Question

Find a difference 10 1/2 - 3 5/7

Answer 1

To find the difference between \( 10 \frac{1}{2} \) and \( 3 \frac{5}{7} \), we first convert the mixed numbers into improper fractions.

1. Convert \( 10 \frac{1}{2} \):
\[
10 \frac{1}{2} = 10 \times 2 + 1 = 20 + 1 = 21 \quad \text{(improper fraction is } \frac{21}{2} \text{)}
\]

2. Convert \( 3 \frac{5}{7} \):
\[
3 \frac{5}{7} = 3 \times 7 + 5 = 21 + 5 = 26 \quad \text{(improper fraction is } \frac{26}{7} \text{)}
\]

Next, we need to find the difference \( \frac{21}{2} - \frac{26}{7} \). To do this, we need a common denominator. The least common multiple of 2 and 7 is 14.

3. Convert \( \frac{21}{2} \) to have a denominator of 14:
\[
\frac{21}{2} = \frac{21 \times 7}{2 \times 7} = \frac{147}{14}
\]

4. Convert \( \frac{26}{7} \) to have a denominator of 14:
\[
\frac{26}{7} = \frac{26 \times 2}{7 \times 2} = \frac{52}{14}
\]

Now, we can subtract the two fractions:
\[
\frac{147}{14} - \frac{52}{14} = \frac{147 - 52}{14} = \frac{95}{14}
\]

The improper fraction \( \frac{95}{14} \) can be converted back to a mixed number. Dividing 95 by 14 gives:
\[
95 \div 14 = 6 \quad \text{(remainder } 11\text{)}
\]
So, \( \frac{95}{14} = 6 \frac{11}{14} \).

Thus, the difference \( 10 \frac{1}{2} - 3 \frac{5}{7} \) is:
\[
\boxed{6 \frac{11}{14}}
\]