To subtract the fractions [tex]\(\frac{7}{8}\)[/tex] and [tex]\(\frac{1}{2}\)[/tex], follow these steps:
1. Find the Least Common Denominator (LCD):
The denominators of the given fractions are 8 and 2.
The least common denominator (LCD) of 8 and 2 is 8.
2. Adjust fractions to have the same denominator:
- The first fraction [tex]\(\frac{7}{8}\)[/tex] already has the denominator 8, so it remains [tex]\(\frac{7}{8}\)[/tex].
- For the second fraction [tex]\(\frac{1}{2}\)[/tex], adjust it to have the denominator 8:
[tex]\[
\frac{1}{2} = \frac{1 \times 4}{2 \times 4} = \frac{4}{8}
\][/tex]
3. Subtract the numerators:
Now that both fractions have the same denominator, subtract the numerators:
[tex]\[
\frac{7}{8} - \frac{4}{8} = \frac{7 - 4}{8} = \frac{3}{8}
\][/tex]
4. Simplify the result:
The fraction [tex]\(\frac{3}{8}\)[/tex] is already in its simplest form because the greatest common divisor (GCD) of 3 and 8 is 1.
Thus, the answer is:
[tex]\[
\boxed{\frac{3}{8}}
\][/tex]
