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
To arrange fractions in ascending order, we need to compare their values. We can do this by finding a common denominator for all fractions or by converting them to decimals. Using a common denominator ensures precision. Step 1: Identify the given fractions. The fractions are (2)/(3), (5)/(7), (5)/(8), (6)/(21). Step 2: Find the least common multiple (LCM) of the denominators. The denominators are 3, 7, 8, and 21. Notice that 21 = 3 × 7. So, the LCM of (3, 7, 8, 21) is the LCM of (3, 7, 8). LCM(3, 7, 8) = 3 × 7 × 8 = 21 × 8 = 168. The common denominator is 168. Step 3: Convert each fraction to an equivalent fraction with the common denominator of 168. For (2)/(3): Multiply numerator and denominator by (168)/(3) = 56. (2)/(3) = (2 × 56)/(3 × 56) = (112)/(168) For (5)/(7): Multiply numerator and denominator by (168)/(7) = 24. (5)/(7) = (5 × 24)/(7 × 24) = (120)/(168) For (5)/(8): Multiply numerator and denominator by (168)/(8) = 21. (5)/(8) = (5 × 21)/(8 × 21) = (105)/(168) For (6)/(21): Multiply numerator and denominator by (168)/(21) = 8. (6)/(21) = (6 × 8)/(21 × 8) = (48)/(168) Step 4: Compare the numerators of the equivalent fractions. The equivalent fractions are (112)/(168), (120)/(168), (105)/(168), (48)/(168). Arranging the numerators in ascending order: 48, 105, 112, 120. Step 5: Write the original fractions in ascending order. Corresponding to the ordered numerators, the fractions in ascending order are: (48)/(168) = (6)/(21) (105)/(168) = (5)/(8) (112)/(168) = (2)/(3) (120)/(168) = (5)/(7) The fractions in ascending order are: (6)/(21), (5)/(8), (2)/(3), (5)/(7) What's next?