How to evaluate 143 + 305 * 70 step by step with intermediate results?
Executive summary
The expression 143 + 305 * 70 should be evaluated by performing the multiplication before the addition, because standard order-of-operations rules (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) require multiplication to be done prior to addition [1][2]. Following that rule produces an intermediate product of 305 × 70 and a final sum after adding 143; online order-of-operations calculators can display these intermediate steps explicitly [3][4].
1. Identify the operations and apply PEMDAS
The expression contains an addition and a multiplication; by the PEMDAS convention multiplication and division are performed before addition and subtraction, so the multiplication 305 × 70 is the first arithmetic step to carry out [1][2]. If the expression had parentheses altering the sequence, those would be resolved first, but here there are no parentheses, so PEMDAS directs immediate evaluation of the multiplication [1].
2. Compute the multiplication (intermediate result)
Compute 305 multiplied by 70 as the first concrete arithmetic action: 305 × 70 = 21,350; this is the intermediate result that replaces the multiplication subexpression in the original sum (note that calculators that show order-of-operations steps will display this substitution) [3][5]. Treating the product as a single number gives an equivalent one-term expression 143 + 21,350, which is ready for the next operation under the order-of-operations rule [4].
3. Perform the addition to reach the final result
With the intermediate product in place, perform the remaining operation—addition—so 143 + 21,350 = 21,493; this is the final evaluated value of the original expression once multiplication-first rules are respected [5][6]. Order-of-operations solver tools can confirm both the intermediate product and the final sum when the full expression is entered [3][7].
4. Explain why not to add first (common mistake)
A frequent error is to read left-to-right and add 143 + 305 first, yielding 448, then multiply by 70 to get 31,360, a different and incorrect result; this mistake violates the PEMDAS rule that places multiplication above addition unless parentheses explicitly change the sequence [1][2]. Teaching resources and worksheets emphasize that division and multiplication share priority above addition and subtraction, and that performing lower-priority operations prematurely yields a different number and therefore an incorrect evaluation [8][2].
5. Tools and verification: how calculators show steps
Several online tools are available that not only compute the value but also list intermediate steps—MathIsFun’s order-of-operations pages and various PEMDAS calculators will accept an expression like 143 + 305 70 and show the multiplication first, then the addition, confirming the intermediate 21,350 and final 21,493 [3][4][5]. Using one of those step-by-step solvers is the practical way to both verify manual work and learn the procedural order if the rule is unfamiliar [6][9].
**6. Alternative conventions and edge cases to watch for**
While PEMDAS is widely taught, some instructors emphasize the paired nature of multiplication/division and addition/subtraction and recommend reading left-to-right within those pairs; this nuance matters when an expression mixes multiplication and division or addition and subtraction without parentheses, though it does not change the outcome for 143 + 305 70 because multiplication still precedes addition [2][1]. If expressions include implied multiplication, fractions, or unary operations, those context-specific rules or parentheses can alter step order, and consulting a step-by-step solver or authoritative textbook example is advisable [5][10].