Question

(5 2/3+(-2,64)÷1 2/75-(-1 4/21-1 3/14))÷(-1 5/6)​

Answer 1

Ответ:

Пошаговое объяснение:

Answer 2

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

1. Start by simplifying the expressions within parentheses:

   a. (-2.64) ÷ (1 2/75 - (-1 4/21 - 1 3/14)):

   First, let's calculate the value inside the innermost parentheses:

   -1 4/21 - 1 3/14 = -22/21 - 46/14 = -22/21 - 23/7

   Now, find a common denominator to subtract these fractions:

   -22/21 - 23/7 = (-22/21 * 7/7) - (23/7 * 3/3)

   -154/147 - 69/147 = (-154 - 69) / 147

   -223/147

   So, (-2.64) ÷ (1 2/75 - (-1 4/21 - 1 3/14)) becomes:

   (-2.64) ÷ (-223/147)

   b. Now, we have (5 2/3 + (-2.64) ÷ (-223/147)) ÷ (-1 5/6):

   To add 5 2/3 to the division result, convert 5 2/3 to an improper fraction:

   5 2/3 = (3 * 5 + 2) / 3 = 17/3

   So, the expression becomes:

   (17/3 + (-2.64) ÷ (-223/147)) ÷ (-1 5/6)

2. Next, divide -2.64 by -223/147:

   (-2.64) ÷ (-223/147) = (-2.64) * (-147/223)

   Simplify the multiplication:

   (-2.64) * (-147/223) = 388.08/223

3. Now, the expression becomes:

   (17/3 + 388.08/223) ÷ (-1 5/6)

4. Convert -1 5/6 to an improper fraction:

   -1 5/6 = (-6 * 1 - 5) / 6 = -11/6

5. Now, we have:

   (17/3 + 388.08/223) ÷ (-11/6)

6. To add these fractions, find a common denominator:

   The common denominator for 3 and 223 is 669:

   (17/3 * 223/223 + 388.08/223) ÷ (-11/6)

   Now, add the fractions:

   (17 * 223 + 388.08) / 669 ÷ (-11/6)

7. Continue to simplify:

   (3791 + 388.08) / 669 ÷ (-11/6)

   (4179.08 / 669) ÷ (-11/6)

8. Divide by -11/6:

   (4179.08 / 669) * (-6/11)

   Simplify the multiplication:

   (357.64 / 669) * (-6/11)

9. Now, divide:

   (357.64 * -6) / (669 * 11)

   -2145.84 / 7359

10. Finally, simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 3:

(-2145.84 / 3) / (7359 / 3)

-715.28 / 2453

So, the final result of the expression is approximately -0.2917 (rounded to four decimal places).