Convert the following mixed fractions into improper fractions :
(i) `7""2/11" (ii) "3""5/48" (iii) "13""7/64" (iv) " 7""2/3`.

Answer

To convert the given mixed fractions into improper fractions, we will follow a systematic approach. Here’s the step-by-step solution for each of the mixed fractions provided:

### (i) Convert `7 2/11` to an improper fraction:

1. **Identify the whole number and the fraction**: The whole number is 7, and the fraction is \( \frac{2}{11} \).
2. **Multiply the whole number by the denominator**:
\[ 7 \times 11 = 77 \]
3. **Add the numerator to the product**:
\[ 77 + 2 = 79 \]
4. **Write the result as an improper fraction**:
\[ \frac{79}{11} \]

### (ii) Convert `3 5/48` to an improper fraction:

1. **Identify the whole number and the fraction**: The whole number is 3, and the fraction is \( \frac{5}{48} \).
2. **Multiply the whole number by the denominator**:
\[ 3 \times 48 = 144 \]
3. **Add the numerator to the product**:
\[ 144 + 5 = 149 \]
4. **Write the result as an improper fraction**:
\[ \frac{149}{48} \]

### (iii) Convert `13 7/64` to an improper fraction:

1. **Identify the whole number and the fraction**: The whole number is 13, and the fraction is \( \frac{7}{64} \).
2. **Multiply the whole number by the denominator**:
\[ 13 \times 64 = 832 \]
3. **Add the numerator to the product**:
\[ 832 + 7 = 839 \]
4. **Write the result as an improper fraction**:
\[ \frac{839}{64} \]

### (iv) Convert `7 2/3` to an improper fraction:

1. **Identify the whole number and the fraction**: The whole number is 7, and the fraction is \( \frac{2}{3} \).
2. **Multiply the whole number by the denominator**:
\[ 7 \times 3 = 21 \]
3. **Add the numerator to the product**:
\[ 21 + 2 = 23 \]
4. **Write the result as an improper fraction**:
\[ \frac{23}{3} \]

### Final Answers:
- (i) \( \frac{79}{11} \)
- (ii) \( \frac{149}{48} \)
- (iii) \( \frac{839}{64} \)
- (iv) \( \frac{23}{3} \)