Question

2 3/4:(-2/5+1 1/2)-(-3/4-5/6):3 1/6

Answer 1

Решение на фото
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Answer 2

Let's break down the expression step by step:

1. Start with the innermost operations in parentheses:

   (-2/5 + 1 1/2) = (-2/5 + 3/2)

2. To add these fractions, you need a common denominator, which is 10. So, multiply the first fraction by 2/2 to get a common denominator:

   (-4/10 + 15/10)

3. Now, you can add these fractions:

   (-4/10 + 15/10) = (11/10)

4. Next, calculate the other set of parentheses:

   (-3/4 - 5/6)

   To subtract these fractions, you also need a common denominator, which is 12. So, multiply the first fraction by 3/3 and the second fraction by 2/2 to get a common denominator:

   (-9/12 - 10/12)

5. Now, subtract these fractions:

   (-9/12 - 10/12) = (-19/12)

6. Finally, calculate the entire expression:

   2 3/4:(11/10 - (-19/12)) ÷ 3 1/6

7. To divide by a fraction, you can multiply by its reciprocal:

   2 3/4 * (10/11 - (-12/19)) * (6/19)

8. Calculate the values inside the parentheses:

   (10/11 - (-12/19)) = (10/11 + 12/19)

9. To add these fractions, you need a common denominator, which is 209. So, multiply the first fraction by 19/19 and the second fraction by 11/11 to get a common denominator:

   (190/209 + 132/209)

10. Now, add these fractions:

(190/209 + 132/209) = (322/209)

11. Plug this value back into the expression:

2 3/4 * (322/209) * (6/19)

12. To multiply mixed numbers, first convert them to improper fractions:

2 3/4 = (42 + 3)/4 = 11/4 3 1/6 = (63 + 1)/6 = 19/6

13. Multiply the fractions:

(11/4) * (322/209) * (6/19)

14. Multiply the numerators together and the denominators together:

(11 * 322 * 6) / (4 * 209 * 19)

15. Perform the multiplications:

(21372) / (15824)

16. Now, simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 4:

(21372 / 4) / (15824 / 4) = 5343 / 3956

So, the result of the expression 2 3/4:(-2/5 + 1 1/2) - (-3/4 - 5/6):3 1/6 is 5343/3956 or approximately 1.349.