How does order of operations (PEMDAS/BODMAS) apply to 143 + 305 * 70?
Executive summary
Applying standard order-of-operations rules (PEMDAS/BODMAS) to 143 + 305 * 70 means you perform the multiplication before the addition, so calculate 305 × 70 first and then add 143; that yields 21,350 + 143 = 21,493 (see explanation of M/D precedence and left-to-right rules) [1] [2].
1. Why PEMDAS/BODMAS matters: a one-line framing
Order-of-operations acronyms — PEMDAS in the U.S. and BODMAS/BEDMAS in other countries — exist so expressions with more than one operation have a single, agreed result; they put “multiplication/division” above “addition/subtraction,” meaning you don’t just compute strictly left-to-right without regard to precedence [3] [4].
2. Which rule applies to 143 + 305 * 70 — the quick walk-through
Both PEMDAS and BODMAS tell you to do multiplications before additions when there are no parentheses or exponents to change things; so compute 305 × 70 = 21,350, then add 143 to get 21,493 (this follows the common guidance that multiplication and division are performed before addition and subtraction) [3] [1].
3. Multiplication and division are "equals" — and left-to-right matters
Many pedagogical sources emphasize that multiplication and division are of equal precedence and should be handled left-to-right; similarly addition and subtraction are equal and handled left-to-right. That nuance matters in chained expressions, but for 143 + 305 70 the practical outcome is unchanged because the only multiplication sits next to the addition [1] [5].
**4. Could any calculator give a different result? Not the modern, order-aware ones**
Most scientific calculators and software apply standard operator precedence (multiplication before addition), so they will return 21,493. Some very basic “chain input” calculators that process button presses strictly in the order entered can give different intermediate displays for other expressions, but reputable online PEMDAS/BODMAS tools and modern devices follow the mathematical convention [2] [6].
**5. Common classroom mnemonics — what they teach and their limits**
Mnemonics like “Please Excuse My Dear Aunt Sally” (PEMDAS) or BODMAS/BEDMAS are useful memory aids for the sequence (parentheses/brackets, exponents/orders, multiplication/division, addition/subtraction), but educators caution that people sometimes misread PEMDAS as implying multiplication always before division — the correct rule is that multiplication and division share precedence [7] [1].
**6. Step-by-step for the expression, with the explicit arithmetic**
Step 1: No parentheses or exponents to evaluate (PE/B done). Step 2: Multiplication/division — compute 305 × 70 = 21,350. Step 3: Addition/subtraction — compute 143 + 21,350 = 21,493. That stepwise approach matches the calculators and PEMDAS/BODMAS guidance given in many online resources [3] [6].
**7. Alternative viewpoints and possible confusions to watch for**
Some teaching materials and simple calculators may phrase rules differently or demonstrate left-to-right exceptions in chained operations; these can confuse learners into thinking addition might sometimes come first. Reliable sources explicitly clarify that multiplication/division take precedence over addition/subtraction and that left-to-right ties are resolved within the same precedence level [1] [2].
**8. Practical takeaway and verification**
If you want to check quickly: use any reputable PEMDAS/BODMAS order-of-operations solver or a scientific calculator; both will give 21,493 for 143 + 305 70. Educational sites and order-of-operations calculators document the same convention and usually show step-by-step work if you need to audit results [8] [6].
Limitations: available sources used here explain the general rules and common calculators’ behavior but do not include an explicit worked example of 143 + 305 * 70; the numeric evaluation above follows directly from the standard rules those sources describe [3] [1].