3) (12 5/12 + 1 2/3 - 3 5/6 + 2 3/4) : (2 1/2 * 2/5 - 7/9)

Решение:

Давай решим этот пример по шагам:

1. Решим первую часть в скобках (целые и дробные части отдельно):
• Целые числа: The OCR result contained some inaccuracies. The correct fractions are: 12 5/12, 1 2/3, 3 5/6, 2 3/4. The calculation is: (12 5/12 + 1 2/3 - 3 5/6 + 2 3/4) : (2 1/2 * 2/5 - 7/9).
• Step 1: Simplify the first parenthesis.
• Convert mixed numbers to improper fractions:
• \[ 12 \frac{5}{12} = \frac{12 \times 12 + 5}{12} = \frac{144 + 5}{12} = \frac{149}{12} \]
• \[ 1 \frac{2}{3} = \frac{1 \times 3 + 2}{3} = \frac{5}{3} \]
• \[ 3 \frac{5}{6} = \frac{3 \times 6 + 5}{6} = \frac{18 + 5}{6} = \frac{23}{6} \]
• \[ 2 \frac{3}{4} = \frac{2 \times 4 + 3}{4} = \frac{8 + 3}{4} = \frac{11}{4} \]
• Find a common denominator for the fractions. The least common multiple of 12, 3, 6, and 4 is 12.
• \[ \frac{5}{3} = \frac{5 \times 4}{3 \times 4} = \frac{20}{12} \]
• \[ \frac{23}{6} = \frac{23 \times 2}{6 \times 2} = \frac{46}{12} \]
• \[ \frac{11}{4} = \frac{11 \times 3}{4 \times 3} = \frac{33}{12} \]
• Combine the fractions:
• \[ \frac{149}{12} + \frac{20}{12} - \frac{46}{12} + \frac{33}{12} = \frac{149 + 20 - 46 + 33}{12} \]
• \[ \frac{169 - 46 + 33}{12} = \frac{123 + 33}{12} = \frac{156}{12} \]
• Simplify the fraction:
• \[ \frac{156}{12} = 13 \]
• Step 2: Simplify the second parenthesis.
• First, perform the multiplication:
• \[ 2 \frac{1}{2} \times \frac{2}{5} \]
• Convert the mixed number to an improper fraction:
• \[ \frac{5}{2} \times \frac{2}{5} \]
• Multiply the fractions:
• \[ \frac{5 \times 2}{2 \times 5} = \frac{10}{10} = 1 \]
• Now, perform the subtraction:
• \[ 1 - \frac{7}{9} \]
• Convert 1 to a fraction with denominator 9:
• \[ \frac{9}{9} - \frac{7}{9} = \frac{9 - 7}{9} = \frac{2}{9} \]
• Step 3: Perform the division.
• \[ 13 \div \frac{2}{9} \]
• Dividing by a fraction is the same as multiplying by its reciprocal:
• \[ 13 \times \frac{9}{2} = \frac{13 \times 9}{2} = \frac{117}{2} \]
• Convert the improper fraction to a mixed number:
• \[ \frac{117}{2} = 58 \frac{1}{2} \]

Ответ:

58 1/2