Question

1. Choose an integer
2. Multiply it by 3
3. Add 6 to the product.
4. Now divide by 3.
5. Subtract 2.
6. The result will be the integer you started with. Why?

How can you explain why the result is always the integer you started with?

Answer 1

let that integer be n

all the steps:
(((n * 3) + 6) / 3) - 2

no simplify:
[(3n + 6) / 3] - 2 = [n + 2] - 2 = n

Answer 2

I have followed the steps already.

Answer 3

so what is the problem ? we got n back.. when you simplify it we see that every thing disappears but the integer

Answer 4

How can you explain why the result is always the integer you started with?

Answer 5

as you can see all the operations we did are cancelled eventually ..

Answer 6

Just a moment please.

Answer 7

...I kind of get it.

Answer 8

Let's say that the integer is 15.
15 times 3 = 45.
45 + 6 = 51
51 divided by 3 = 17
17 - 2 = 15

Answer 9

I don't quite understand how you simplified it.

Answer 10

the first step is 15 * 3 (dont write 45 leave it as 15 * 3 )

the second is 15 * 3 + 6
third is
(15 * 3 + 6) / 3
forth
(15 * 3 + 6)/3 - 2
right ?

Answer 11

now lets work it out ..
(15 * 3 + 6)/3 - 2

(15 * 3 + 6)/3 = 15 + 2

15 + 2 - 2 = 15

Answer 12

When working it out, for the second step, why does it equal 15 + 2?

Answer 13

without the subtraction of the 2.. i just looked at this part: (15 * 3 + 6)/3

(15 * 3 + 6)/3 = (15*3)/3 + 6/3 = 15 + 2

Answer 14

I'm going to eat right now. I can't really focus at the moment. I'll message you if I have any questions.

Answer 15

ok enjoy

Answer 16

Thanks, and I understand what you wrote. :)