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Message Subject Math: 6÷2(1+2) = ?
Poster Handle Anonymous Coward
Post Content
This is how you are supposed to do it, with an explanation of WHY...

Distribute 2 into the parentheses. Why? because it is a factor of the original terms INSIDE them, and cannot be ripped apart. I will show you why:
6 = 4+2 = 2(2+1) = 2(3) The 2 is a common factor of 4 & 2.
No matter which way you view it, the value 6 MUST maintain its value. Just as you cannot take the 4 from (4+2) and divide it into a number with the "+ 2". I cannot take the 2 from 2(2+1) and divide it into another number without the (2+1).
You ARE allowed to distribute before division, or any other operator, since you are allowed to simplify any equation first. There are MANY references which state "Remove parentheses by distribution" Try Googling that as a search term.
6÷2(2+1) = 6÷(4+2) = 1
Now, some people have argued that you don't NEED to distribute the 2; you just add the 2+1, and end up with 2(3). Then they go on the say that this is the same as 2*(3). WRONG! You STILL have parentheses and STILL need to distribute that 2 inside them, for the reasons discussed about factoring above. Therefore you have this:
6÷2(3) and must distribute like this:
6÷2(3+0) = 6÷[2(3) + 2(0)] = 6÷6 = 1
These people who get 9 try and rip the 2 away from the parentheses by inserting a times symbol like this:
6÷2*(3), and then do the division of 6÷2 first. I explained the illegalities of doing this, since the 2 is a factor of the 2+1.
Lastly, 6÷2 is NOT (6/2), as in (6/2)(2+1). This is totally incorrect, since it lacks that parentheses in the original equation. Check any online or written text. Leading fractions as a coefficient ALWAYS have ( ) around them.
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