Simplify

$[3\frac{2}{5}\times \{2\frac{3}{4}+3.3(5\frac{1}{3}+3\frac{1}{3}-2\frac{1}{3})\left\}\right]$

The correct answer is 80.41.

We need to simplify the expression following the BODMAS rule — working from the innermost brackets outward: ( ) first, then { }, then [ ].

The full expression is:

$[3\frac{2}{5}\times \{2\frac{3}{4}+3.3(5\frac{1}{3}+3\frac{1}{3}-2\frac{1}{3})\left\}\right]$

Step 1: Convert all mixed numbers to improper fractions (or decimals).

$3\frac{2}{5}=\frac{17}{5}=3.4$

$2\frac{3}{4}=\frac{11}{4}=2.75$

$5\frac{1}{3}=\frac{16}{3},3\frac{1}{3}=\frac{10}{3},2\frac{1}{3}=\frac{7}{3}$

Step 2: Solve the innermost ( ) bracket.

$\frac{16}{3}+\frac{10}{3}-\frac{7}{3}=\frac{16+10-7}{3}=\frac{19}{3}$

Step 3: Multiply 3.3 by the result of Step 2.

$3.3\times \frac{19}{3}=\frac{33}{10}\times \frac{19}{3}=\frac{33\times 19}{10\times 3}=\frac{627}{30}=20.9$

Step 4: Solve the { } curly bracket.

$2.75+20.9=23.65$

Step 5: Solve the [ ] square bracket — multiply 3.4 by 23.65.

$3.4\times 23.65=(3\times 23.65)+(0.4\times 23.65)=70.95+9.46=80.41$

Therefore, the simplified value of the given expression is 80.41.