Pick a number. Multiply by 2. Subtract 8. Divide by 2. Add 4. What is the result? Use algebra to show why the tricks work.
Not my Question lol
Let's go step by step through the calculations and use algebra to explain why each trick works.
1. Pick a number: Let's call this number "x".
2. Multiply by 2: We have 2x.
3. Subtract 8: We have 2x - 8.
4. Divide by 2: We have (2x - 8) / 2.
5. Add 4: We have (2x - 8) / 2 + 4.
To simplify this expression, we can first divide (2x - 8) by 2:
(2x - 8) / 2 = (2/2)x - 8/2 = x - 4.
Now we can rewrite our expression as:
x - 4 + 4.
When we add 4 to x - 4, the 4 cancels out the -4, leaving us with:
x.
So, the result of this set of operations is x, the number we initially picked.
Explanation:
The reason why this set of tricks works is because each step is designed to undo the previous step, resulting in the original number. Let's break it down:
1. Multiply by 2: When we multiply a number by 2, we are essentially doubling it. This is the opposite of dividing by 2.
2. Subtract 8: When we subtract 8, we are essentially "undoing" the addition of 8.
3. Divide by 2: Dividing by 2 is the inverse operation of multiplying by 2.
4. Add 4: Adding 4 is the inverse operation of subtracting 4.
By performing these steps in reverse order, we can see that each operation cancels out the previous one, leaving us with the original number we started with.
In algebraic terms, we can think of each step as an equation:
Step 1: 2x
Step 2: 2x - 8
Step 3: (2x - 8)/2
Step 4: (2x - 8)/2 + 4
When we simplify step 3, the division by 2 cancels out the multiplication by 2, leaving us with (2x - 8)/2 = x - 4. Then, when we add 4 in step 4, it cancels out the -4 from step 3, resulting in x.
In summary, this set of tricks works because each step undoes the previous one, allowing us to arrive at the original number we started with.
x = your number
( x * 2 - 8 ) / 2 + 4 = x * 2 / 2 - 8 / 2 + 4 = x - 4 + 4 = x
Try first with a number...
say 7
first multiply by 2, that is 7x2=14
subtract 8, that is 14-8=6
divide by 2, that is 6/2= 3
add 4, that is 3 + 4 = 7
So what happened to your original number??