Convert each of the following into a mixed fraction:
(i)`38/7`
(ii)`47/15`
(iii)`189/16`

Answer

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

### Step 1: Convert `38/7` into a mixed fraction
1. **Divide the numerator by the denominator**:
- \( 38 \div 7 = 5 \) (whole number part)
- Remainder: \( 38 - (7 \times 5) = 38 - 35 = 3 \)
2. **Write the mixed fraction**:
- The whole number part is \( 5 \) and the remainder is \( 3 \), so the mixed fraction is \( 5 \frac{3}{7} \).

### Step 2: Convert `47/15` into a mixed fraction
1. **Divide the numerator by the denominator**:
- \( 47 \div 15 = 3 \) (whole number part)
- Remainder: \( 47 - (15 \times 3) = 47 - 45 = 2 \)
2. **Write the mixed fraction**:
- The whole number part is \( 3 \) and the remainder is \( 2 \), so the mixed fraction is \( 3 \frac{2}{15} \).

### Step 3: Convert `189/16` into a mixed fraction
1. **Divide the numerator by the denominator**:
- \( 189 \div 16 = 11 \) (whole number part)
- Remainder: \( 189 - (16 \times 11) = 189 - 176 = 13 \)
2. **Write the mixed fraction**:
- The whole number part is \( 11 \) and the remainder is \( 13 \), so the mixed fraction is \( 11 \frac{13}{16} \).

### Final Answers:
- (i) \( 38/7 = 5 \frac{3}{7} \)
- (ii) \( 47/15 = 3 \frac{2}{15} \)
- (iii) \( 189/16 = 11 \frac{13}{16} \)

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