My thought process: if I had 8÷(4+4) = 1 and factored out a 2, I get 8÷2(2+2) = 1. However, if I say 2(2+2) = 2*(2+2), then 8÷2(2+2) = 8÷2*(2+2) = 1, BUT 8÷2*(2+2) = 16.
Please help I’m feeling dumber by the second
In: Mathematics
The issue is the implicit multiplication between the 2 and the 2+2. That is, it’s written as 2(2+2) and not 2*(2+2). By some conventions, this implicit multiplication has a higher priority than other multiplication or division operations, superseding the normal left-to-right order they would be done in.
Why is this the case? Essentially, it’s because if I write something like 1/xy, it’s pretty clear that what I *mean* is 1/(xy), and not (1/x)y. Having it be an explicit rule to give implicit multiplication a higher priority means you can write out quotients of products without needing to use as many brackets or multiplication symbols, thereby making it easier to read.
With this rule, the answer is 1, because you resolve the 2(2+2) first to get 8, and then 8÷8=1. Without this rule, you apply the multiplications and divisions from left to right, meaning the 8÷2 becomes 4, which is then multiplied by the (2+2) to give 16.
Both answers are right, it just depends on which convention you use. Personally, I prefer the implicit multiplication convention, as it results in equations with fewer symbols.
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