# What is the justification to teach the (redundant) use of parentheses in multiplications?

Example: 5 x 18 = (5 x 10) + (5 x 8) instead of 5 x 10 + 5 x 8?

• The teacher must have been offended by dear Aunt Sally and refused to excuse her. Commented Jan 28, 2023 at 15:56
• If I see 5 x 10 + 5 x 8 then very first thing I need to do is think about order of precedence and mentally map that to (5 x 10) + (5 x 8) anyway. So certainly presenting it as such up front saves me a step. What would be the justification for not doing it? You think that the extra step is worthwhile in itself? Or just that you personally find doing it so intuitive you think everyone else will too? Commented Jan 28, 2023 at 18:19
• It's actually required if you're brave enough to use Windows Calculator in standard mode. :-/ Commented Jan 28, 2023 at 19:57
• @RobertColumbia or somebody forgot to email the teacher's dad a shark. Commented Jan 29, 2023 at 4:25
• The parentheses in (5 x 10) + (5 x 8) are only redundant because we have a convention that says 5 x 10 + 5 x 8 should be parsed as (5 x 10) + (5 x 8) rather than as 5 x ((10 + 5) x 8) or any of the other possible ways. You need to teach that convention before you can rely on that convention. Using parentheses is pretty convenient to teach that convention.
– Stef
Commented Jan 29, 2023 at 20:02

• or have machine-like reading ability for complicated logical expressions. In my own writing I've mostly ignored each approach, and freely use different bracketing symbols for better comprehension and short-cut terms (e.g. "(line 3)" rather than writing out what "line 3" is). For example, see the style used in this MSE answer. I think it would be better to spend less time testing the evaluation of "artificial interpretation problems" like $5 \times 10 + 5 \times 8$ (continued) Commented Jan 28, 2023 at 19:08
• @anjama Especially when dealing with operators which aren’t handled uniformly across languages. For example exponentiation is left-associative in some languages (Python for example) and right-associative in others (Wolfram Alpha for example), so 4^3^2 is ambiguous without parenthesis, and possibly misunderstood without a proper knowledge of the language in the absence of parenthesis. Commented Jan 29, 2023 at 2:55