Find the rational number, which is `(-4)/(9)` more than `(6)/(7).`

Options

A. `(-26)/(63)`
B. `(-82)/(63)`
C. `(26)/(63)`
D. `(82)/(63)`

Answer

To find the rational number that is \(-\frac{4}{9}\) more than \(\frac{6}{7}\), we can follow these steps:

### Step 1: Define the Rational Number
Let the rational number be \(x\). According to the problem, we have:
\[ x = \frac{6}{7} - \frac{4}{9} \]

### Step 2: Find a Common Denominator
To subtract the fractions, we need a common denominator. The denominators are 7 and 9. The least common multiple (LCM) of 7 and 9 is 63.

### Step 3: Convert Each Fraction
Now, we convert each fraction to have the common denominator of 63:
- For \(\frac{6}{7}\):
\[ \frac{6}{7} = \frac{6 \times 9}{7 \times 9} = \frac{54}{63} \]
- For \(\frac{4}{9}\):
\[ \frac{4}{9} = \frac{4 \times 7}{9 \times 7} = \frac{28}{63} \]

### Step 4: Subtract the Fractions
Now we can subtract the two fractions:
\[ x = \frac{54}{63} - \frac{28}{63} = \frac{54 - 28}{63} = \frac{26}{63} \]

### Step 5: Conclusion
Thus, the rational number that is \(-\frac{4}{9}\) more than \(\frac{6}{7}\) is:
\[ \boxed{\frac{26}{63}} \]