What is the value of (13.8 × 1.9 ÷ 5.7 + 11.2 of 1/16 − 1/20)?

Simplification problems with mixed operators (×, ÷, 'of', +, −) are solved using the order of operations (BODMAS/VBODMAS): brackets first, then 'of' (treated as a fraction multiplication), then division and multiplication left to right, and finally addition and subtraction left to right. Each term in the expression must be reduced to a decimal independently before combining.

1. Evaluate the multiplication-division term: 13.8 × 1.9 = 26.22, then 26.22 ÷ 5.7 = 4.6.

2. Evaluate the 'of' term: 11.2 of 1/16 means 11.2 × 1/16 = 0.7.

3. Evaluate the closing fraction: 1/20 = 0.05.

4. Combine left to right following the sign of each term: 4.6 + 0.7 − 0.05 = 5.25.

As an independent check, notice 1.9 ÷ 5.7 simplifies exactly to 1/3, so 13.8 × 1.9 ÷ 5.7 = 13.8 × 1/3 = 4.6 — the same result reached via direct division, confirming the first step.

So the value of the expression is 5.25.