If parentheses changed to (143 + 305) * 70, how would the result differ?
Executive summary
Changing the expression to (143 + 305) 70 forces the addition inside the parentheses to be done first, producing 448 70 = 31,360; evaluated without those parentheses following standard order-of-operations conventions (multiplication before addition) the equivalent expression 143 + 305 70 would be computed as 143 + (305 70) = 143 + 21,350 = 21,493 (parentheses take precedence) [1] [2].
1. Why parentheses matter: the rule that decides the answer
Parentheses are the highest-precedence operation in the conventional order of operations, so anything inside them is calculated first; that rule is the explicit reason (143 + 305) 70 is not the same as 143 + 305 70 [1] [2]. Educational resources and computer-science texts repeatedly state that parentheses “force an expression to evaluate in the order you want,” so adding parentheses changes the operation tree and therefore the numeric result [3] [4].
2. The two concrete outcomes: what each expression equals
If you write (143 + 305) 70, you first compute 143 + 305 = 448, then multiply by 70 to get 31,360. If instead the expression is written without those external parentheses as 143 + 305 70, the multiplication is done before addition, giving 305 70 = 21,350, then 143 + 21,350 = 21,493 [1] [4]. Those two totals differ by 9,867 — numerically large enough that the choice of parentheses is decisive.
**3. How textbooks and teachers present this difference**
Introductory algebra guides and classroom materials use examples exactly like this to show that operations performed in different orders yield different results; they advise using parentheses when you need a nonstandard order and warn that omitting them produces a different expression by convention [2] [5]. Guides for children and math-help sites emphasize PEMDAS/BODMAS to teach that parentheses/brackets must be resolved before multiplication and addition [4] [6].
**4. Technical and programming perspective: parentheses as a control mechanism**
Computer-science texts note that programming languages follow the same precedence rules and that parentheses are the mechanism to force evaluation order; for example, Python evaluates expressions inside parentheses first, so (143 + 305) 70 yields the same result in code as in math notation [3]. This matters in software because changing evaluation order without parentheses can produce radically different outcomes; coders are advised to add parentheses to make intent explicit [3].
5. Why ambiguity sometimes appears in other forms (context on common controversies)
Some controversial expressions — notably forms like 48/2(9+3) — have sparked public debates because typography and convention can leave interpretation ambiguous when division and implicit multiplication are mixed; specialists recommend making the intended grouping explicit with parentheses to avoid the two possible readings [7]. While that particular ambiguity involves division notation and implied multiplication, the lesson is the same: when in doubt, add parentheses [7].
6. Takeaway and practical advice
If your goal is to add 143 and 305 first and then multiply by 70, write (143 + 305) 70; if you intend to multiply 305 by 70 and then add 143, write 143 + 305 70. Educational and technical sources uniformly recommend using parentheses to render intent unambiguous [1] [3]. Available sources do not mention any alternate standard conventions that would treat (143 + 305) 70 and 143 + 305 70 as equivalent without parentheses (not found in current reporting).