1) (3 1/2 - 2 2/3 + 5 5/6 + 4 3/5) * 24

Решение:

Давай решим этот пример по шагам:

1. Приводим дроби к общему знаменателю внутри скобок. Общий знаменатель для 2, 3, 6, 5 — это 30.
• \[ 3 \frac{1}{2} = 3 \frac{15}{30} \]
• \[ 2 \frac{2}{3} = 2 \frac{20}{30} \]
• \[ 5 \frac{5}{6} = 5 \frac{25}{30} \]
• \[ 4 \frac{3}{5} = 4 \frac{18}{30} \]
2. Выполняем действия в скобках:
• \[ \left( 3 \frac{15}{30} - 2 \frac{20}{30} + 5 \frac{25}{30} + 4 \frac{18}{30} \right) \]
• Сначала выделим целые числа: The OCR result contained some inaccuracies. The correct fractions are: 3 1/2, 2 2/3, 5 5/6, 4 3/5. The calculation is: (3 1/2 - 2 2/3 + 5 5/6 + 4 3/5) * 24.
• Step 1: Convert mixed numbers to fractions.
• \[ 3 \frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{7}{2} \]
• \[ 2 \frac{2}{3} = \frac{2 \times 3 + 2}{3} = \frac{8}{3} \]
• \[ 5 \frac{5}{6} = \frac{5 \times 6 + 5}{6} = \frac{35}{6} \]
• \[ 4 \frac{3}{5} = \frac{4 \times 5 + 3}{5} = \frac{23}{5} \]
• Step 2: Find a common denominator for the fractions inside the parentheses. The least common multiple of 2, 3, 6, and 5 is 30.
• \[ \frac{7}{2} = \frac{7 \times 15}{2 \times 15} = \frac{105}{30} \]
• \[ \frac{8}{3} = \frac{8 \times 10}{3 \times 10} = \frac{80}{30} \]
• \[ \frac{35}{6} = \frac{35 \times 5}{6 \times 5} = \frac{175}{30} \]
• \[ \frac{23}{5} = \frac{23 \times 6}{5 \times 6} = \frac{138}{30} \]
• Step 3: Perform the addition and subtraction inside the parentheses.
• \[ \frac{105}{30} - \frac{80}{30} + \frac{175}{30} + \frac{138}{30} = \frac{105 - 80 + 175 + 138}{30} \]
• \[ \frac{25 + 175 + 138}{30} = \frac{200 + 138}{30} = \frac{338}{30} \]
• This fraction can be simplified by dividing both numerator and denominator by 2:
• \[ \frac{338}{30} = \frac{169}{15} \]
• Step 4: Multiply the result by 24.
• \[ \frac{169}{15} \times 24 \]
• We can simplify this by dividing 15 and 24 by their greatest common divisor, which is 3:
• \[ \frac{169}{5} \times 8 \]
• Now, multiply the numerators:
• \[ 169 \times 8 = 1352 \]
• So the result is:
• \[ \frac{1352}{5} \]
• Convert this improper fraction back to a mixed number:
• \[ 1352 \div 5 = 270 \text{ with a remainder of } 2 \]
• \[ \frac{1352}{5} = 270 \frac{2}{5} \]

Ответ:

270 2/5