8/9 + 3/7 + 2/3 + ? = 158/63

Concept

To find an unknown addend in a sum of fractions, isolate it: ? = (target total) - (sum of the known fractions). Adding or subtracting fractions requires a common denominator, the least common multiple (LCM) of all the denominators; convert each fraction to that denominator, then add or subtract the numerators.

Application

Denominators are 9, 7, 3 and 63. Their LCM is 63 (since 63 = 9 x 7 and 3 divides 63).

1. Convert each known fraction to /63: 8/9 = 56/63, 3/7 = 27/63, 2/3 = 42/63.

2. Add the known fractions: 56/63 + 27/63 + 42/63 = 125/63.

3. Isolate the unknown: ? = 158/63 - 125/63 = 33/63.

4. Reduce 33/63 by dividing numerator and denominator by their GCD, 3: 33/63 = 11/21.

So ? = 11/21.

Cross-check

Add everything back at denominator 63: 56/63 + 27/63 + 42/63 + 33/63 = 158/63, which matches the target total. Confirmed.