Monica is taking tennis lessons. She practised for `6 (8)/(9)` hours in the first week and `7 (5)/(6)` hours in the second week. Find:
b. the week in which she practised more and by how much?

Answer

To solve the problem, we need to compare the hours Monica practiced in the first and second week and find out by how much one is greater than the other.

### Step-by-Step Solution:

1. **Convert Mixed Numbers to Improper Fractions:**
- For the first week:
\[ 6 \frac{8}{9} = \frac{6 \times 9 + 8}{9} = \frac{54 + 8}{9} = \frac{62}{9} \]
- For the second week:
\[ 7 \frac{5}{6} = \frac{7 \times 6 + 5}{6} = \frac{42 + 5}{6} = \frac{47}{6} \]

**Hint:** To convert a mixed number to an improper fraction, multiply the whole number by the denominator, add the numerator, and place the result over the original denominator.

2. **Find a Common Denominator:**
- The denominators are 9 and 6. The least common multiple (LCM) of 9 and 6 is 18.

**Hint:** To find the LCM of two numbers, list the multiples of each number until you find the smallest common multiple.

3. **Convert Fractions to Have the Same Denominator:**
- Convert \(\frac{62}{9}\) to a denominator of 18:
\[ \frac{62}{9} = \frac{62 \times 2}{9 \times 2} = \frac{124}{18} \]
- Convert \(\frac{47}{6}\) to a denominator of 18:
\[ \frac{47}{6} = \frac{47 \times 3}{6 \times 3} = \frac{141}{18} \]

**Hint:** To convert a fraction to a different denominator, multiply both the numerator and denominator by the same number.

4. **Compare the Two Fractions:**
- Now we have:
\[ \frac{124}{18} \text{ (first week) and } \frac{141}{18} \text{ (second week)} \]
- Since \(141 > 124\), Monica practiced more in the second week.

**Hint:** When comparing fractions with the same denominator, simply compare the numerators.

5. **Calculate the Difference:**
- To find out by how much she practiced more in the second week:
\[ \frac{141}{18} - \frac{124}{18} = \frac{141 - 124}{18} = \frac{17}{18} \]

**Hint:** To find the difference between two fractions with the same denominator, subtract the numerators and keep the denominator the same.

### Final Answer:
Monica practiced more in the second week by \(\frac{17}{18}\) hours.