Question

3 wholes and 4 sevenths minus 1 whole and 5 forteenths

Answer 1

To solve the problem \(3 \frac{4}{7} - 1 \frac{5}{14}\), we first need to convert both mixed numbers into improper fractions.

1. Convert \(3 \frac{4}{7}\) into an improper fraction:
\[
3 \frac{4}{7} = \frac{(3 \times 7) + 4}{7} = \frac{21 + 4}{7} = \frac{25}{7}
\]

2. Convert \(1 \frac{5}{14}\) into an improper fraction:
\[
1 \frac{5}{14} = \frac{(1 \times 14) + 5}{14} = \frac{14 + 5}{14} = \frac{19}{14}
\]

Now, we have:
\[
\frac{25}{7} - \frac{19}{14}
\]

To subtract the fractions, we need a common denominator. The least common multiple of 7 and 14 is 14.

3. Convert \(\frac{25}{7}\) to have a denominator of 14:
\[
\frac{25}{7} = \frac{25 \times 2}{7 \times 2} = \frac{50}{14}
\]

Now we can subtract the two fractions:
\[
\frac{50}{14} - \frac{19}{14} = \frac{50 - 19}{14} = \frac{31}{14}
\]

Finally, converting \(\frac{31}{14}\) back to a mixed number:
\[
\frac{31}{14} = 2 \frac{3}{14}
\]

Therefore, the final answer is:
\[
\boxed{2 \frac{3}{14}}
\]