Convert each of the following into a mixed fraction:
(i) `(17)/(5)`
(ii) `(62)/(7)`
(iii) `(101)/(8)`
(iv) `(95)/(13)`
(v) `(81)/(11)`
(vi) `(87)/(16)`
(vii) `(103)/(12)`
(viii) `(117)/(20)`

Answer

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

### Step-by-Step Solutions:

**(i) Convert \( \frac{17}{5} \) into a mixed fraction:**

1. Divide 17 by 5.
- \( 17 \div 5 = 3 \) (whole number)
- Remainder: \( 17 - (5 \times 3) = 17 - 15 = 2 \)

2. Write the mixed fraction.
- Mixed fraction: \( 3 \frac{2}{5} \)

**(ii) Convert \( \frac{62}{7} \) into a mixed fraction:**

1. Divide 62 by 7.
- \( 62 \div 7 = 8 \) (whole number)
- Remainder: \( 62 - (7 \times 8) = 62 - 56 = 6 \)

2. Write the mixed fraction.
- Mixed fraction: \( 8 \frac{6}{7} \)

**(iii) Convert \( \frac{101}{8} \) into a mixed fraction:**

1. Divide 101 by 8.
- \( 101 \div 8 = 12 \) (whole number)
- Remainder: \( 101 - (8 \times 12) = 101 - 96 = 5 \)

2. Write the mixed fraction.
- Mixed fraction: \( 12 \frac{5}{8} \)

**(iv) Convert \( \frac{95}{13} \) into a mixed fraction:**

1. Divide 95 by 13.
- \( 95 \div 13 = 7 \) (whole number)
- Remainder: \( 95 - (13 \times 7) = 95 - 91 = 4 \)

2. Write the mixed fraction.
- Mixed fraction: \( 7 \frac{4}{13} \)

**(v) Convert \( \frac{81}{11} \) into a mixed fraction:**

1. Divide 81 by 11.
- \( 81 \div 11 = 7 \) (whole number)
- Remainder: \( 81 - (11 \times 7) = 81 - 77 = 4 \)

2. Write the mixed fraction.
- Mixed fraction: \( 7 \frac{4}{11} \)

**(vi) Convert \( \frac{87}{16} \) into a mixed fraction:**

1. Divide 87 by 16.
- \( 87 \div 16 = 5 \) (whole number)
- Remainder: \( 87 - (16 \times 5) = 87 - 80 = 7 \)

2. Write the mixed fraction.
- Mixed fraction: \( 5 \frac{7}{16} \)

**(vii) Convert \( \frac{103}{12} \) into a mixed fraction:**

1. Divide 103 by 12.
- \( 103 \div 12 = 8 \) (whole number)
- Remainder: \( 103 - (12 \times 8) = 103 - 96 = 7 \)

2. Write the mixed fraction.
- Mixed fraction: \( 8 \frac{7}{12} \)

**(viii) Convert \( \frac{117}{20} \) into a mixed fraction:**

1. Divide 117 by 20.
- \( 117 \div 20 = 5 \) (whole number)
- Remainder: \( 117 - (20 \times 5) = 117 - 100 = 17 \)

2. Write the mixed fraction.
- Mixed fraction: \( 5 \frac{17}{20} \)

### Final Mixed Fractions:
1. \( \frac{17}{5} = 3 \frac{2}{5} \)
2. \( \frac{62}{7} = 8 \frac{6}{7} \)
3. \( \frac{101}{8} = 12 \frac{5}{8} \)
4. \( \frac{95}{13} = 7 \frac{4}{13} \)
5. \( \frac{81}{11} = 7 \frac{4}{11} \)
6. \( \frac{87}{16} = 5 \frac{7}{16} \)
7. \( \frac{103}{12} = 8 \frac{7}{12} \)
8. \( \frac{117}{20} = 5 \frac{17}{20} \)