Resolve the following arithmetic expressions: (12 5/12 + 1 2/3 - 3 5/6 + 2 3/4) : (2 1/2 * 2/5 - 7/9) 48 3/5 : 6 3/4 * 5/12 - 2 5/6 + 1 75/94 * (1 1/2 * 1/3 - 13 : 26)

The problem requires solving two complex arithmetic expressions involving mixed numbers, fractions, addition, subtraction, multiplication, and division.

Expression 1:

• Part 1: (12 5/12 + 1 2/3 - 3 5/6 + 2 3/4)
• Convert mixed numbers to improper fractions:
• 12 5/12 = (12*12 + 5)/12 = 149/12
• 1 2/3 = (1*3 + 2)/3 = 5/3
• 3 5/6 = (3*6 + 5)/6 = 23/6
• 2 3/4 = (2*4 + 3)/4 = 11/4
• Find a common denominator for 12, 3, 6, and 4, which is 12.
• 149/12 + (5/3)*(4/4) - (23/6)*(2/2) + (11/4)*(3/3)
• 149/12 + 20/12 - 46/12 + 33/12
• (149 + 20 - 46 + 33) / 12 = 156 / 12 = 13

• 2 1/2 = (2*2 + 1)/2 = 5/2

Expression 2:

• 48 3/5 : 6 3/4 * 5/12 - 2 5/6 + 1 75/94 * (1 1/2 * 1/3 - 13 : 26)
• Convert mixed numbers to improper fractions:
• 48 3/5 = (48*5 + 3)/5 = 243/5
• 6 3/4 = (6*4 + 3)/4 = 27/4
• 2 5/6 = (2*6 + 5)/6 = 17/6
• 1 75/94 = (1*94 + 75)/94 = 169/94
• 1 1/2 = (1*2 + 1)/2 = 3/2
• Apply order of operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
• Innermost Parentheses first: (1 1/2 * 1/3 - 13 : 26)
• (3/2) * (1/3) - 13/26
• 3/6 - 1/2
• 1/2 - 1/2 = 0

Final Answers:

• Expression 1: 117/2
• Expression 2: 1/6