1. R is an abelian group under addition, meaning that:
2. R is a monoid under multiplication, meaning that:
3. Multiplication is distributive with respect to addition:
On several occasions I replied by giving the method for the actual question, rather than the final answer.
What annoyed me far more than the questioners' laziness in wanting the actual answer rather than help to determine it personally, were several regular respondents who set themselves up as mathematical experts, for a section on Imperial - Metric conversions. These characters gave utterly ridiculous "methods" for solving simple "How many miles in so-many km?" or "How many litres in so-many gallons?" type questions, and sometimes managed to tangle themselves so much their own numerical answer was wrong!
Typically they'd use terms like "algebra" and "dimensional analysis" - clearly not understanding that these are wrong, and why they are wrong, in such an application! No wonder the poor children struggled to learn ISO units - which will be their future as the USA, the only major nation still using Imperial as a matter of course, is reluctantly having to adopt the metric-based ISO scales.
(I heard on the radio yesterday, a NASA flight engineer commentating the happily-successful descent of a Mars lander. She was using metres, not feet, for its altitude.)
I did have to be careful - I am in the UK and I know the US invented its own "gallon", of different volume. I would though insist on spelling the ISO-standard unit names correctly: '~tre' not '~ter', and saying why (French words, and I think the ISO itself respects that)!
Your last sentence raises a question... A vicious circle? Are the pictorial keyboards actually contributing to their own need by removing the cashiers' need to maintain simple numerical ability?
I recall one of my young nephews reckoning you don't need to learn much maths because the calculator does it for you. He seemed right puzzled when I said it's only an arithmetical tool - you need to know the maths so you can ask it to perform the right calculations!