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 678 × 58 using the lattice method: Step 1: Set up the lattice grid. Imagine a grid with 3 columns (for the digits of 678) and 2 rows (for the digits of 58). Each cell in the grid is divided by a diagonal line from the top-right to the bottom-left. Step 2: Multiply and fill the grid. Multiply each digit from the top number by each digit from the side number. Write the tens digit of the product in the upper triangle of the cell and the units digit in the lower triangle. • For the first row (multiplied by 5): • 6 × 5 = 30 → Cell (row 1, col 1) gets 3 (top), 0 (bottom). • 7 × 5 = 35 → Cell (row 1, col 2) gets 3 (top), 5 (bottom). • 8 × 5 = 40 → Cell (row 1, col 3) gets 4 (top), 0 (bottom). • For the second row (multiplied by 8): • 6 × 8 = 48 → Cell (row 2, col 1) gets 4 (top), 8 (bottom). • 7 × 8 = 56 → Cell (row 2, col 2) gets 5 (top), 6 (bottom). • 8 × 8 = 64 → Cell (row 2, col 3) gets 6 (top), 4 (bottom). The filled grid values (top/bottom) are: Row 1: 3/0 3/5 4/0 Row 2: 4/8 5/6 6/4 Step 3: Sum along the diagonals. Starting from the bottom-right, sum the numbers in each diagonal band. If a sum is 10 or more, write down the units digit and carry over the tens digit to the next diagonal sum. • Diagonal 1 (rightmost): 4 • Diagonal 2: 0 + 6 + 6 = 12. Write 2, carry 1. • Diagonal 3: 5 + 4 + 5 + 8 + 1 (carry) = 23. Write 3, carry 2. • Diagonal 4: 0 + 3 + 4 + 2 (carry) = 9. • Diagonal 5 (leftmost): 3 Step 4: Read the final product. Read the digits from the top-left diagonal sum to the bottom-right diagonal sum. The digits are 3, 9, 3, 2, 4. The final answer is: 678 × 58 = 39324 Send me the next one 📸