48÷2(9+3) = ?

About

48÷2(9+3) = ? is a math problem that leads to two different answers depending on the order of operations^[1] used. Since 2011, message board users have debated over whether 2 or 288 is the correct answer to the problem, with no conclusive answer. This and another seemingly impossible equations have been a hot topic of forum debate that are sometimes used to troll other posters who will vehemently argue that their answer is the definitive one.

Origin

On April 7th, 2011, a user of the local Texas message board Hot Pursuit^[3] known as al_carl polled other users about the equation 48÷2(9+3), found in his son's homework the previous night. He offered four different answers, 2, 3.14, 219 and 288. The answers were relatively evenly split, with 50 people choosing 2 and 55 choosing 288. The question generated 95 replies of debate about the correct answer.

Spread

Later that day, someone reposted the equation to the Bodybuilding.com message board^[4], where more than 2,500 replies were posted. Also on April 7th, debate about the equation took place on dozens of message boards, ranging from communities surrounding broad topics to fan spaces for local sports teams including the Physics Forums^[5], Wall Street Oasis^[6], MSU Red Cedar^[7], Grass City^[8], Tennis Warehouse^[9], Inside MD Sports^[10] and The Ecapist.^[11] Later that day, the equation was posed on Yahoo! Answers^[11], where the user Phyxius Ænimus broke down the two approaches to the problem, noting that sometimes math does not provide definitive answers.

The next day, additional discussions of the equation took place on the Sneaker Talk forums^[12], Yahoo! Answers Australia^[13] and DIY Mobile Audio.^[14]

Solution

The reason different calculators offer different answers to the equation depends on how the machine interprets the order of operations. Most calculators follow the traditional order, completing expressions within brackets before anything else, resulting in an answer of 288, as determined by WolframAlpha^[17] and Google.^[18] In this case, the problem is solved as follows:

However, others will follow PEMDAS, a mnemonic term that stands for Parentheses, Exponentiation, Multiplication, Division, Addition and Subtraction. By this logic, multiplication must take place before division, resulting in solving the problem as follows:

Order of Operations and PEMDAS are not the only rules that can be applied to complete the equation. If one applies the distributive property, which requires numbers outside of an equation in parentheses be multiplied to each number in the enclosed equation separately, both results of 2 and 288 can be observed, depending on whether or not the division takes place first.

There is also an argument^[15] that implied multiplication, as seen in the algebraic phrase 2x takes precedence over explicit multiplication using the "x" symbol. For example, in the problem 2/5x, the implicit multiplication suggested by 5x would come before the explicit division of 2/5. Following this logic, the equation can be solved as follows:

The final approach suggests the obelus, the term for the symbol "÷", represents the division of all terms preceding it by all terms after it^[20][21], separating the two components of the equation at hand. Using this interpretation, the equation is solved like so:

Related Problem: 6÷2(1+2)= ?

On April 27th, 2011, Redditor and math professor rob1n posted an image macro to the /r/WTF subreddit^[16] featuring a screenshot of a Facebook poll debating the answer to variation of this equation, 6÷2(1+2), which results in the answers of 1 or 9. Within two days, it received more than 1,200 comments, gaining more than 2,500 upvotes and 786 points overall. Throughout April and May, this equation was discussed on Yahoo! Answers^[17], IGN^[22] the Wolfram Alpha Community Forum^[24], and the Penny Arcade forum.^[25] The equation saw a resurgence in early 2013, resulting in discussions on Snopes^[26] and Slate^[27], who investigated why people get so worked up over the differing answers.

Search Interest

External References