First, let's look at the expression: 8÷2(2+2). The parentheses contain 2+2, so we handle that first, resulting in 4. The expression can be written as 8÷2(4), and everyone agrees up to this point.
Common Misconceptions: How to Interpret 2(4).
Some people believe that there shouldn't be only one number inside the parentheses. A multiplication sign should be used. Following this logic, the expression is rewritten as 8÷2x4. Then, following the order of operations for multiplication and division (from left to right), 8÷2x4=4x4=16, answering 16.
However, another group of people has a different approach. They believe that 2(4) should not be separated. This depends on the interpretation of implicit multiplication. Different math textbooks use different conventions. Therefore, the expression should be written as 8÷2(4)=8÷8=1. This is where answer 1 comes from.
Symbol Conventions
Therefore, both interpretations are valid because they are arbitrary symbol conventions. Scientific calculators also use these different conventions. This is simply an ambiguity in notation. Professor Keith Devlin, a mathematics expert, also stated that both 1 and 16 are possible answers to this problem, but neither is correct. The problem itself is ambiguous, allowing for two possible answers.
Summary
Look, math is supposed to be precise, so whoever wrote this problem should've been clearer rather than providing an ambiguous formula. Parentheses should be used to eliminate ambiguity when necessary. For this problem, the correct question should be either 8÷(2(2+2)) or (8÷2)(2+2).
