**Problem 7:**(a) Use an expanded array to compute \(345 \times 78\).(b) Use the lattice algorithm to compute \(345 \times 78\).(c) In the lattice algorithm, look at the three digits in the diagonal between 7 and 1, and indicate where each of those digits shows up in the expanded array.(d) Max decided to try the lattice algorithm with the diagonals going the other direction. He is computing \(345 \times 78\) below.**Lattice Diagram Explanation:**- The diagram is a 3x2 lattice with the numbers 345 (top, digits right-aligned) and 78 (side, digits downward).- Each box is divided diagonally.- The top row of boxes is filled in with the products of 3 with 7 and 8, yielding numbers 21 and 24.- The middle row is filled with the products of 4 with 7 and 8, yielding 28 and 32.- The bottom row is filled with the products of 5 with 7 and 8, yielding 35 and 40.- Diagonals are formed, but Max uses them in the incorrect direction, leading to the wrong total.According to Max’s lattice, \(345 \times 78 = 29,916\), but Max knows that the correct answer is 26,910. Explain to Max why the diagonals going in this direction give him the wrong answer.**Educational Explanation:**Max incorrectly reads the diagonals in the opposite direction. The correct way to sum the diagonals in lattice multiplication is from upper right to lower left, which accurately consolidates all partial products into the final product. Max's method likely summed the squares incorrectly, leading to a miscalculation. By changing the diagonal direction, Max would align with the traditional method and find the correct answer.

Answered: Image /qna-images/answer/24485fab-da81-4e1b-a4e4-c9151431ad90.jpg

(a) Use an expanded array to compute 345 x 78. (b) Use the lattice algorithm to compute 345 × 78. (c) In the lattice algorithm look at the three digits in the diagonal between 7 and 1, and indicate where each of those digits show up in the expanded array. (d) Max decided to try the lattice algorithm with the diagonals going the other direction. He is computing 345 x 78 below. 3 4. According to Max's lattice, 345 x 78 = 29, 916, but Max knows that the correct answer is 26,910. Explain to Max why the diagonals going in this direction give him the 7 2 8. 3 4 3 0. 4. 8. 1 wrong answer. 6.