How would the result change if addition were done before multiplication in 143 + 305 * 70?
Executive summary
If you follow standard order-of-operations conventions, 143 + 305 × 70 evaluates as 143 + (305 × 70) = 143 + 21,350 = 21,493 because multiplication is performed before addition (see textbooks and guides) [1] [2]. If, instead, addition were forced to happen first (by parentheses or a different convention), you would get (143 + 305) × 70 = 448 × 70 = 31,360 — a markedly larger result; the difference between the two results is 9,867 (available sources do not mention which convention a specific calculator or language might use by default for this exact expression) [3] [1].
1. The standard rule and why it gives 21,493
Mathematics teaching and references agree that multiplication and division are performed before addition and subtraction unless parentheses indicate otherwise; applying that rule to 143 + 305 × 70 means do 305 × 70 first and then add 143 to get 21,493 [1] [2]. Multiple education sites and encyclopedic entries explain this hierarchy using PEMDAS/BODMAS-style mnemonics and examples showing multiplication is “stronger” than addition when no grouping symbols are present [3] [4].
2. The alternative — force addition first — and its numeric effect
If the expression is written so addition must occur first (for example, using parentheses: (143 + 305) × 70), you compute 143 + 305 = 448 and then 448 × 70 = 31,360. That alternative interpretation produces a result 31,360, which is 9,867 larger than the standard 21,493 result [3] [1]. Textbooks and pedagogy explicitly show similar examples (e.g., (2 + 3) × 4 = 20) to illustrate how parentheses change precedence [3].
3. Why the rule exists — avoiding ambiguity and making expressions consistent
The order-of-operations convention was adopted to prevent different readers from getting different answers; historically multiplication has been given precedence over addition because algebraic notation and properties (like distributivity) make that a natural hierarchy [3] [5]. Education resources emphasize that without these shared rules “two people could get two different answers” and that parentheses are the tool to signal a different intended order [6] [1].
4. Where confusion still arises — mnemonics and left-to-right subtleties
Although PEMDAS-style mnemonics are widespread, they sometimes cause students to misapply rules (for example thinking multiplication must always come before division rather than treating multiplication and division at the same level left-to-right). Reliable guides stress that multiplication/division are a tied pair and addition/subtraction are another tied pair — each pair is evaluated left to right — but both sources still place multiplication/division above addition/subtraction [7] [8].
5. Practical takeaways — how to write and check expressions
If you mean “add first,” write parentheses: (143 + 305) × 70. If you rely on standard conventions, write nothing and the multiplication will be done first: 143 + 305 × 70 = 21,493 [1] [2]. To avoid educational pitfalls, teaching resources recommend explicitly grouping calculations when the intended order might be nonstandard, since mnemonics and different regional names (PEMDAS, BODMAS, BEDMAS) can confuse learners [4] [2].
Limitations and note on scope: the sources provided describe the conventional rules and give examples, but they do not list behavior for every calculator or programming language for this exact expression; therefore I do not assert how any particular device would display or compute it without parentheses (available sources do not mention that) [3] [9].