To subtract the fractions [tex]\(\frac{1}{8}\)[/tex] and [tex]\(\frac{1}{4}\)[/tex], we need to follow a few mathematical steps.
1. Find a common denominator: The denominators in the given fractions are 8 and 4. The smallest common denominator that both 8 and 4 can divide into without leaving a remainder is 8.
2. Rewrite each fraction with the common denominator:
- [tex]\(\frac{1}{8}\)[/tex] remains [tex]\(\frac{1}{8}\)[/tex] because it already has the common denominator.
- To rewrite [tex]\(\frac{1}{4}\)[/tex] with a denominator of 8, we multiply both the numerator and the denominator by 2:
[tex]\[
\frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8}
\][/tex]
3. Subtract the fractions:
Now that both fractions have the same denominator, we can subtract the numerators while keeping the denominator constant:
[tex]\[
\frac{1}{8} - \frac{2}{8} = \frac{1 - 2}{8} = \frac{-1}{8}
\][/tex]
4. Simplify the result:
The fraction [tex]\(\frac{-1}{8}\)[/tex] is already in its simplest form, as the numerator and denominator have no common factors other than 1.
Therefore, the final answer is:
[tex]\[
\frac{1}{8} - \frac{1}{4} = -\frac{1}{8}
\][/tex]
In decimal form, the result of this subtraction is [tex]\(-0.125\)[/tex].
