is equal to

Concept: When several mixed numbers share the same fractional part, split every term into its whole-number part and its fractional part. Add the whole-number parts together, add the fractional parts together, and then combine the two subtotals. This separation avoids repeatedly realigning mixed numbers and reduces arithmetic slips.

1. Separate each mixed number into its whole-number part and its fractional part: the whole-number parts are 1, 11, 111, and 1111, and each fractional part is 1/2.

2. Add the whole-number parts: 1 + 11 + 111 + 1111 = 1234.

3. Add the fractional parts: 1/2 + 1/2 + 1/2 + 1/2 = 4 x (1/2) = 2.

4. Combine the two subtotals: 1234 + 2 = 1236.

Cross-check by adding the terms sequentially as decimals: 1.5 + 11.5 = 13; 13 + 111.5 = 124.5; 124.5 + 1111.5 = 1236 -- the same result confirms the total.