Convert the following improper fractions into mixed numbers :
(i) `17/3" (ii) " 119/15" (iii) "961/13" (iv) " 117/32`

Answer

To convert the given improper fractions into mixed numbers, we will follow these steps:

### Step-by-Step Solution:

**(i) Convert \( \frac{17}{3} \) into a mixed number:**

1. **Divide the numerator by the denominator:**
- \( 17 \div 3 = 5 \) (Quotient)
- Remainder: \( 17 - (5 \times 3) = 17 - 15 = 2 \)

2. **Write the mixed number:**
- The mixed number is \( 5 \frac{2}{3} \).

**(ii) Convert \( \frac{119}{15} \) into a mixed number:**

1. **Divide the numerator by the denominator:**
- \( 119 \div 15 = 7 \) (Quotient)
- Remainder: \( 119 - (7 \times 15) = 119 - 105 = 14 \)

2. **Write the mixed number:**
- The mixed number is \( 7 \frac{14}{15} \).

**(iii) Convert \( \frac{961}{13} \) into a mixed number:**

1. **Divide the numerator by the denominator:**
- \( 961 \div 13 = 73 \) (Quotient)
- Remainder: \( 961 - (73 \times 13) = 961 - 949 = 12 \)

2. **Write the mixed number:**
- The mixed number is \( 73 \frac{12}{13} \).

**(iv) Convert \( \frac{117}{32} \) into a mixed number:**

1. **Divide the numerator by the denominator:**
- \( 117 \div 32 = 3 \) (Quotient)
- Remainder: \( 117 - (3 \times 32) = 117 - 96 = 21 \)

2. **Write the mixed number:**
- The mixed number is \( 3 \frac{21}{32} \).

### Final Answers:
1. \( \frac{17}{3} = 5 \frac{2}{3} \)
2. \( \frac{119}{15} = 7 \frac{14}{15} \)
3. \( \frac{961}{13} = 73 \frac{12}{13} \)
4. \( \frac{117}{32} = 3 \frac{21}{32} \)