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 are the solutions to the modular arithmetic problems: 2. -31 + 31 + 4 ±od 9 Step 1: Simplify the expression. -31 + 31 + 4 = 4 Step 2: Find the remainder when 4 is divided by 9. Since 4 < 9, the remainder is 4. -31 + 31 + 4 4 ±od 9 The final answer is 4. 3. 12 - 14 ±od 6 Step 1: Simplify the expression. 12 - 14 = -2 Step 2: Find the remainder when -2 is divided by 6. To get a positive remainder, add the modulus until the number is non-negative. -2 + 6 = 4 12 - 14 4 ±od 6 The final answer is 4. 4. 99 ±od 5 - 34 ±od 5 Step 1: Find 99 ±od 5. 99 = 19 × 5 + 4 So, 99 4 ±od 5. Step 2: Find 34 ±od 5. 34 = 6 × 5 + 4 So, 34 4 ±od 5. Step 3: Substitute the remainders and perform the subtraction. 99 ±od 5 - 34 ±od 5 4 - 4 ±od 5 4 - 4 = 0 Step 4: Find the remainder when 0 is divided by 5. 0 0 ±od 5 The final answer is 0. 5. 12 × 12 ±od 5 Step 1: Find 12 ±od 5. 12 = 2 × 5 + 2 So, 12 2 ±od 5. Step 2: Substitute the remainder into the expression and multiply. 12 × 12 ±od 5 2 × 2 ±od 5 2 × 2 = 4 Step 3: Find the remainder when 4 is divided by 5. Since 4 < 5, the remainder is 4. 12 × 12 4 ±od 5 The final answer is 4. Send me the next one 📸