Determine three fractions from sum and comparative conditions (set 2): The sum of three fractions is 2 11/24. The greatest divided by the smallest equals 7/6, and this quotient exceeds the middle fraction by 1/3. Find the three fractions.

Question

Solve this multiple-choice question and choose the correct option.

Accepted Answer

Introduction / Context:This is a restatement of the prior problem with the same conditions and numbers. We again use two comparative constraints along with a total-sum requirement to fix the three unknown fractions uniquely. The method mirrors proportional reasoning and sum balancing. Given Data / Assumptions: Total sum = 2 11/24 = 59/24. (Greatest)/(Smallest) = 7/6. Middle = 7/6 − 1/3 = 5/6. Concept / Approach:Let smallest = x, greatest = (7/6)x, middle = 5/6. Solve x from the sum equation, then compute the other two fractions, and verify all constraints, including the quotient and the additive total. Step-by-Step Solution: x + (7/6)x + 5/6 = 59/24 ⇒ (13/6)x = 59/24 − 5/6.Compute RHS: 59/24 − 20/24 = 39/24 = 13/8.Thus (13/6)x = 13/8 ⇒ x = (13/8)*(6/13) = 6/8 = 3/4.Greatest = (7/6)*(3/4) = 7/8; middle = 5/6. Verification / Alternative check: Sum: 7/8 + 5/6 + 3/4 = 59/24; quotient 7/6; and 7/6 − 1/3 = 5/6 as required. Why Other Options Are Wrong: All other sets fail either the exact sum or the exact quotient/middle relationship. Common Pitfalls: Miscalculating the mixed fraction 2 11/24. Confusing the phrase “greater by 1/3” and applying it to the wrong quantity. Final Answer: 7/8, 5/6, 3/4

Determine three fractions from sum and comparative conditions (set 2): The sum of three fractions is 2 11/24. The greatest divided by the smallest equals 7/6, and this quotient exceeds the middle fraction by 1/3. Find the three fractions.

More Questions from Decimal Fraction

Discussion & Comments