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
You're on a roll — Here are the solutions for Question 13: Given the condition: a > b. We will assume a and b are positive numbers, which is standard for these types of problems. 1. (1)/(a) vs (1)/(b) Step 1: Consider the given inequality a > b. Step 2: When taking the reciprocal of two positive numbers, the inequality sign reverses. For example, if a=5 and b=2, then 5 > 2. Taking reciprocals: (1)/(5) = 0.2 and (1)/(2) = 0.5. Since 0.2 < 0.5, we have (1)/(a) < (1)/(b). The sign to fill in the box is <. 2. (a)/(b) vs (b)/(a) Step 1: Consider the given inequality a > b. Step 2: Since a > b and assuming a, b are positive: Divide both sides of a > b by b (which is positive, so the inequality direction doesn't change): (a)/(b) > (b)/(b) (a)/(b) > 1 Step 3: Divide both sides of a > b by a (which is positive, so the inequality direction doesn't change): (a)/(a) > (b)/(a) 1 > (b)/(a) Step 4: Combine the results from Step 2 and Step 3. We have (a)/(b) > 1 and 1 > (b)/(a). This implies (a)/(b) > (b)/(a). For example, if a=5 and b=2, then (a)/(b) = (5)/(2) = 2.5 and (b)/(a) = (2)/(5) = 0.4. Since 2.5 > 0.4, we have (a)/(b) > (b)/(a). The sign to fill in the box is >. One more to go today! Send it over.