The sum of the largest and smallest fractions among 6/7, 2 3/5, 3/8 and 2 8/15…

Concept: To compare fractions that have different denominators, convert each one to a decimal (or a common denominator) so their sizes can be judged directly; the value asked for here is simply (largest fraction) + (smallest fraction).

Application: Compare all four given fractions as decimals, then add the two extreme values.

1. Convert every mixed number to an improper fraction: 2 3/5 = 13/5 and 2 8/15 = 38/15. The other two values, 6/7 and 3/8, are already single fractions.

2. Express each of the four fractions as a decimal so their sizes can be compared: 6/7 ≈ 0.857, 13/5 = 2.6, 3/8 = 0.375, and 38/15 ≈ 2.533.

3. Reading off these decimals, 13/5 (2.6) is the largest of the four values and 3/8 (0.375) is the smallest.

4. Add the largest and smallest fractions over their LCM denominator, 40: 13/5 = 104/40 and 3/8 = 15/40, so the sum is 104/40 + 15/40 = 119/40.

5. Write 119/40 as a mixed number: 119 ÷ 40 = 2, remainder 39, so 119/40 = 2 39/40.

Cross-check: Adding the same two values as decimals gives 2.6 + 0.375 = 2.975, and 2 39/40 = 2 + 39/40 = 2 + 0.975 = 2.975 — the two methods agree, confirming the total.