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
Fresh day alishabayambumagar, let's solve. To find the digit in the blank space such that the number is divisible by 11, we use the divisibility rule for 11: a number is divisible by 11 if the alternating sum of its digits (starting from the rightmost digit) is divisible by 11. a) 27.......3 Let the missing digit be x. The number is 27x3. Step 1: Calculate the alternating sum of the digits. 3 - x + 7 - 2 = 8 - x Step 2: For the number to be divisible by 11, the alternating sum must be a multiple of 11 (e.g., 0, 11, -11, etc.). Since x is a single digit (0-9), the only multiple of 11 possible for 8-x is 0. 8 - x = 0 x = 8 The number is 2783. 8 b) 1....... 574 Let the missing digit be x. The number is 1x574. Step 1: Calculate the alternating sum of the digits. 4 - 7 + 5 - x + 1 = 3 - x Step 2: For the number to be divisible by 11, the alternating sum must be a multiple of 11. Since x is a single digit (0-9), the only multiple of 11 possible for 3-x is 0. 3 - x = 0 x = 3 The number is 13574. 3 c) 939....... Let the missing digit be x. The number is 939x. Step 1: Calculate the alternating sum of the digits. x - 9 + 3 - 9 = x - 15 Step 2: For the number to be divisible by 11, the alternating sum must be a multiple of 11. Since x is a single digit (0-9), the only multiple of 11 possible for x-15 is -11. x - 15 = -11 x = 15 - 11 x = 4 The number is 9394. 4 d) 10....... 5 Let the missing digit be x. The number is 10x5. Step 1: Calculate the alternating sum of the digits. 5 - x + 0 - 1 = 4 - x Step 2: For the number to be divisible by 11, the alternating sum must be a multiple of 11. Since x is a single digit (0-9), the only multiple of 11 possible for 4-x is 0. 4 - x = 0 x = 4 The number is 1045. 4 Send me the next one 📸