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: Write out the given expression. The expression is: (4 × 6 × 10 × 14) ( (1)/(4) + (1)/(6) + (1)/(10) + (1)/(14) ) Step 2: Distribute the product (4 × 6 × 10 × 14) to each term inside the parenthesis. Let P = 4 × 6 × 10 × 14. The expression becomes: P × (1)/(4) + P × (1)/(6) + P × (1)/(10) + P × (1)/(14) Substitute P back into each term: (4 × 6 × 10 × 14) × (1)/(4) + (4 × 6 × 10 × 14) × (1)/(6) + (4 × 6 × 10 × 14) × (1)/(10) + (4 × 6 × 10 × 14) × (1)/(14) Step 3: Simplify each term by canceling out common factors. Term 1: (4 × 6 × 10 × 14)/(4) = 6 × 10 × 14 Term 2: (4 × 6 × 10 × 14)/(6) = 4 × 10 × 14 Term 3: (4 × 6 × 10 × 14)/(10) = 4 × 6 × 14 Term 4: (4 × 6 × 10 × 14)/(14) = 4 × 6 × 10 Step 4: Calculate the value of each simplified term. Term 1: 6 × 10 × 14 = 60 × 14 = 840 Term 2: 4 × 10 × 14 = 40 × 14 = 560 Term 3: 4 × 6 × 14 = 24 × 14 = 336 Term 4: 4 × 6 × 10 = 24 × 10 = 240 Step 5: Sum the values of all terms. 840 + 560 + 336 + 240 = 1,976 The final answer is 1,976. 3 done, 2 left today. You're making progress.