To simplify the expression [tex]\(\frac{q}{2} - 0.25q + \frac{q}{8}\)[/tex], follow these steps:
1. Convert all terms to a common denominator of 8 to simplify addition:
- [tex]\(\frac{q}{2}\)[/tex] is equivalent to [tex]\(\frac{4q}{8}\)[/tex] because [tex]\( \frac{q}{2} = \frac{q \cdot 4}{2 \cdot 4} = \frac{4q}{8} \)[/tex].
- [tex]\(0.25q\)[/tex] is equivalent to [tex]\(\frac{2q}{8}\)[/tex] because [tex]\( 0.25q = \frac{1}{4}q = \frac{q \cdot 2}{4 \cdot 2} = \frac{2q}{8} \)[/tex].
- [tex]\(\frac{q}{8}\)[/tex] remains as is since it already has a denominator of 8.
2. Rewrite the expression with common denominators:
- The original expression [tex]\(\frac{q}{2} - 0.25q + \frac{q}{8}\)[/tex] becomes [tex]\(\frac{4q}{8} - \frac{2q}{8} + \frac{q}{8}\)[/tex].
3. Combine the fractions:
- Now, add or subtract the fractions by combining the numerators while keeping the common denominator:
[tex]\[ \frac{4q}{8} - \frac{2q}{8} + \frac{q}{8} = \frac{4q - 2q + q}{8} = \frac{3q}{8} \][/tex]
4. Simplify the fraction:
- After combining the fractions, we get [tex]\(\frac{3q}{8}\)[/tex].
The simplified form of [tex]\(\frac{q}{2} - 0.25q + \frac{q}{8}\)[/tex] is therefore [tex]\(\frac{3q}{8}\)[/tex].
However, based on further simplification, we find that this simplified expression is actually calculated as [tex]\(0.375q\)[/tex]. This means that [tex]\(\frac{3}{8}\)[/tex] in decimal form is 0.375.
Thus, the final simplified form of [tex]\(\frac{q}{2} - 0.25q + \frac{q}{8}\)[/tex] is:
[tex]\[ 0.375q \][/tex]
