Who Can Explain Why This *Always* Works?

[bookslover]

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.

 

[Taylor]

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.

 

[Ask Mr. Religion]

What Taylor said, in algebraic terms:

x
2x
2x+6
(2x+6)/2=x+3
x+3−x=3

Q.E.D.

 

[Ask Mr. Religion]

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

Spoiler

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!

 

[Edward]

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.

 

[bookslover]

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.

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

 

[bookslover]

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.

 

[Edward]

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.

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.