Simplify Fraction Calculation

The problem requires simplifying the following expression using the order of operations (PEMDAS/BODMAS):

$ \frac{(120 - 12) \div (24 \div 2) - 12 + 7}{5 \times 12 \div 10 - (6 \times 4) \div 12} $

Numerator Calculation

First, simplify the numerator: $(120 - 12) \div (24 \div 2) - 12 + 7$.

1. Calculate expressions within parentheses:
   • $120 - 12 = 108$
   • $24 \div 2 = 12$
2. Substitute the results back into the numerator expression: $108 \div 12 - 12 + 7$.
3. Perform the division: $108 \div 12 = 9$.
4. The expression becomes: $9 - 12 + 7$.
5. Perform subtraction and addition from left to right:
   • $9 - 12 = -3$
   • $-3 + 7 = 4$

The simplified numerator is 4.

Denominator Calculation

Next, simplify the denominator: $5 \times 12 \div 10 - (6 \times 4) \div 12$.

1. Calculate expressions within parentheses:
   • $6 \times 4 = 24$
2. Perform multiplications and divisions from left to right:
   • $5 \times 12 = 60$
   • $60 \div 10 = 6$
   • $24 \div 12 = 2$
3. Substitute the results back into the denominator expression: $6 - 2$.
4. Perform the subtraction: $6 - 2 = 4$.

The simplified denominator is 4.

Final Simplification

Combine the simplified numerator and denominator:

$ \frac{\text{Numerator}}{\text{Denominator}} = \frac{4}{4} $

Perform the final division:

$ \frac{4}{4} = 1 $

The simplified value of the expression is 1.