`5(5)/(6) -3(8)/(9)` -? =1

Options

A. `(2)/(3)`
B. `(3)/(2)`
C. `(17)/(18)`
D. 3

Answer

To solve the equation \(5\frac{5}{6} - 3\frac{8}{9} - ? = 1\), we will follow these steps:

### Step 1: Convert the mixed numbers to improper fractions
- For \(5\frac{5}{6}\):
\[ 5\frac{5}{6} = 5 \times 6 + 5 = 30 + 5 = 35 \quad \text{(numerator)} \quad \Rightarrow \quad \frac{35}{6} \]

- For \(3\frac{8}{9}\):
\[ 3\frac{8}{9} = 3 \times 9 + 8 = 27 + 8 = 35 \quad \text{(numerator)} \quad \Rightarrow \quad \frac{35}{9} \]

### Step 2: Rewrite the equation with improper fractions
Now, substituting the improper fractions back into the equation:
\[ \frac{35}{6} - \frac{35}{9} - ? = 1 \]

### Step 3: Find the least common multiple (LCM) of the denominators
The denominators are 6 and 9. The LCM of 6 and 9 is 18.

### Step 4: Convert the fractions to have a common denominator
- Convert \(\frac{35}{6}\) to a denominator of 18:
\[ \frac{35}{6} = \frac{35 \times 3}{6 \times 3} = \frac{105}{18} \]

- Convert \(\frac{35}{9}\) to a denominator of 18:
\[ \frac{35}{9} = \frac{35 \times 2}{9 \times 2} = \frac{70}{18} \]

### Step 5: Substitute back into the equation
Now, the equation becomes:
\[ \frac{105}{18} - \frac{70}{18} - ? = 1 \]

### Step 6: Combine the fractions
Combine the fractions on the left side:
\[ \frac{105 - 70}{18} - ? = 1 \]
This simplifies to:
\[ \frac{35}{18} - ? = 1 \]

### Step 7: Isolate the question mark
To isolate \(?\), we rearrange the equation:
\[ ? = \frac{35}{18} - 1 \]

### Step 8: Convert 1 to a fraction with a denominator of 18
Convert 1 to a fraction:
\[ 1 = \frac{18}{18} \]

### Step 9: Perform the subtraction
Now, perform the subtraction:
\[ ? = \frac{35}{18} - \frac{18}{18} = \frac{35 - 18}{18} = \frac{17}{18} \]

### Final Answer
Thus, the value of \(?\) is:
\[ ? = \frac{17}{18} \]