Question

( 5 3/8– 4 5/6) : (–1 5/8)

Answer 1

Ответ:

-1/3

Пошаговое объяснение:

(5 3/8-4 5/6)÷(-1 5/8)=(43/8-29/6)÷(-13/8)=(129/24-116/24)÷(-13/8)=13/24÷(-13/8)=

13/24×(-8/13)= -1/3

Answer 2

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

First, let's simplify the fractions within the parentheses:

$5 \frac{3}{8} = \frac{5 \cdot 8 + 3}{8} = \frac{43}{8}$

$4 \frac{5}{6} = \frac{4 \cdot 6 + 5}{6} = \frac{29}{6}$

Now, we have:

$\frac{43}{8} - \frac{29}{6}$

To subtract these fractions, we need a common denominator, which is the least common multiple of 8 and 6, which is 24.

$\frac{43 \cdot 3}{8 \cdot 3} - \frac{29 \cdot 4}{6 \cdot 4}$

$\frac{129}{24} - \frac{116}{24}$

Now we can subtract:

$\frac{129 - 116}{24} = \frac{13}{24}$

So, the expression within the first set of parentheses simplifies to $\frac{13}{24}$.

Next, let's simplify the expression in the second set of parentheses:

$-1 \frac{5}{8} = -\frac{8 \cdot 1 + 5}{8} = -\frac{13}{8}$

Now, we can proceed to the division of the two results:

$\frac{\frac{13}{24}}{-\frac{13}{8}}$

When dividing fractions, you can multiply the first fraction by the reciprocal of the second fraction:

$\frac{13}{24} \cdot \left(-\frac{8}{13}\right)$

The $13$ in the numerator and denominator of the first fraction cancel out:

$\frac{1}{24} \cdot \left(-\frac{8}{1}\right)$

Finally, multiply the numerators and denominators:

$\frac{-8}{24} = -\frac{1}{3}$

So, $(5 \frac{3}{8} - 4 \frac{5}{6}) : (-1 \frac{5}{8}) = -\frac{1}{3}$.