Simplify $20÷5\mathrm{ of}\mathrm{ 4}\times 8+6÷\mathrm{24 }\mathrm{of}\mathrm{ 3}\times 48-6÷18\times 9.$

The correct answer is 9.

To simplify the given expression, we follow the BODMAS rule (Brackets, Orders/'of', Division, Multiplication, Addition, Subtraction). According to this rule, the 'of' operation takes priority over regular division and multiplication.

The given expression is:

$20÷5 \mathrm{of} 4\times 8+6÷24 \mathrm{of} 3\times 48-6÷18\times 9$

Step 1: Simplify the 'of' operations first.

• First 'of' term:
$5 \mathrm{of} 4=5\times 4=20$
• Second 'of' term:
$24 \mathrm{of} 3=24\times 3=72$

Substituting these values into the expression gives:

$20÷20\times 8+6÷72\times 48-6÷18\times 9$

Step 2: Simplify each term using division and multiplication from left to right.

• First term:
$20÷20\times 8=1\times 8=8$

• Second term:
$6÷72\times 48=\frac{6}{72}\times 48=\frac{1}{12}\times 48=4$

• Third term:
$6÷18\times 9=\frac{6}{18}\times 9=\frac{1}{3}\times 9=3$

Step 3: Perform addition and subtraction.

Combine the results from each part:

$8+4-3=12-3=9$

Thus, the simplified result of the expression is 9.