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 — To arrange these mixed numbers in ascending order, we first compare their whole number parts. Since all the whole number parts are 4, we need to compare their fractional parts. Step 1: Identify the fractional parts of the mixed numbers. The mixed numbers are 4(2)/(3), 4(1)/(2), 4(3)/(5). The fractional parts are (2)/(3), (1)/(2), (3)/(5). Step 2: Find the least common multiple (LCM) of the denominators of the fractional parts. The denominators are 3, 2, and 5. The LCM of 3, 2, and 5 is 3 × 2 × 5 = 30. Step 3: Convert each fractional part to an equivalent fraction with the common denominator of 30. For (2)/(3): (2)/(3) = (2 × 10)/(3 × 10) = (20)/(30) For (1)/(2): (1)/(2) = (1 × 15)/(2 × 15) = (15)/(30) For (3)/(5): (3)/(5) = (3 × 6)/(5 × 6) = (18)/(30) Step 4: Compare the numerators of the equivalent fractional parts. The equivalent fractional parts are (20)/(30), (15)/(30), (18)/(30). Arranging the numerators in ascending order: 15, 18, 20. Step 5: Write the original mixed numbers in ascending order based on their fractional parts. The order of the fractional parts from smallest to largest is (15)/(30), (18)/(30), (20)/(30). This corresponds to the original fractions: 4(1)/(2) (since (1)/(2) = (15)/(30)) 4(3)/(5) (since (3)/(5) = (18)/(30)) 4(2)/(3) (since (2)/(3) = (20)/(30)) The fractions in ascending order are: 4(1)/(2), 4(3)/(5), 4(2)/(3) Drop the next question.