Question

(4 5/9-3 7/12):(-1 8/27)

Answer 1

Ответ:

-3/4

Пошаговое объяснение:

(4 5/9-3 7/12):(-1 8/27) = (4 20/36 - 3 21/36) : (-35/27) = 35/36 * (-27/35) = -3/4

Answer 2

To solve this expression, we'll follow the order of operations: parentheses, then multiplication and division, and finally addition and subtraction.

Let's start by simplifying the fraction inside the parentheses:

$-1 \frac{8}{27}$ can be written as $-\frac{27}{27} + \frac{8}{27} = -\frac{19}{27}$.

Now, let's perform the division outside the parentheses:

$\frac{4 \frac{5}{9} - 3 \frac{7}{12}}{-\frac{19}{27}}$.

To perform the division, we'll multiply by the reciprocal of $-\frac{19}{27}$, which is $-\frac{27}{19}$:

$$\frac{4 \frac{5}{9} - 3 \frac{7}{12}}{-\frac{19}{27}} = \left(4 \frac{5}{9} - 3 \frac{7}{12}\right) \times \left(-\frac{27}{19}\right)$$

Now, let's work on simplifying the mixed fractions:

$4 \frac{5}{9}$ can be written as $\frac{4 \times 9 + 5}{9} = \frac{41}{9}$.

$3 \frac{7}{12}$ can be written as $\frac{3 \times 12 + 7}{12} = \frac{43}{12}$.

Now we can rewrite the expression and simplify:

$$\left(\frac{41}{9} - \frac{43}{12}\right) \times \left(-\frac{27}{19}\right)$$

To subtract the fractions, we need a common denominator, which is the least common multiple of 9 and 12, which is 36:

$$\frac{41 \times 4}{36} - \frac{43 \times 3}{36} = \frac{164}{36} - \frac{129}{36} = \frac{35}{36}$$

Now, let's multiply by $-\frac{27}{19}$:

$$\frac{35}{36} \times \left(-\frac{27}{19}\right) = -\frac{35 \times 27}{36 \times 19} = -\frac{945}{684} = -\frac{35}{26}$$