To subtract the fractions \( 9 \frac{7}{10} - 6 \frac{1}{4} \), we can first convert the mixed numbers into improper fractions.
-
Convert \( 9 \frac{7}{10} \) to an improper fraction: \[ 9 \frac{7}{10} = 9 \times 10 + 7 = 90 + 7 = 97 \quad \text{so} \quad 9 \frac{7}{10} = \frac{97}{10} \]
-
Convert \( 6 \frac{1}{4} \) to an improper fraction: \[ 6 \frac{1}{4} = 6 \times 4 + 1 = 24 + 1 = 25 \quad \text{so} \quad 6 \frac{1}{4} = \frac{25}{4} \]
Now we have: \[ \frac{97}{10} - \frac{25}{4} \]
Next, we need to find a common denominator to subtract these fractions. The least common denominator (LCD) of 10 and 4 is 20.
- Convert each fraction to have a denominator of 20: \[ \frac{97}{10} = \frac{97 \times 2}{10 \times 2} = \frac{194}{20} \] \[ \frac{25}{4} = \frac{25 \times 5}{4 \times 5} = \frac{125}{20} \]
Now we can subtract: \[ \frac{194}{20} - \frac{125}{20} = \frac{194 - 125}{20} = \frac{69}{20} \]
We can convert \( \frac{69}{20} \) back to a mixed number if necessary. The whole number part is: \[ 69 \div 20 = 3 \quad \text{with a remainder of} \quad 9 \]
Thus, \[ \frac{69}{20} = 3 \frac{9}{20} \]
The difference \( 9 \frac{7}{10} - 6 \frac{1}{4} \) is \( \boxed{3 \frac{9}{20}} \).