1. Вычислите: 2 $\frac{14}{41}$ $\cdot$ $\frac{2}{24} - \frac{1}{16} + \frac{2}{3}$ : $4 \frac{2}{3}$ / ( $1 \frac{1}{10}$ + 7 : $3 \frac{1}{12} - 1 \frac{5}{8}$ $\cdot$ $1 \frac{1}{59}$ )

Question

$Фото задания: 1. Вычислите: 2 $\frac{14}{41}$ $\cdot$ $\frac{2}{24} - \frac{1}{16} + \frac{2}{3}$ : $4 \frac{2}{3}$ / ( \(1…$ Фото задания

Accepted Answer

1. Вычислим числитель:

$2 \frac{14}{41} \cdot \frac{2}{24} = \frac{2 \cdot 41 + 14}{41} \cdot \frac{2}{24} = \frac{96}{41} \cdot \frac{2}{24} = \frac{4 \cdot 2}{41} = \frac{8}{41}$
$\frac{1}{16} + \frac{2}{3} : 4 \frac{2}{3} = \frac{1}{16} + \frac{2}{3} : \frac{14}{3} = \frac{1}{16} + \frac{2}{3} \cdot \frac{3}{14} = \frac{1}{16} + \frac{1}{7} = \frac{7 + 16}{112} = \frac{23}{112}$
$\frac{8}{41} - \frac{23}{112} = \frac{8 \cdot 112 - 23 \cdot 41}{41 \cdot 112} = \frac{896 - 943}{4592} = -\frac{47}{4592}$

2. Вычислим знаменатель:

$3 \frac{1}{12} - 1 \frac{5}{8} = \frac{37}{12} - \frac{13}{8} = \frac{74 - 39}{24} = \frac{35}{24}$
$\frac{35}{24} \cdot \frac{1}{59} = \frac{35}{1416}$
$1 \frac{1}{10} + 7 : \frac{35}{1416} = \frac{11}{10} + 7 \cdot \frac{1416}{35} = \frac{11}{10} + \frac{1416}{5} = \frac{11 + 2832}{10} = \frac{2843}{10}$

3. Вычислим дробь:

$\frac{-47}{4592} : \frac{2843}{10} = \frac{-47}{4592} \cdot \frac{10}{2843} = \frac{-470}{12948676} = -\frac{235}{6474338}$

Ответ: -$\frac{235}{6474338}$.

1. Вычислите: 2 \(\frac{14}{41}\) \(\cdot\) \(\frac{2}{24} - \frac{1}{16} + \frac{2}{3}\) : \(4 \frac{2}{3}\) / ( \(1 \frac{1}{10}\) + 7 : \(3 \frac{1}{12} - 1 \frac{5}{8}\) \(\cdot\) \(1 \frac{1}{59}\) )