How do you compute 143 + 305 * 70 step by step by hand?
Executive summary
The expression 143 + 305 * 70 evaluates to 21,493 when computed by hand by following the standard order of operations: perform multiplication before addition (PEMDAS/MULT before ADD) and then add the results [1] [2]. This piece lays out the step‑by‑step mental and written method, shows the arithmetic, and closes with quick verification tips and common pitfalls [3] [4].
1. Identify what the problem is asking and which rule applies
The first and decisive step is recognizing that the expression contains both addition and multiplication, so the order of operations dictates that multiplication must be performed before addition—commonly memorized as PEMDAS or the rule “Parentheses, Exponents, Multiplication/Division, Addition/Subtraction” [1] [2]. Treat the expression 143 + 305 70 as a small program: evaluate the multiplication 305 70 first, then take that product and apply the final addition of 143 [1].
2. Carry out the multiplication step by step
Compute 305 70 by breaking the multiplication into easier pieces: 70 = 7 × 10, so 305 × 70 = (305 × 7) × 10. Multiply 305 by 7: 300 × 7 = 2,100 and 5 × 7 = 35, so 305 × 7 = 2,135. Now multiply that intermediate product by 10 to account for the ×10 factor, giving 2,135 × 10 = 21,350. This decomposition mirrors the practical “split and scale” approach used in hand arithmetic and is consistent with standard operation order and multiplication techniques taught in arithmetic references [2] [5].
**3. Perform the addition and present the final result**
With the product in hand, add the remaining term: 21,350 + 143. Add the hundreds, tens, and ones: 21,350 + 100 = 21,450; +40 = 21,490; +3 = 21,493. Thus the entire expression 143 + 305 70 evaluates to 21,493. This is the straightforward consequence of doing the multiplication first and then the addition, exactly as ordered by PEMDAS [1] [5].
4. Quick verification, common pitfalls, and tools
A quick parity check or alternative calculation can confirm the result: recompute 305 × 70 directly via long multiplication or use any reputable order‑of‑operations calculator to show the same sequence—these online tools demonstrate PEMDAS and will output matching step‑by‑step work for expressions of this form (examples include interactive calculators and solvers that follow PEMDAS) [3] [4]. The most common mistakes are adding before multiplying (which would yield a radically different and incorrect value) or misplacing a zero when scaling by 10; both are eliminated by explicitly writing the intermediate product 21,350 before doing the addition [1] [2].
5. Practical takeaway
When confronted with any numerical expression that mixes multiplication and addition, always isolate and compute the multiplication (or division) parts first, write down those intermediate results to avoid place‑value errors, then perform the remaining additions/subtractions—this reliable sequence prevents errors and aligns with standard references on order of operations [1] [2]. For reassurance, paste the expression into an order‑of‑operations solver and compare the step‑by‑step output to the hand work; the numerical result here is 21,493 [3] [4].