![Use the associative property to calculate the following: a) [(-6) + (4 + 2)] b) [3 + 7 + (-5)] c) [(6 + 4) + (-2)] d) [(-3) + 7 + 5]](/_next/image?url=https%3A%2F%2Fohijasnjvprzodcmxltt.supabase.co%2Fstorage%2Fv1%2Fobject%2Fpublic%2Fwhatsapp-images%2F1777865879007-26c8e3412ed6808f.png&w=3840&q=75)
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 work through these problems using the associative property. 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 calculations: 1. Use the associative property to calculate the following. a) [(-6) + (4 + 2)] Step 1: Apply the associative property. ((-6) + 4) + 2 = (-6) + (4 + 2) Step 2: Calculate the Left Hand Side (LHS). ((-6) + 4) + 2 = (-2) + 2 = 0 Step 3: Calculate the Right Hand Side (RHS). (-6) + (4 + 2) = (-6) + 6 = 0 Step 4: Verify the equality. 0 = 0 The final value is 0. b) [3 + 7 + (-5)] Step 1: Apply the associative property. (3 + 7) + (-5) = 3 + (7 + (-5)) Step 2: Calculate the LHS. (3 + 7) + (-5) = 10 + (-5) = 5 Step 3: Calculate the RHS. 3 + (7 + (-5)) = 3 + 2 = 5 Step 4: Verify the equality. 5 = 5 The final value is 5. c) [(6 + 4) + (-2)] Step 1: Apply the associative property. (6 + 4) + (-2) = 6 + (4 + (-2)) Step 2: Calculate the LHS. (6 + 4) + (-2) = 10 + (-2) = 8 Step 3: Calculate the RHS. 6 + (4 + (-2)) = 6 + 2 = 8 Step 4: Verify the equality. 8 = 8 The final value is 8. d) [(-3) + 7 + 5] Step 1: Apply the associative property. ((-3) + 7) + 5 = (-3) + (7 + 5) Step 2: Calculate the LHS. ((-3) + 7) + 5 = 4 + 5 = 9 Step 3: Calculate the RHS. (-3) + (7 + 5) = (-3) + 12 = 9 Step 4: Verify the equality. 9 = 9 The final value is 9. e) [(-4) + (6 + 2)] Step 1: Apply the associative property. ((-4) + 6) + 2 = (-4) + (6 + 2) Step 2: Calculate the LHS. ((-4) + 6) + 2 = 2 + 2 = 4 Step 3: Calculate the RHS. (-4) + (6 + 2) = (-4) + 8 = 4 Step 4: Verify the equality. 4 = 4 The final value is 4. f) [3 + (-7) + 5] Step 1: Apply the associative property. (3 + (-7)) + 5 = 3 + ((-7) + 5) Step 2: Calculate the LHS. (3 + (-7)) + 5 = (-4) + 5 = 1 Step 3: Calculate the RHS. 3 + ((-7) + 5) = 3 + (-2) = 1 Step 4: Verify the equality. 1 = 1 The final value is 1. g) [(-9) + (3 + 11)] Step 1: Apply the associative property. ((-9) + 3) + 11 = (-9) + (3 + 11) Step 2: Calculate the LHS. ((-9) + 3) + 11 = (-6) + 11 = 5 Step 3: Calculate the RHS. (-9) + (3 + 11) = (-9) + 14 = 5 Step 4: Verify the equality. 5 = 5 The final value is 5. h) [(12 + 13) + (-10)] Step 1: Apply the associative property. (12 + 13) + (-10) = 12 + (13 + (-10)) Step 2: Calculate the LHS. (12 + 13) + (-10) = 25 + (-10) = 15 Step 3: Calculate the RHS. 12 + (13 + (-10)) = 12 + 3 = 15 Step 4: Verify the equality. 15 = 15 The final value is 15. i) [(-3) + (9 + 11)] Step 1: Apply the associative property. ((-3) + 9) + 11 = (-3) + (9 + 11) Step 2: Calculate the LHS. ((-3) + 9) + 11 = 6 + 11 = 17 Step 3: Calculate the RHS. (-3) + (9 + 11) = (-3) + 20 = 17 Step 4: Verify the equality. 17 = 17 The final value is 17. j) [(-12) + (13 + 10)] Step 1: Apply the associative property. ((-12) + 13) + 10 = (-12) + (13 + 10) Step 2: Calculate the LHS. ((-12) + 13) + 10 = 1 + 10 = 11 Step 3: Calculate the RHS. (-12) + (13 + 10) = (-12) + 23 = 11 Step 4: Verify the equality. 11 = 11 The final value is 11. That's 2 down. 3 left today — send the next one.