Convert each of the following Into an improper fraction:
(i) `5(5)/(7)`
(ii) `9(3)/(8)`
(iii) `6(3)/(10)`
(iv) `3(5)/(11)`
(v) `10(9)/(14)`
(vi) `12(7)/(15)`
(vii) `8(8)/(13)`
(viii) `51(2)/(3)`

Answer

To convert each mixed fraction into an improper fraction, we follow these steps:

### Step-by-Step Solution:

**(i) Convert `5(5)/(7)` into an improper fraction:**
1. Multiply the whole number (5) by the denominator (7):
\( 5 \times 7 = 35 \)
2. Add the numerator (5) to the result from step 1:
\( 35 + 5 = 40 \)
3. Write the result over the original denominator (7):
\[ \frac{40}{7} \]

**(ii) Convert `9(3)/(8)` into an improper fraction:**
1. Multiply the whole number (9) by the denominator (8):
\( 9 \times 8 = 72 \)
2. Add the numerator (3) to the result from step 1:
\( 72 + 3 = 75 \)
3. Write the result over the original denominator (8):
\[ \frac{75}{8} \]

**(iii) Convert `6(3)/(10)` into an improper fraction:**
1. Multiply the whole number (6) by the denominator (10):
\( 6 \times 10 = 60 \)
2. Add the numerator (3) to the result from step 1:
\( 60 + 3 = 63 \)
3. Write the result over the original denominator (10):
\[ \frac{63}{10} \]

**(iv) Convert `3(5)/(11)` into an improper fraction:**
1. Multiply the whole number (3) by the denominator (11):
\( 3 \times 11 = 33 \)
2. Add the numerator (5) to the result from step 1:
\( 33 + 5 = 38 \)
3. Write the result over the original denominator (11):
\[ \frac{38}{11} \]

**(v) Convert `10(9)/(14)` into an improper fraction:**
1. Multiply the whole number (10) by the denominator (14):
\( 10 \times 14 = 140 \)
2. Add the numerator (9) to the result from step 1:
\( 140 + 9 = 149 \)
3. Write the result over the original denominator (14):
\[ \frac{149}{14} \]

**(vi) Convert `12(7)/(15)` into an improper fraction:**
1. Multiply the whole number (12) by the denominator (15):
\( 12 \times 15 = 180 \)
2. Add the numerator (7) to the result from step 1:
\( 180 + 7 = 187 \)
3. Write the result over the original denominator (15):
\[ \frac{187}{15} \]

**(vii) Convert `8(8)/(13)` into an improper fraction:**
1. Multiply the whole number (8) by the denominator (13):
\( 8 \times 13 = 104 \)
2. Add the numerator (8) to the result from step 1:
\( 104 + 8 = 112 \)
3. Write the result over the original denominator (13):
\[ \frac{112}{13} \]

**(viii) Convert `51(2)/(3)` into an improper fraction:**
1. Multiply the whole number (51) by the denominator (3):
\( 51 \times 3 = 153 \)
2. Add the numerator (2) to the result from step 1:
\( 153 + 2 = 155 \)
3. Write the result over the original denominator (3):
\[ \frac{155}{3} \]

### Final Answers:
1. \( \frac{40}{7} \)
2. \( \frac{75}{8} \)
3. \( \frac{63}{10} \)
4. \( \frac{38}{11} \)
5. \( \frac{149}{14} \)
6. \( \frac{187}{15} \)
7. \( \frac{112}{13} \)
8. \( \frac{155}{3} \)