Question

(2 3/4 : 1 1/10 + 3 1/3) : 5/7 : 2 1/2 - 1 1/3

Answer 1

Ответ:

1 14/15

Пошаговое объяснение:

1) 2 3/4:1 1/10=11/4:11/10=11/4•10/11=5/2=2 1/2

2) 2 1/2+3 1/3= 2 3/6+3 2/6= 5 5/6

3) 5 5/6:5/7= 35/6•7/5=49/6

4) 49/6:2 1/2= 49/6:5/2=49/6•2/5=

=49/15=3 4/15

5) 3 4/15-1 1/3= 3 4/15-1 5/15= 2 19/15-1 5/15=

=1 14/15

Answer 2

To solve this expression, we can break it down step by step.

1. Start with the innermost parentheses: (2 3/4 : 1 1/10 + 3 1/3) : 5/7 : (2 1/2 - 1 1/3)

2. Next, calculate the values inside the parentheses:

   2 3/4 : (1 1/10 + 3 1/3) : 5/7 : (2 1/2 - 1 1/3)

3. Calculate the addition inside the second set of parentheses:

   1 1/10 + 3 1/3 = 1 1/10 + 3 1/3 = 4 4/30 + 10/30 = 4 14/30 = 4 7/15

4. Now, simplify the expression:

   2 3/4 : (4 7/15) : 5/7 : (2 1/2 - 1 1/3)

5. Calculate the subtraction inside the last set of parentheses:

   2 1/2 - 1 1/3 = 2 3/6 - 1 2/6 = 1 1/6

6. Simplify the expression further:

   2 3/4 : 4 7/15 : 5/7 : 1 1/6

7. Divide the fractions by finding their reciprocals and multiplying:

   2 3/4 ÷ 4 7/15 = (11/4) ÷ (67/15) = 11/4 * 15/67

   5/7 ÷ 1 1/6 = 5/7 ÷ 7/6 = (5/7) * (6/7)

8. Convert mixed numbers to improper fractions:

   2 3/4 = (4 * 2 + 3) / 4 = 11/4

   1 1/6 = (6 * 1 + 1) / 6 = 7/6

9. Perform the multiplications:

   (11/4) * (15/67) = (11 * 15) / (4 * 67)

   (5/7) * (6/7) = (5 * 6) / (7 * 7)

10. Calculate the products:

(11 * 15) / (4 * 67) = 165 / 268

(5 * 6) / (7 * 7) = 30 / 49

11. Now, perform the divisions:

(165/268) ÷ (30/49)

12. To divide fractions, multiply by the reciprocal:

(165/268) ÷ (30/49) = (165/268) * (49/30)

13. Multiply the fractions:

(165/268) * (49/30) = (165 * 49) / (268 * 30)

14. Calculate the product:

(165 * 49) / (268 * 30) = 8085 / 8040

15. Simplify the fraction by finding the greatest common divisor (GCD) of 8085 and 8040, which is 15:

(8085 / 15) / (8040 / 15) = 539 / 536

So, the final result is 539/536.