To solve the expression \( 10 \frac{1}{9} - 9 \frac{3}{4} \), we'll first convert the mixed numbers into improper fractions and then subtract them.

### Step 1: Convert Mixed Numbers to Improper Fractions
1. \( 10 \frac{1}{9} \) can be converted as:
   \[
   10 \frac{1}{9} = \frac{10 \times 9 + 1}{9} = \frac{90 + 1}{9} = \frac{91}{9}
   \]
2. \( 9 \frac{3}{4} \) can be converted as:
   \[
   9 \frac{3}{4} = \frac{9 \times 4 + 3}{4} = \frac{36 + 3}{4} = \frac{39}{4}
   \]

### Step 2: Find a Common Denominator
The denominators are 9 and 4. The least common denominator (LCD) is 36.

- Convert \( \frac{91}{9} \) to have a denominator of 36:
  \[
  \frac{91}{9} = \frac{91 \times 4}{9 \times 4} = \frac{364}{36}
  \]
- Convert \( \frac{39}{4} \) to have a denominator of 36:
  \[
  \frac{39}{4} = \frac{39 \times 9}{4 \times 9} = \frac{351}{36}
  \]

### Step 3: Subtract the Fractions
Now subtract the two fractions:
\[
\frac{364}{36} - \frac{351}{36} = \frac{364 - 351}{36} = \frac{13}{36}
\]

### Final Answer
\[
10 \frac{1}{9} - 9 \frac{3}{4} = \frac{13}{36}
\]

Would you like more details, or do you have any questions about this?

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Here are five related questions for further practice:
1. Simplify \( 7 \frac{5}{6} - 4 \frac{2}{3} \).
2. What is the sum of \( 8 \frac{1}{5} + 3 \frac{4}{7} \)?
3. Subtract \( 12 \frac{2}{9} - 5 \frac{7}{8} \).
4. Convert \( 11 \frac{3}{4} \) to an improper fraction.
5. Add \( 6 \frac{1}{2} + 2 \frac{3}{5} \).

**Tip:** When working with mixed numbers, always convert them to improper fractions before performing addition or subtraction for easier calculations.

Learn how to subtract mixed numbers by converting them into improper fractions. This detailed step-by-step solution covers the subtraction of 10 1/9 and 9 3/4, focusing on finding a common denominator and simplifying the result. Perfect for students in Grades 6-8.

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