To subtract the fractions [tex]\(\frac{4}{7}\)[/tex] and [tex]\(\frac{1}{2}\)[/tex], follow these steps:
1. Find a common denominator: The denominators here are 7 and 2. The least common multiple of 7 and 2 is 14. So, we will convert both fractions to have a denominator of 14.
2. Convert each fraction to the common denominator:
- For [tex]\(\frac{4}{7}\)[/tex]:
[tex]\[
\frac{4}{7} = \frac{4 \times 2}{7 \times 2} = \frac{8}{14}
\][/tex]
- For [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[
\frac{1}{2} = \frac{1 \times 7}{2 \times 7} = \frac{7}{14}
\][/tex]
3. Subtract the numerators while keeping the common denominator:
[tex]\[
\frac{8}{14} - \frac{7}{14} = \frac{8 - 7}{14} = \frac{1}{14}
\][/tex]
4. Simplify the fraction (if necessary): In this case, [tex]\(\frac{1}{14}\)[/tex] is already in its simplest form.
Therefore, the result of [tex]\(\frac{4}{7} - \frac{1}{2}\)[/tex] is [tex]\(\frac{1}{14}\)[/tex].
For verification, the decimal form of [tex]\(\frac{1}{14}\)[/tex] is approximately [tex]\(0.07142857142857142\)[/tex].
[tex]\[
\boxed{\frac{1}{14}}
\][/tex]
