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
Here's how to solve the multiplication problem in base 5: 1) Multiply 4213_5 × 23_5 Step 1: Set up the multiplication. c & 4 & 2 & 1 & 3_5 \\ × & & & 2 & 3_5 \\ Step 2: Multiply 4213_5 by 3_5. • 3_5 × 3_5 = 9_10 = 14_5. Write down 4, carry over 1. • 3_5 × 1_5 + 1_5 (carry) = 3_10 + 1_10 = 4_10 = 4_5. Write down 4. • 3_5 × 2_5 = 6_10 = 11_5. Write down 1, carry over 1. • 3_5 × 4_5 + 1_5 (carry) = 12_10 + 1_10 = 13_10 = 23_5. Write down 23. The first partial product is 23144_5. Step 3: Multiply 4213_5 by 2_5 (shifted one place to the left). • 2_5 × 3_5 = 6_10 = 11_5. Write down 1, carry over 1. • 2_5 × 1_5 + 1_5 (carry) = 2_10 + 1_10 = 3_10 = 3_5. Write down 3. • 2_5 × 2_5 = 4_10 = 4_5. Write down 4. • 2_5 × 4_5 = 8_10 = 13_5. Write down 13. The second partial product is 134310_5. Step 4: Add the partial products in base 5. c & & 2 & 3 & 1 & 4 & 4_5 \\ + & 1 & 3 & 4 & 3 & 1 & 0_5 \\ & 1 & 1 & 3 & 0 & 0 & 4_5 \\ • 4+0 = 4_5 • 4+1 = 5_10 = 10_5. Write 0, carry 1. • 1+3+1 (carry) = 5_10 = 10_5. Write 0, carry 1. • 3+4+1 (carry) = 8_10 = 13_5. Write 3, carry 1. • 2+3+1 (carry) = 6_10 = 11_5. Write 1, carry 1. • 0+1 (carry) = 1_5. Write 1. The final answer is: 4213_5 × 23_5 = 113004_5 That's 2 down. 3 left today — send the next one.