Question

(2/7:3/7+(4 1/2-3 5/6)*3 1/3):(6 1/2:9)как решить ??

Answer 1

Ответ:

4

Пошаговое объяснение:

Answer 2

To solve the expression, let's 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)

The given expression is:

(2/7) : (3/7 + (4 1/2 - 3 5/6) * 3 1/3) : (6 1/2 : 9)

First, let's simplify the expression inside the parentheses:

(4 1/2 - 3 5/6) * 3 1/3

Step 1: Convert mixed numbers to improper fractions: 4 1/2 = (2 * 4 + 1)/2 = 9/2 3 5/6 = (6 * 3 + 5)/6 = 23/6

Step 2: Find the difference: (9/2 - 23/6)

Step 3: Get a common denominator, which is 6 in this case: (9/2 * 3/3 - 23/6)

Step 4: Perform the subtraction: (27/6 - 23/6) = 4/6 = 2/3

Now, the expression becomes:

(2/7) : (3/7 + 2/3 * 3 1/3) : (6 1/2 : 9)

Next, let's simplify the expression inside the second parentheses:

2/3 * 3 1/3

Step 1: Convert mixed numbers to improper fractions: 3 1/3 = (3 * 3 + 1)/3 = 10/3

Step 2: Perform the multiplication: (2/3 * 10/3)

Step 3: Simplify the result: (20/9)

Now, the expression becomes:

(2/7) : (3/7 + 20/9) : (6 1/2 : 9)

Now, let's simplify the expression further:

(3/7 + 20/9)

Step 1: Find a common denominator, which is 63 in this case (7 * 9): (27/63 + 140/63)

Step 2: Perform the addition: (167/63)

Now, the expression becomes:

(2/7) : (167/63) : (6 1/2 : 9)

Next, let's convert the mixed number to an improper fraction:

6 1/2 = (2 * 6 + 1)/2 = 13/2

Now, the expression becomes:

(2/7) : (167/63) : (13/2 : 9)

Finally, let's proceed with the division:

Step 1: Convert the whole numbers to fractions with a denominator of 1: 13/2 : 9 = (13/2) : (9/1)

Step 2: Invert the second fraction and multiply: (13/2) * (1/9) = 13/18

Now, the expression becomes:

(2/7) : (167/63) : (13/18)

Step 3: Find a common denominator, which is 63 in this case (7 * 9): (18/63) : (167/63) : (13/18)

Step 4: Perform the divisions: (18/63) ÷ (167/63) ÷ (13/18) = (18/63) * (63/167) * (18/13)

Step 5: Cancel out common factors: (1/1) * (1/1) * (6/13) = 6/13

Therefore, the simplified value of the expression is 6/13.