Question

3 3/4+3×(2 3/8-5/6):6 1/6​

Answer 1

Ответ:

3 3/4+3×(2 3/8-5/6):6 1/6

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, deal with the parentheses/brackets: 2 3/8 - 5/6

To subtract these fractions, we need to find a common denominator, which in this case is 24: (19/8) - (20/24)

Now, adjust the fractions to have a common denominator: (19/8) - (5/6) * (4/4) = (19/8) - (20/24)

2. Next, calculate the result of the subtraction: (19/8) - (20/24) = (19/8) - (5/6)

3. Now, let's simplify the subtraction: To subtract fractions, we need a common denominator, which in this case is 24. (19/8) * (3/3) = (57/24) - (10/24)

4. Subtract the fractions: (57/24) - (10/24) = 47/24

Now, we have simplified the expression within the parentheses:

3 3/4 + 3 * (47/24) / 6 1/6

5. Next, deal with the multiplication and division, working from left to right: 3 * (47/24) = 141/24

6. Now, the expression becomes: 3 3/4 + (141/24) / 6 1/6

7. Now, deal with the division: (141/24) / 6 1/6

To divide fractions, multiply by the reciprocal of the second fraction: (141/24) * (6 6/1)

8. Simplify the multiplication: (141/24) * (42/1)

9. Now, multiply the fractions: (141 * 42) / (24 * 1) = 5922/24

10. Simplify the fraction: 5922/24 = 247/1

So, the final expression is: 3 3/4 + 247/1

11. Convert the mixed number to an improper fraction: 3 3/4 = (4 * 3 + 3)/4 = 15/4

Now, add the fractions: 15/4 + 247/1

12. To add these fractions, you need a common denominator, which is 4 for both fractions: (15/4) + (247/4)

13. Add the fractions: (15 + 247)/4 = 262/4 = 131/2

So, the final result is 131/2 or 65.5.