Question

(1 4/9+2 5/6-2 3/4):(4 1/2-1/4)​

Answer 1

Ответ:

5 180/224

Пошаговое объяснение:

1 4/9+2 5/6=4 15/56

4 15/56-2 3/4=1 101/224

4 1/2-1/4=4 1/4

1 101/224:1//4=5 180/224

Answer 2

To solve the given expression, we'll follow the order of operations (PEMDAS/BODMAS):

1. Parentheses/Brackets
2. Exponents/Orders
3. Multiplication and Division (from left to right)
4. Addition and Subtraction (from left to right)

Given expression: (1 4/9 + 2 5/6 - 2 3/4) ÷ (4 1/2 - 1/4)

Step 1: Perform operations within parentheses. 1 4/9 + 2 5/6 - 2 3/4

To add mixed numbers, convert them to improper fractions: 1 4/9 = (9 * 1 + 4) / 9 = 13/9 2 5/6 = (6 * 2 + 5) / 6 = 17/6 2 3/4 = (4 * 2 + 3) / 4 = 11/4

So, the expression becomes: (13/9 + 17/6 - 11/4)

Step 2: Find a common denominator to perform addition and subtraction. The common denominator for 9, 6, and 4 is 36.

Converting each fraction to have a denominator of 36: (13/9) * (4/4) = 52/36 (17/6) * (6/6) = 102/36 (11/4) * (9/9) = 99/36

The expression becomes: (52/36 + 102/36 - 99/36)

Step 3: Perform addition and subtraction from left to right. (52/36 + 102/36 - 99/36) = (154/36 - 99/36)

Now, let's perform the division: (154/36) ÷ (9/4)

To divide fractions, we invert and multiply: (154/36) * (4/9) = (154 * 4) / (36 * 9) = 616 / 324

Step 4: Simplify the result, if possible. To simplify the fraction, find the greatest common divisor (GCD) and divide both numerator and denominator by it: GCD(616, 324) = 4 616 ÷ 4 = 154 324 ÷ 4 = 81

So, the simplified fraction is: 154/81

Therefore, the result of the expression is 154/81.