To solve the problem \( 5 \frac{1}{2} - 1 \frac{3}{7} \), we can follow these steps:
- Convert the mixed numbers to improper fractions.
- Find a common denominator.
- Subtract the fractions.
- Simplify if necessary.
Step 1: Convert mixed numbers to improper fractions
For \( 5 \frac{1}{2} \): \[ 5 \frac{1}{2} = 5 \times 2 + 1 = 10 + 1 = \frac{11}{2} \]
For \( 1 \frac{3}{7} \): \[ 1 \frac{3}{7} = 1 \times 7 + 3 = 7 + 3 = \frac{10}{7} \]
Step 2: Find a common denominator
The denominators are 2 and 7. The least common multiple of 2 and 7 is 14.
Step 3: Convert both fractions to have the common denominator
For \( \frac{11}{2} \): \[ \frac{11}{2} = \frac{11 \times 7}{2 \times 7} = \frac{77}{14} \]
For \( \frac{10}{7} \): \[ \frac{10}{7} = \frac{10 \times 2}{7 \times 2} = \frac{20}{14} \]
Step 4: Subtract the fractions
Now, we can subtract: \[ \frac{77}{14} - \frac{20}{14} = \frac{77 - 20}{14} = \frac{57}{14} \]
Step 5: Simplify if necessary
The fraction \( \frac{57}{14} \) is already in its simplest form, but we can convert it back to a mixed number: \[ 57 \div 14 = 4 \quad \text{(the whole part)} \] The remainder is: \[ 57 - 4 \times 14 = 57 - 56 = 1 \] So, \[ \frac{57}{14} = 4 \frac{1}{14} \]
Conclusion
The difference \( 5 \frac{1}{2} - 1 \frac{3}{7} \) is \( 4 \frac{1}{14} \).