To add the fractions [tex]\(\frac{1}{8}\)[/tex] and [tex]\(\frac{3}{4}\)[/tex], follow these steps:
1. Find a Common Denominator:
- The denominators of the given fractions are 8 and 4.
- The smallest common multiple of 8 and 4 is 8. Thus, we will use 8 as our common denominator.
2. Convert the Fractions:
- The first fraction is already expressed with the denominator 8: [tex]\(\frac{1}{8}\)[/tex].
- For the second fraction [tex]\(\frac{3}{4}\)[/tex], we need to convert it to have the denominator 8.
- To do this, notice that [tex]\(4 \times 2 = 8\)[/tex]. Therefore, we need to multiply the numerator and the denominator of [tex]\(\frac{3}{4}\)[/tex] by 2:
[tex]\[\frac{3}{4} = \frac{3 \cdot 2}{4 \cdot 2} = \frac{6}{8}\][/tex]
3. Add the Fractions:
- Now that the fractions have the same denominator, we can add the numerators:
[tex]\[\frac{1}{8} + \frac{6}{8} = \frac{1 + 6}{8} = \frac{7}{8}\][/tex]
Thus, the complete step-by-step solution is:
- [tex]\(\frac{1}{8} = \frac{1}{8}\)[/tex]
- [tex]\(\frac{3}{4} = \frac{6}{8}\)[/tex]
- [tex]\(\frac{1}{8} + \frac{6}{8} = \frac{7}{8}\)[/tex]
So, the result of adding [tex]\(\frac{1}{8}\)[/tex] and [tex]\(\frac{3}{4}\)[/tex] is:
[tex]\[
\boxed{\frac{7}{8}}
\][/tex]
