D

    12+15+22+5+15+6+7+15+4 = 101%

    Therefore,

    While Hard Work and Knowledge will get you close,
    and Attitude will get you there,
    It's the Love of God that will put you over the top! [​IMG]
     
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  5. Edward

    Edward Puritan Board Doctor

    You've gotten longer answers, but basically steps 1, 2, and 5 cancel each other out. They are just garbage to obscure the real math. Do steps 3 and 4, and you get the result shown in step 6.
     
  6. bookslover

    bookslover Puritan Board Post-Graduate

    For step 4, uh...wouldn't 16 - 8 be easier? Gets you the same result.
     
  7. bookslover

    bookslover Puritan Board Post-Graduate

    When I was in elementary school (early 1960s), we had the "new math" inflicted on us. Suddenly, it wasn't enough that 2 + 2 = 4. Now, you had to have a 2-page explanation as to why 2 + 2 = 4. An explanation that, of course, no one gave two flying pigs about, especially elementary school children. As long as it equals 4, that's all that matters.

    Sort of sounds like the Common Core nonsense being inflicted on today's students.
     
  8. Edward

    Edward Puritan Board Doctor

    No, they've moved far beyond new math. Now, the "equals 4" part doesn't matter. It's the effort that counts, not the actual result.
     
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