This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Set up the multiplication of 271 by 31. r@r@r@r & & 2 & 7 & 1 \\ × & & & 3 & 1 \\ Step 2: Multiply 271 by 1 (ones place). Formula: 271 × 1 = 271 Substitute: 200 × 1 = 200, 70 × 1 = 70, 1 × 1 = 1 Simplify: 200 + 70 + 1 = 271 Write 271 aligned to the right: r@r@r@r@r & & & 2 & 7 & 1 \\ × & & & & 3 & 1 \\ & & & 2 & 7 & 1 \\ Step 3: Multiply 271 by 3 (tens place), then shift left by 1 position (add a zero). Formula: 271 × 3 = ?, then × 10. First, 271 × 3: 1 × 3 = 3 7 × 3 = 21 (write 1, carry 2) 2 × 3 + 2 = 8 So, 813. Then shift: 8130. Write 813 starting under the tens column: r@r@r@r@r@r & & & & 2 & 7 & 1 \\ × & & & & & 3 & 1 \\ & & & & 2 & 7 & 1 \\ + & & 8 & 1 & 3 & & \\ Step 4: Add the partial products. Formula: 271 + 8130 = ? Column by column, right to left: Units: 1 + 0 = 1 Tens: 7 + 3 = 10 (write 0, carry 1) Hundreds: 2 + 1 + 1 = 4 Thousands: 8 = 8 Simplify: 8401 r@r@r@r@r@r & & & & 2 & 7 & 1 \\ × & & & & & 3 & 1 \\ & & & & 2 & 7 & 1 \\ + & & 8 & 1 & 3 & 0 & \\ & 8 & 4 & 0 & 1 & & \\ 8401