The following equation appeared on my FB page with the answer a friend gave:
6 ÷ 2(1+2)=?
Now, when I went to answer this I was given two options: 1 or 9. After a moment's thought, I got the answer and selected it. (The answer's 9, by the way.) It wasn't even a thing for me. Then a girl I know challenged my answer saying it should have been 1. Her logic being as follows:
6 ÷ 2(3) is equivalent to 6 ÷ 6 which equals 1.
I have to admit, despair clutched at my heart for the briefest of seconds. Could I have been proven wrong?? Could a simple equation stab me to the quick and destroy my math prowess? No, I thought!! There was something wrong here, and I set to prove my logic. The answer my dear friends lies in the mathematical rule that establishes the Order of Operations or Precedence of Operators.
This rule states the order in which we must resolve mathematical operations to solve any given equation:
1 - Anything inside parenthesis
2 - Exponents & roots
3 - Multiplication & Division
4 - Addition & Subtraction
Armed with this knowledge, I gave my proof as follows, starting with the original equation:
6 ÷ 2(1+2)=?
Now resolve the terms inside the parenthesis first:
6 ÷ 2(3)=?
Now, here's where it gets tricky, and where my friend went wrong. Most people would misinterpret the Order of Operations and then resolve 2(3). but the order states terms INSIDE the parenthesis. Not the operation of the parenthesis ITSELF, which is multiplication. The equation could easily be re-written like this and be exactly the same:
6 ÷ 2 * 3 =?
Okay, so now what? Do we divide first? Multiply first?? If you paid attention in math class, and who did besides me?, you'd know that division doesn't really exist. Division is just a fancy form of multiplication. The expression: 6 ÷ 2 could easily be re-written as 6 * ½ and mean the same thing. So let's plug that in and see where it goes, solving from left to right:
6 * ½ * 3
3 * 3
And that's how I got the answer. (This is why teachers always ask you to show your work. That way they can see where you misinterpreted the rules of math and got the wrong answer.)
Now, being the smart woman that she is, my friend went and got independent verification from the Internet, and my answer was justified. To use a famous actor's catchphrase: WINNING!!!
Still, I have to thank my friend. She gave me a chance to use my brain in an arena I haven't touched in awhile. Mathematical proofs. So, thank you! You know who you are!! As for the rest of you, my dear readers, take a moment and learn from this post, or use it to teach someone else. Because any day in which you've learned something is a good day!