Convert each of the following into an improper fraction:
(i)`1 3/4`
(ii)`4 5/7`
(iii)`7 9/13`
`12 6/25`

Answer

To convert mixed numbers into improper fractions, follow these steps:

### Step-by-Step Solution:

**(i) Convert `1 3/4` into an improper fraction:**

1. **Identify the whole number and the fraction:** The whole number is `1` and the fraction is `3/4`.
2. **Multiply the whole number by the denominator of the fraction:**
\[ 1 \times 4 = 4 \]
3. **Add the result to the numerator of the fraction:**
\[ 4 + 3 = 7 \]
4. **Write the result over the original denominator:**
\[ \frac{7}{4} \]

So, `1 3/4` as an improper fraction is \(\frac{7}{4}\).

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**(ii) Convert `4 5/7` into an improper fraction:**

1. **Identify the whole number and the fraction:** The whole number is `4` and the fraction is `5/7`.
2. **Multiply the whole number by the denominator of the fraction:**
\[ 4 \times 7 = 28 \]
3. **Add the result to the numerator of the fraction:**
\[ 28 + 5 = 33 \]
4. **Write the result over the original denominator:**
\[ \frac{33}{7} \]

So, `4 5/7` as an improper fraction is \(\frac{33}{7}\).

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**(iii) Convert `7 9/13` into an improper fraction:**

1. **Identify the whole number and the fraction:** The whole number is `7` and the fraction is `9/13`.
2. **Multiply the whole number by the denominator of the fraction:**
\[ 7 \times 13 = 91 \]
3. **Add the result to the numerator of the fraction:**
\[ 91 + 9 = 100 \]
4. **Write the result over the original denominator:**
\[ \frac{100}{13} \]

So, `7 9/13` as an improper fraction is \(\frac{100}{13}\).

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**(iv) Convert `12 6/25` into an improper fraction:**

1. **Identify the whole number and the fraction:** The whole number is `12` and the fraction is `6/25`.
2. **Multiply the whole number by the denominator of the fraction:**
\[ 12 \times 25 = 300 \]
3. **Add the result to the numerator of the fraction:**
\[ 300 + 6 = 306 \]
4. **Write the result over the original denominator:**
\[ \frac{306}{25} \]

So, `12 6/25` as an improper fraction is \(\frac{306}{25}\).

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### Final Answers:
1. \(1 \frac{3}{4} = \frac{7}{4}\)
2. \(4 \frac{5}{7} = \frac{33}{7}\)
3. \(7 \frac{9}{13} = \frac{100}{13}\)
4. \(12 \frac{6}{25} = \frac{306}{25}\)

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