Question

(1 4/9+2 5/6)÷(4 1/15-2 7/9)​

Answer 1

Ответ:

Пошаговое объяснение:

$(1\frac{4}{9} +2\frac{5}{6}):(4\frac{1}{15} -2\frac{7}{9} )=3 \frac{111}{348} \\\\ 1)1\frac{4}{9} +2\frac{5}{6} =\frac{13}{9} +\frac{17}{6} =\frac{78}{54} +\frac{153}{54} =\frac{231}{54} \\\\2)4\frac{1}{15} -2\frac{7}{9} =\frac{61}{15} -\frac{25}{9} =\frac{183}{45} -\frac{125}{45} =\frac{58}{45} \\\\3)\frac{231}{54} :\frac{58}{45} =\frac{231}{54} *\frac{45}{58}=\frac{1155}{348} =3\frac{111}{348}$

Answer 2

To solve this arithmetic expression, let's break it down step by step:

1. Convert mixed numbers to improper fractions:

   • $1 \frac{4}{9} = \frac{9}{9} + \frac{4}{9} = \frac{13}{9}$
   • $2 \frac{5}{6} = \frac{12}{6} + \frac{5}{6} = \frac{17}{6}$
   • $4 \frac{1}{15} = \frac{60}{15} + \frac{1}{15} = \frac{61}{15}$
   • $2 \frac{7}{9} = \frac{18}{9} + \frac{7}{9} = \frac{25}{9}$

2. Now the expression becomes: $\frac{\frac{13}{9} + \frac{17}{6}}{\frac{61}{15} - \frac{25}{9}}$

3. Perform the additions and subtractions within the numerator and denominator:

   • Numerator: $\frac{13}{9} + \frac{17}{6} = \frac{13 \cdot 6}{9 \cdot 6} + \frac{17 \cdot 9}{6 \cdot 9} = \frac{78}{54} + \frac{153}{54} = \frac{231}{54}$
   • Denominator: $\frac{61}{15} - \frac{25}{9} = \frac{61 \cdot 9}{15 \cdot 9} - \frac{25 \cdot 15}{9 \cdot 15} = \frac{549}{135} - \frac{375}{135} = \frac{174}{135}$

4. Simplify the fractions:

   • Numerator: $\frac{231}{54} = \frac{77}{18}$
   • Denominator: $\frac{174}{135} = \frac{58}{45}$

5. Finally, divide the two fractions: $\frac{\frac{77}{18}}{\frac{58}{45}}$

6. To divide fractions, multiply the first fraction by the reciprocal of the second fraction: $\frac{77}{18} \cdot \frac{45}{58} = \frac{77 \cdot 45}{18 \cdot 58}$

7. Calculate the final result: $\frac{3465}{1044} = \frac{1155}{348}$

So, $\left(1 \frac{4}{9} + 2 \frac{5}{6}\right) \div \left(4 \frac{1}{15} - 2 \frac{7}{9}\right) = \frac{1155}{348}$