Determine the Sign in (6²-3+5):16 + Complex Expression Comparison

We'll simplify each expression separately using the order of operations:

Expression 1: $\frac{1}{4} \times ((6^2 - 3 + 5) : 16 + (4 + 2) : 3)$

• Calculate the exponent: $6^2 = 36$.

• Inside the parentheses: $36 - 3 + 5 = 38$.

• Division: $38 : 16 \approx 2.375$.

• Second division: $(4 + 2) : 3 = 6 : 3 = 2$.

• Add the results of division: $2.375 + 2 = 4.375$.

• Multiply by $\frac{1}{4}$: $\frac{1}{4} \times 4.375 = 1.09375$.

After simplification, the value of the first expression is approximately $1.09375$.

Expression 2: $(98 + 5 - 3) : 10 + 5 - 15$

• Inside the parentheses: $98 + 5 - 3 = 100$.

• Division: $100 : 10 = 10$.

• Add and subtract remaining terms: $10 + 5 - 15 = 0$.

After simplification, the value of the second expression is $0$.

Comparing the final values, we have approximately $1.09375$ (from Expression 1) and $0$ (from Expression 2). Since these two are not equal, the correct relation between the expressions is $\ne$.

Therefore, the solution to the problem is $\ne$.