What is the step-by-step evaluation of 143 + 305 * 70 using PEMDAS/BODMAS?
Executive summary
Using standard order-of-operations conventions (PEMDAS/BODMAS), you must compute multiplication before addition, so 143 + 305 * 70 is evaluated as 143 + (305 × 70) = 143 + 21,350 = 21,493. Multiple calculators and pedagogical sources reiterate that multiplication and division have the same priority and are done before addition and subtraction (PEMDAS: perform M and D next, left to right) [1][2].
1. The rule that decides the answer: PEMDAS/BODMAS explained
PEMDAS is an acronym teachers and many online tools use to order operations: Parentheses, Exponents, Multiplication and Division (treated as a pair, left to right), Addition and Subtraction (treated as a pair, left to right) [1][2]. Sources emphasize that M does not automatically trump D or that A automatically comes before S in every practical sense; rather, the convention is to do multiplication and division before addition and subtraction, resolving ties left-to-right [1][2].
2. Step-by-step evaluation of 143 + 305 * 70
1) Identify operations: addition (+) and multiplication (×). According to PEMDAS, perform multiplication before addition [1][2].
2) Compute the multiplication: 305 × 70 = 21,350. This intermediate result follows the “M before A” rule in PEMDAS [1][2].
3) Add the remaining term: 143 + 21,350 = 21,493. Final result is 21,493. Online PEMDAS solvers will present the same sequence [3][4].
3. Why people sometimes get this wrong
A common misread is to do operations strictly left-to-right without grouping multiplication/division or addition/subtraction as pairs, or to assume the letters in PEMDAS imply strict left-to-right priority across all letters. Authoritative explainers stress that PEMDAS is shorthand; correct practice treats M and D as equally ranked and A and S as equally ranked, each pair resolved left-to-right [1][2]. Many online “PEMDAS calculators” exist to prevent these mistakes by showing the steps explicitly [5][3].
4. Tools and verification
Multiple order-of-operations calculators and educational sites provide step-by-step displays for this exact kind of expression and would show the multiplication first, then the addition [5][3][4]. Math education sites reiterate the same procedure with examples so users can verify results themselves [6][7].
5. Alternate viewpoints and limitations
Sources agree on the numeric procedure for an expression like 143 + 305 70; there is no substantive disagreement in the provided reporting about the order for these operations [1][2]. Available sources do not mention any competing arithmetic convention that would produce a different numeric answer for this expression. Where confusion exists in public discourse, it stems from mnemonic misuse rather than mathematical ambiguity [1][2].
**6. Practical takeaway**
When evaluating mixed expressions, always scan for parentheses first, then exponents, then perform all multiplications and divisions as they appear left-to-right, and finally additions/subtractions left-to-right. Applying that to 143 + 305 70 yields 21,493; calculators and pedagogical sites confirm this sequence [1][3].