Simplify

$1898÷[\frac{13}{4}\times (35+45)-\frac{91}{4}]$

The correct answer is 8.

To simplify the given numerical expression, we follow the order of operations (BODMAS/PEMDAS): evaluate expressions inside parentheses first, followed by operations inside square brackets, and finally complete the outer division.

The given expression is:

$1898÷[\frac{13}{4}\times (35+45)-\frac{91}{4}]$

Step 1: Simplify the term inside the inner parentheses.

Add the numbers inside $(35+45)$:

$35+45=80$

Substituting 80 back into the expression gives:

$1898÷[\frac{13}{4}\times 80-\frac{91}{4}]$

Step 2: Perform multiplication inside the brackets.

Multiply $\frac{13}{4}$ by 80:

$\frac{13}{4}\times 80=13\times 20=260$

Now the bracketed portion simplifies to:

$260-\frac{91}{4}$

Step 3: Perform subtraction inside the brackets.

Convert 260 into a fraction with a common denominator of 4:

$260=\frac{260\times 4}{4}=\frac{1040}{4}$

Subtract $\frac{91}{4}$ from $\frac{1040}{4}$:

$\frac{1040}{4}-\frac{91}{4}=\frac{1040-91}{4}=\frac{949}{4}$

Step 4: Perform the final division outside the brackets.

Divide 1898 by $\frac{949}{4}$:

$1898÷\frac{949}{4}=1898\times \frac{4}{949}$

Since 1898 divided by 949 equals 2:

$2\times 4=8$

Thus, the final simplified answer is 8.