How to verify 143 + 305*70 using a calculator and by hand?
Executive summary
The arithmetic expression 143 + 305 * 70 equals 21,493 when evaluated with standard order of operations (multiplication before addition) — compute 305×70 = 21,350, then add 143 to get 21,493 (sources show online calculators that perform multiplication and addition operations) [1][2][3].
1. Why order of operations decides the result
Every standard calculator and algebra system applies multiplication before addition: you must evaluate 305 70 first, then add 143. That is why tools like the basic online calculator referenced (CalculatorSoup) will return the single numeric result rather than treating the expression left to right without precedence [1]. Symbolic solvers that show step-by-step simplification (Symbolab) follow the same convention and will present 305·70 computed before adding 143 [2][3].
**2. How to verify quickly on a physical or phone calculator**
Enter 305 × 70, note the product, then press + 143, then =. A basic online calculator like CalculatorSoup replicates handheld behavior: multiply first, then add the remaining number [1]. If your calculator has a full-expression entry (some smartphone and web calculators do), you can type the whole expression 143+30570 and it will apply precedence rules and return 21,493 [1].
3. Step-by-step “by hand” multiplication and addition
Multiply 305 by 70: treat 70 as 7×10, so 305×7 = 2,135 and then multiply that by 10 to get 21,350. Then add 143: 21,350 + 143 = 21,493. Symbolic solvers provide the same simplified steps when asked to simplify 143+305·70 [2][3].
4. Quick mental shortcuts and checks
Use factorization and rounding to sanity-check: 305×70 ≈ 300×70 = 21,000, plus 5×70 = 350 gives 21,350 — add 143 to reach 21,493. You can also check with any basic online calculator or math solver referenced in search results to confirm the arithmetic [1][3].
5. When calculators might confuse you (and how to avoid mistakes)
Some simple four-function calculators evaluate strictly left-to-right (older models or certain “immediate-execute” modes), so entering 143 + 305 × 70 without using the multiply first might yield wrong intermediate steps unless you use parentheses or compute 305×70 first. The online basic calculators cited emulate standard precedence, but if in doubt compute the product separately and then add [1].
6. Sources, tools and further reading
For hands-on verification use a basic online calculator such as CalculatorSoup’s simple calculator [1], or a step-by-step algebra tool like Symbolab which shows simplification of 143+305·70 [2][3]. General calculator portals (Calculator.net, calculator.com) also provide environments to run and recheck arithmetic quickly [4][5].
Limitations: available sources do not provide a printed textbook citation of PEMDAS/BODMAS but the calculators and symbolic solvers shown implement those conventional precedence rules; I relied on these calculator/symbolic solver sources to demonstrate expected behavior and numerical result [1][2][3].