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
Okay, Christina, let's continue with these problems, applying the associative property of addition. The associative property of addition states that for any three numbers a, b, and c, the way in which the numbers are grouped does not affect the sum: (a + b) + c = a + (b + c). Here are the solutions: a) If: a = 4, b = -5, c = 3 Equation: (a + b) + c = a + (b + c) Step 1: Substitute the values into the equation. (4 + (-5)) + 3 = 4 + ((-5) + 3) Step 2: Calculate the Left Hand Side (LHS). (4 - 5) + 3 = (-1) + 3 = 2 Step 3: Calculate the Right Hand Side (RHS). 4 + (-5 + 3) = 4 + (-2) = 2 Step 4: Verify the equality. 2 = 2 The final value is 2. b) If: a = 2, b = 9, c = -4 Equation: (a + b) + c = a + (b + c) Step 1: Substitute the values into the equation. (2 + 9) + (-4) = 2 + (9 + (-4)) Step 2: Calculate the LHS. (11) + (-4) = 11 - 4 = 7 Step 3: Calculate the RHS. 2 + (9 - 4) = 2 + 5 = 7 Step 4: Verify the equality. 7 = 7 The final value is 7. c) If: a = -8, b = 1, c = 2 Equation: a + (b + c) = (a + b) + c Step 1: Substitute the values into the equation. (-8) + (1 + 2) = ((-8) + 1) + 2 Step 2: Calculate the LHS. (-8) + (3) = -8 + 3 = -5 Step 3: Calculate the RHS. (-7) + 2 = -5 Step 4: Verify the equality. -5 = -5 The final value is -5. d) If: a = -2, b = 11, c = 12 Equation: a + (b + c) = (a + b) + c Step 1: Substitute the values into the equation. (-2) + (11 + 12) = ((-2) + 11) + 12 Step 2: Calculate the LHS. (-2) + (23) = -2 + 23 = 21 Step 3: Calculate the RHS. (9) + 12 = 21 Step 4: Verify the equality. 21 = 21 The final value is 21. 3 done, 2 left today. You're making progress.