Henry needs to solve the problem 5 and 1/2−1 and 3/7

Question

. What is the difference?(1 point)

Answer 1

To solve the problem \( 5 \frac{1}{2} - 1 \frac{3}{7} \), we first need to convert the mixed numbers into improper fractions.

1. Convert \( 5 \frac{1}{2} \): \[ 5 \frac{1}{2} = \frac{5 \times 2 + 1}{2} = \frac{10 + 1}{2} = \frac{11}{2} \]

2. Convert \( 1 \frac{3}{7} \): \[ 1 \frac{3}{7} = \frac{1 \times 7 + 3}{7} = \frac{7 + 3}{7} = \frac{10}{7} \]

Now we need to perform the subtraction \( \frac{11}{2} - \frac{10}{7} \). To do this, we need a common denominator. The least common multiple of 2 and 7 is 14.

3. Convert \( \frac{11}{2} \) and \( \frac{10}{7} \) to have a denominator of 14: \[ \frac{11}{2} = \frac{11 \times 7}{2 \times 7} = \frac{77}{14} \] \[ \frac{10}{7} = \frac{10 \times 2}{7 \times 2} = \frac{20}{14} \]

4. Now subtract the two fractions: \[ \frac{77}{14} - \frac{20}{14} = \frac{77 - 20}{14} = \frac{57}{14} \]

5. Convert \( \frac{57}{14} \) back to a mixed number: \[ 57 \div 14 = 4 \quad \text{with a remainder of } 1 \] Thus, \( \frac{57}{14} = 4 \frac{1}{14} \).

Therefore, the difference \( 5 \frac{1}{2} - 1 \frac{3}{7} \) is \( \boxed{4 \frac{1}{14}} \).