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The simplest way is to look at it algebraically.

So, suppose you start with a number. Let's call it N.

Step 1: You times it by 2. So N becomes 2*N or 2N.

Step 2: You add 10. So 2N becomes 2N + 10

Step 3: You divide by 2: So 2N + 10 becomes ("N+10)/2 which is N + 5

Step 4: You subtract the original number: So the N+5 becomes N+5-N, or 5.

Hope that's proved it for you.

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Q: How come when you think of a number and times it by 2 and add ten and divide it by 2 and subtract that number it is always 5?
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