What is the order of operations for solving expressions like 143 + 305 * 70?
Executive summary
When evaluating 143 + 305 × 70, standard order‑of‑operations rules say do multiplication before addition, so compute 305 × 70 = 21,350 and then add 143 to get 21,493 (sources teach multiplication before addition and that multiply/divide are done before add/subtract) [1] [2]. Different mnemonic acronyms exist (PEMDAS, BODMAS, GEMDAS) but major math education sources agree that multiplication and division share precedence and are handled left-to-right, as do addition and subtraction [3] [4] [5].
1. Why this problem looks trivial — and why conventions matter
A simple expression like 143 + 305 × 70 exposes the convention that some operations are ranked higher than others: multiplication outranks addition, so the multiplication must be evaluated first rather than performing the operations strictly left to right; that convention is taught widely with acronyms such as PEMDAS/BEDMAS/BODMAS to help recall the ranking [3] [6] [5].
2. How teachers and resources frame the steps
Textbooks and online guides outline the steps as parentheses (or grouping), exponents (orders), multiplication and division (same rank, left-to-right), and addition and subtraction (same rank, left-to-right). Practical guidance: simplify inside any parentheses first, then exponents, then carry out multiplications and divisions in the order they appear from left to right, and finally do additions and subtractions left to right [1] [4] [7].
3. Applying the rule to 143 + 305 × 70 — step by step
Following the standard convention, compute the single multiplication first: 305 × 70 = 21,350. Then perform the addition: 143 + 21,350 = 21,493. This sequence (multiply, then add) is exactly what elementary and middle‑school order‑of‑operations guides teach for expressions without parentheses [2] [6].
4. Why some students get confused by PEMDAS or similar acronyms
A common misconception arises when memorizing PEMDAS: learners sometimes think multiplication always comes before division and addition always before subtraction. But reliable sources stress that multiplication and division share the same precedence and are evaluated left to right; likewise addition and subtraction share precedence and are left-to-right [6] [1]. Education resources now sometimes use variants (like PEMA) or explicit left-to-right guidance to reduce that confusion [6].
5. Competing conventions and edge cases to watch for
Most mathematics and programming conventions align on the precedence ranking, but reporting and reference sources note there is “no universal convention” for some notations (for example, different historical treatments of ÷ versus ×), and the safest practice is to add parentheses when you want a specific, unambiguous order [5]. In classroom practice, authors repeatedly recommend rewriting the expression step by step and using parentheses to make intent explicit [4] [8].
6. Practical advice for exams, calculators and code
On paper or in an exam, follow the hierarchy: parentheses → exponents → multiply/divide left-to-right → add/subtract left-to-right. Calculators and programming languages implement conventions too; if you must be certain, use parentheses to force the intended grouping. Educational sites and worksheets emphasize breaking problems into smaller parts and rewriting as you compute to avoid mistakes [4] [8].
7. Final takeaway — one rule to remember for this problem
Compute 305 × 70 first, then add 143; that produces 21,493. That result and the reasoning follow the standard order‑of‑operations pedagogy used across the cited educational resources [1] [2].
Limitations and sourcing note: this explanation relies on educational references and pedagogical materials cited above; available sources do not mention any alternative numeric result for 143 + 305 × 70 beyond what follows from the standard conventions described [7] [5].