Convert each of the following as a mixed fraction:
(i) 5.6
(ii) 12.25
(iii) 6.004
(iv) 4.625

Answer

To convert the given decimal numbers into mixed fractions, we will follow these steps for each number:

### (i) Convert 5.6 to a mixed fraction

1. **Remove the decimal**: Write 5.6 as a fraction. Since there is one digit after the decimal, we can express it as:
\[ 5.6 = \frac{56}{10} \]

2. **Simplify the fraction**: Divide both the numerator and the denominator by their greatest common divisor (GCD), which is 2:
\[ \frac{56 \div 2}{10 \div 2} = \frac{28}{5} \]

3. **Convert to mixed fraction**: Divide 28 by 5:
- 5 goes into 28 five times (5 × 5 = 25).
- The remainder is 3 (28 - 25 = 3).
- Thus, we can express it as:
\[ 5 \frac{3}{5} \]

### (ii) Convert 12.25 to a mixed fraction

1. **Remove the decimal**: Write 12.25 as a fraction. Since there are two digits after the decimal, we can express it as:
\[ 12.25 = \frac{1225}{100} \]

2. **Simplify the fraction**: Divide both the numerator and the denominator by their GCD, which is 25:
\[ \frac{1225 \div 25}{100 \div 25} = \frac{49}{4} \]

3. **Convert to mixed fraction**: Divide 49 by 4:
- 4 goes into 49 twelve times (4 × 12 = 48).
- The remainder is 1 (49 - 48 = 1).
- Thus, we can express it as:
\[ 12 \frac{1}{4} \]

### (iii) Convert 6.004 to a mixed fraction

1. **Remove the decimal**: Write 6.004 as a fraction. Since there are three digits after the decimal, we can express it as:
\[ 6.004 = \frac{6004}{1000} \]

2. **Simplify the fraction**: Divide both the numerator and the denominator by their GCD, which is 4:
\[ \frac{6004 \div 4}{1000 \div 4} = \frac{1501}{250} \]

3. **Convert to mixed fraction**: Divide 1501 by 250:
- 250 goes into 1501 six times (250 × 6 = 1500).
- The remainder is 1 (1501 - 1500 = 1).
- Thus, we can express it as:
\[ 6 \frac{1}{250} \]

### (iv) Convert 4.625 to a mixed fraction

1. **Remove the decimal**: Write 4.625 as a fraction. Since there are three digits after the decimal, we can express it as:
\[ 4.625 = \frac{4625}{1000} \]

2. **Simplify the fraction**: Divide both the numerator and the denominator by their GCD, which is 125:
\[ \frac{4625 \div 125}{1000 \div 125} = \frac{37}{8} \]

3. **Convert to mixed fraction**: Divide 37 by 8:
- 8 goes into 37 four times (8 × 4 = 32).
- The remainder is 5 (37 - 32 = 5).
- Thus, we can express it as:
\[ 4 \frac{5}{8} \]

### Summary of Mixed Fractions

- (i) \( 5.6 = 5 \frac{3}{5} \)
- (ii) \( 12.25 = 12 \frac{1}{4} \)
- (iii) \( 6.004 = 6 \frac{1}{250} \)
- (iv) \( 4.625 = 4 \frac{5}{8} \)