How to use order of operations to compute 143 + 305*70 step by step?
Executive summary
The expression 143 + 305*70 is evaluated by applying standard order-of-operations rules that require multiplication before addition, so the product 305 × 70 is computed first and then added to 143, yielding 21,493 as the final result [1] [2] [3]. This article walks through the step-by-step process, explains why the rules exist, and notes alternative notations and potential student traps using the cited instructional sources [4] [5].
1. What "order of operations" means and why it matters
Order of operations is a convention that tells which arithmetic steps to carry out first in an expression so everyone gets the same answer; common mnemonics include PEMDAS (parentheses, exponents, multiplication/division left-to-right, addition/subtraction left-to-right) and equivalent schemes such as BODMAS, as described in standard references [1] [2]. Without these conventions, a simple expression like 2 + 3 × 4 could be interpreted multiple ways, producing different numeric results, which is why textbooks and teaching resources emphasize the ranking of operations [4] [5].
2. Identify the operations in 143 + 305*70
The expression contains only addition and multiplication: a constant 143, a multiplication 30570, and the plus sign that joins them; there are no parentheses or exponents to change the normal sequence (this identification follows the instructional definitions of operations) [5] [4]. Because multiplication has higher precedence than addition under the standard convention, the multiplication must be performed before the addition [2] [1].
**3. Step 1 — compute the multiplication 305 × 70**
Applying the rule to compute multiplication first, carry out 305 times 70; one reliable computational check is to use established order-of-operations calculators which perform and display these intermediate products (for example Symbolab and CalculatorSoup provide step-by-step evaluation) [3] [6]. Performing the arithmetic yields 305 × 70 = 21,350; this can be seen by recognizing 70 = 7 × 10 so 305 × 7 = 2,135 and then multiplying by 10 gives 21,350 (the decomposition method is standard arithmetic practice, consistent with calculator outputs) [3] [6].
**4. Step 2 — add the product to 143**
With the multiplication complete, the remaining operation is addition: 143 + 21,350. Performing that addition yields 21,493, the final evaluated value of the original expression; calculators and order-of-operations tools confirm this sequential approach and result [3] [6]. This two-step approach—evaluate higher-precedence operations, then lower-precedence ones—follows the teaching recommendations in elementary algebra resources [4] [5].
**5. Common student traps and alternative conventions**
A frequent mistake is to read left-to-right blindly and add 143 + 305 first, which would produce the wrong intermediate and final values; reminders that multiplication outranks addition help avoid that error and are emphasized in worksheets and practice materials [7] [8]. There is also nuance in how multiply/divide and add/subtract are treated: they are paired operations that are handled left-to-right at the same precedence level (multiply/divide together, add/subtract together), a detail stressed by pedagogical sources to prevent misapplication of mnemonics like PEMDAS [2] [1].
**6. Tools and references for verification**
Multiple free online calculators and educational pages will show the same step-by-step result for 143 + 30570 and are useful for cross-checking student work; examples include Symbolab, CalculatorSoup, and MathIsFun’s order-of-operations pages which demonstrate the precedence rules and can evaluate custom expressions [3] [6] [5]. Instructional libraries like LibreTexts and worksheet collections provide practice problems to reinforce the rule and reduce common errors through repetition [4] [8].
7. Final takeaway and limitations of the reporting
Applying standard order-of-operations conventions—multiplication before addition—gives the clear, unambiguous result 21,493 for 143 + 305*70, and verified calculator and pedagogy sources support the two-step computation shown here [1] [3]. If there were parentheses or other operators omitted from the original expression, that would change the sequence, but the sources provided do not suggest any alternate parsing for this exact expression; this report relied on general order-of-operations references and calculators rather than a source that lists this specific arithmetic example verbatim [4] [6].