Вопрос:

2) \(\frac{3\frac{1}{3}\cdot 1,9+19,5:4\frac{1}{2}}{\frac{62}{75}-\frac{4}{25}}\)

Смотреть решения всех заданий с листа

Ответ:

Let's break this down into smaller pieces!

  1. Numerator:
    • Convert mixed numbers to improper fractions:

      \[ 3\frac{1}{3} = \frac{10}{3} \quad \text{and} \quad 4\frac{1}{2} = \frac{9}{2} \]

    • Convert decimals to fractions:

      \[ 1.9 = \frac{19}{10} \quad \text{and} \quad 19.5 = \frac{195}{10} = \frac{39}{2} \]

    • Calculate the multiplication and division:

      \[ \frac{10}{3} \cdot \frac{19}{10} = \frac{19}{3} \]

      \[ \frac{39}{2} : \frac{9}{2} = \frac{39}{2} \times \frac{2}{9} = \frac{39}{9} = \frac{13}{3} \]

    • Add the results:

      \[ \frac{19}{3} + \frac{13}{3} = \frac{32}{3} \]

  2. Denominator:
    • Find a common denominator for \(\frac{62}{75}\) and \(\frac{4}{25}\). The common denominator is 75.

      \[ \frac{4}{25} = \frac{4 \times 3}{25 \times 3} = \frac{12}{75} \]

    • Subtract the fractions:

      \[ \frac{62}{75} - \frac{12}{75} = \frac{50}{75} = \frac{2}{3} \]

  3. Divide the numerator by the denominator:

    \[ \frac{32}{3} : \frac{2}{3} = \frac{32}{3} \times \frac{3}{2} = \frac{32}{2} = 16 \]

Answer: 16

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