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 are the comparisons for the given fractions: Step 1: Compare (3)/(4) and (4)/(5). To compare these fractions, find a common denominator, which is 20. (3)/(4) = (3 × 5)/(4 × 5) = (15)/(20) (4)/(5) = (4 × 4)/(5 × 4) = (16)/(20) Since 15 < 16, we have (15)/(20) < (16)/(20). Therefore, (3)/(4) < (4)/(5). Step 2: Compare (2)/(5) and (1)/(4). To compare these fractions, find a common denominator, which is 20. (2)/(5) = (2 × 4)/(5 × 4) = (8)/(20) (1)/(4) = (1 × 5)/(4 × 5) = (5)/(20) Since 8 > 5, we have (8)/(20) > (5)/(20). Therefore, (2)/(5) > (1)/(4). Step 3: Compare (1)/(2) and (4)/(8). Simplify the fraction (4)/(8). (4)/(8) = (4 ÷ 4)/(8 ÷ 4) = (1)/(2) Since both fractions are equal to (1)/(2). Therefore, (1)/(2) = (4)/(8). Step 4: Compare (2)/(3) and (4)/(6). Simplify the fraction (4)/(6). (4)/(6) = (4 ÷ 2)/(6 ÷ 2) = (2)/(3) Since both fractions are equal to (2)/(3). Therefore, (2)/(3) = (4)/(6). Step 5: Compare (3)/(4) and (2)/(3). To compare these fractions, find a common denominator, which is 12. (3)/(4) = (3 × 3)/(4 × 3) = (9)/(12) (2)/(3) = (2 × 4)/(3 × 4) = (8)/(12) Since 9 > 8, we have (9)/(12) > (8)/(12). Therefore, (3)/(4) > (2)/(3). Here are the final answers: (3)/(4) < (4)/(5) (2)/(5) > (1)/(4) (1)/(2) = (4)/(8) (2)/(3) = (4)/(6) (3)/(4) > (2)/(3) Send me the next one 📸