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МатематикаВопрос:
\frac{19}{36} - \frac{5}{8} : \left(5 - 2\frac{3}{16}\right) + \frac{1}{12}
Ответ:
\begin{enumerate}- Convert the mixed number to an improper fraction: $$2\frac{3}{16} = \frac{2 \times 16 + 3}{16} = \frac{35}{16}$$.
- Perform the subtraction inside the parentheses: $$5 - \frac{35}{16} = \frac{5 \times 16 - 35}{16} = \frac{80 - 35}{16} = \frac{45}{16}$$.
- Perform the division: $$\frac{5}{8} : \frac{45}{16} = \frac{5}{8} \times \frac{16}{45} = \frac{5 \times 16}{8 \times 45} = \frac{80}{360} = \frac{2}{9}$$.
- Perform the subtraction: $$\frac{19}{36} - \frac{2}{9} = \frac{19}{36} - \frac{2 \times 4}{9 \times 4} = \frac{19 - 8}{36} = \frac{11}{36}$$.
- Perform the addition: $$\frac{11}{36} + \frac{1}{12} = \frac{11}{36} + \frac{1 \times 3}{12 \times 3} = \frac{11 + 3}{36} = \frac{14}{36} = \frac{7}{18}$$.
