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
Step 1: Find the first rational number between -2 and -3. We use the formula for the midpoint of two numbers, (1)/(2)(a+b). Let a = -2 and b = -3. x_1 = (1)/(2)(-2 + (-3)) x_1 = (1)/(2)(-2 - 3) x_1 = (1)/(2)(-5) x_1 = -(5)/(2) Step 2: Find the second rational number. Now, find a rational number between -2 and -(5)/(2). Let a = -2 and b = -(5)/(2). x_2 = (1)/(2)(-2 + (-(5)/(2))) To add these, find a common denominator: x_2 = (1)/(2)(-(4)/(2) - (5)/(2)) x_2 = (1)/(2)(-(9)/(2)) x_2 = -(9)/(4) Step 3: Find the third rational number. Now, find a rational number between -(5)/(2) and -3. Let a = -(5)/(2) and b = -3. x_3 = (1)/(2)(-(5)/(2) + (-3)) To add these, find a common denominator: x_3 = (1)/(2)(-(5)/(2) - (6)/(2)) x_3 = (1)/(2)(-(11)/(2)) x_3 = -(11)/(4) The three rational numbers between -2 and -3 are -(5)/(2), -(9)/(4), -(11)/(4). That's 2 down. 3 left today — send the next one.