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
Right, let's go. Step 1: Solve 28 × 43 We use the distributive method: 28 × 43 = (20 + 8) × (40 + 3) = (20 × 40) + (20 × 3) + (8 × 40) + (8 × 3) = 800 + 60 + 320 + 24 = 1180 + 24 = 1204 The student's calculation for 28 × 43 was: 8 × 3 = 24 20 × 3 = 60 8 × 40 = 320 20 × 40 = 800 Summing these: 24 + 60 + 320 + 800 = 1204. The student's final answer for a) is 1204. Step 2: Solve 39 × 48 We use the distributive method: 39 × 48 = (30 + 9) × (40 + 8) = (30 × 40) + (30 × 8) + (9 × 40) + (9 × 8) = 1200 + 240 + 360 + 72 = 1440 + 360 + 72 = 1800 + 72 = 1872 The student's calculation for b) is: 9 × 8 = 72 30 × 8 = 240 9 × 40 = 360 30 × 40 = 1200 Summing these: 72 + 240 + 360 + 1200 = 1872. The student's final answer for b) is 1872. Step 3: Solve 46 × 57 We use the distributive method: 46 × 57 = (40 + 6) × (50 + 7) = (40 × 50) + (40 × 7) + (6 × 50) + (6 × 7) = 2000 + 280 + 300 + 42 = 2280 + 300 + 42 = 2580 + 42 = 2622 The student's calculation for c) is: 6 × 7 = 42 40 × 7 = 280 6 × 50 = 300 40 × 50 = 2000 Summing these: 42 + 280 + 300 + 2000 = 2622. The student's final answer for c) is 2622. Step 4: Solve 67 × 72 The student's given answer is 136. We use the distributive method: 67 × 72 = (60 + 7) × (70 + 2) = (60 × 70) + (60 × 2) + (7 × 70) + (7 × 2) = 4200 + 120 + 490 + 14 = 4320 + 490 + 14 = 4810 + 14 = 4824 The student's answer of 136 is ❌ Incorrect. The correct answer is 4824. Step 5: Solve 84 × 93 We use the distributive method: 84 × 93 = (80 + 4) × (90 + 3) = (80 × 90) + (80 × 3) + (4 × 90) + (4 × 3) = 7200 + 240 + 360 + 12 = 7440 + 360 + 12 = 7800 + 12 = 7812 The final answer is 7812.