Question

5/9+4/9×3 1/6×(4/19+1 5/38- 75/76)​

Answer 1

Ответ:

Найдем значение выражения:

5/9 + 4/9 × 3 целых 1/6 × (4/19 +1 целая 5/38 - 75/76) по действиям:

1) 4/19 +1 целая 5/38 = ( 4 * 2) / ( 19 * 2) + 1 целая 5/38 = 8/38 + 1 целая 5/38 = 1 целая 13/38;

2) 1 целая 13/38 - 75/76 = 1 целая (13 * 2)/( 38 * 2) - 75/76 = 1 целая 26/76 - 75/76 = 102/76 - 75/76 = 27/76;

3) 4/9 × 3 целых 1/6 = 4/9 × (3 * 6 +1) = 4/9 × 19/6 = ( 4 * 19)/ ( 9 * 6) = (2 * 19)/ (9 * 3) = 38/27;

4) 38/27 × 27/76 = ( 38 * 27) /( 27 * 76) = (1 * 1)/ ( 1 * 2) = 1/2;

5) 5/9 + 1/2 = 10/18 + 9/18 = 19/18 = 1 целая 1/18.

Ответ: 1 целая 1/18.

Answer 2

To solve this expression, follow the order of operations (PEMDAS/BODMAS), which stands for Parentheses/Brackets, Exponents/Orders (i.e., powers and square roots, etc.), Multiplication and Division (left-to-right), and Addition and Subtraction (left-to-right).

Let's break down the expression step by step:

1. First, simplify the expression inside the innermost parentheses: 4/19 + 1 5/38 - 75/76

2. Convert the mixed numbers to improper fractions: 4/19 + 43/38 - 75/76

3. Find a common denominator for these fractions, which is 76: (4/19 * 4/4) + (43/38 * 2/2) - (75/76)

4. Now, add and subtract the fractions: (16/76) + (86/76) - (75/76)

5. Combine the fractions: (16/76 + 86/76 - 75/76)

6. Add the fractions together: (16 + 86 - 75) / 76 (27/76)

Now, we have simplified the expression inside the innermost parentheses to 27/76. Let's move on to the rest of the expression:

7. Next, multiply the result from step 6 (27/76) by the expression inside the outer parentheses: 27/76 * (27/76)

8. Multiply the fractions: (27 * 27) / (76 * 76) 729 / 5776

Now, we have simplified the expression inside the outermost parentheses to 729/5776.

9. Finally, add the result from step 8 (729/5776) to the expression outside the parentheses: 5/9 + (4/9 * 3 1/6 * 729/5776)

10. Perform the multiplication: 5/9 + (4/9 * 3 1/6 * 729/5776) 5/9 + (4/9 * 19/6 * 729/5776)

11. Multiply the fractions: 5/9 + (4 * 19 * 729) / (9 * 6 * 5776)

12. Calculate the products in the numerator: 5/9 + (4392/31296)

13. Find a common denominator: (5 * 3488) / (9 * 3488) + (4392/31296)

14. Add the fractions: (17440/31392) + (4392/31296)

15. Find a common denominator: (17440/31392) + (4392/31296 * 8/8)

16. Add the fractions: (17440/31392) + (35136/31392)

17. Combine the fractions: (17440 + 35136) / 31392

18. Add the numerators: 52576 / 31392

Now, this fraction cannot be simplified further. So, the final result is: 52576 / 31392