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's how to show the associative property for addition holds for integers: *a) If a=4, b=-5, c=3 The associative property is (a+b)+c = a+(b+c). Left side: (a+b)+c Step 1: Substitute the values into the expression. (4 + (-5)) + 3 Step 2: Perform the addition inside the parenthesis. (-1) + 3 Step 3: Perform the final addition. 2 Right side: a+(b+c) Step 1: Substitute the values into the expression. 4 + ((-5) + 3) Step 2: Perform the addition inside the parenthesis. 4 + (-2) Step 3: Perform the final addition. 2 Since 2 = 2, the property holds. *b) If a=2, b=9, c=-4 The associative property is (a+b)+c = a+(b+c). Left side: (a+b)+c Step 1: Substitute the values into the expression. (2 + 9) + (-4) Step 2: Perform the addition inside the parenthesis. 11 + (-4) Step 3: Perform the final addition. 7 Right side: a+(b+c) Step 1: Substitute the values into the expression. 2 + (9 + (-4)) Step 2: Perform the addition inside the parenthesis. 2 + 5 Step 3: Perform the final addition. 7 Since 7 = 7, the property holds. *c) If a=-8, b=1, c=2 The associative property is a+(b+c) = (a+b)+c. Left side: a+(b+c) Step 1: Substitute the values into the expression. (-8) + (1 + 2) Step 2: Perform the addition inside the parenthesis. (-8) + 3 Step 3: Perform the final addition. -5 Right side: (a+b)+c Step 1: Substitute the values into the expression. ((-8) + 1) + 2 Step 2: Perform the addition inside the parenthesis. (-7) + 2 Step 3: Perform the final addition. -5 Since -5 = -5, the property holds. *d) If a=-2, b=11, c=12 The associative property is a+(b+c) = (a+b)+c. Left side: a+(b+c) Step 1: Substitute the values into the expression. (-2) + (11 + 12) Step 2: Perform the addition inside the parenthesis. (-2) + 23 Step 3: Perform the final addition. 21 Right side: (a+b)+c Step 1: Substitute the values into the expression. ((-2) + 11) + 12 Step 2: Perform the addition inside the parenthesis. 9 + 12 Step 3: Perform the final addition. 21 Since 21 = 21, the property holds. That's 2 down. 3 left today — send the next one.