Yes, this is correct and is the reason why I set implicit multiplication to a higher precedence in the calculators I've written. Obviously not everyone agrees t

Yes, this is correct and is the reason why I set implicit multiplication to a higher precedence in the calculators I've written. Obviously not everyone agrees though, but it's certainly the way it's always been interpreted in written algebra textbooks. Precedence rules are essentially arbitrary. We have to make them up. Going by most common historical use is a reasonable choice.