Sure! Let's solve the problem of adding the fractions [tex]\( \frac{3}{4} \)[/tex] and [tex]\( \frac{1}{8} \)[/tex].
1. Identify the fractions:
We are given the fractions [tex]\( \frac{3}{4} \)[/tex] and [tex]\( \frac{1}{8} \)[/tex].
2. Find a common denominator:
The denominators of the fractions are 4 and 8. To add the fractions, we need a common denominator. The smallest common multiple of 4 and 8 is 8.
3. Convert each fraction to an equivalent fraction with the common denominator:
- For [tex]\( \frac{3}{4} \)[/tex]:
[tex]\[
\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}
\][/tex]
- For [tex]\( \frac{1}{8} \)[/tex]:
[tex]\[
\frac{1}{8} \text{ (this fraction already has 8 as the denominator)}
\][/tex]
4. Add the fractions:
Now that both fractions have the same denominator, we can add the numerators while keeping the denominator the same:
[tex]\[
\frac{6}{8} + \frac{1}{8} = \frac{6 + 1}{8} = \frac{7}{8}
\][/tex]
5. Write the result:
The sum of [tex]\( \frac{3}{4} \)[/tex] and [tex]\( \frac{1}{8} \)[/tex] is [tex]\( \frac{7}{8} \)[/tex].
6. Convert the answer to a decimal (optional):
[tex]\( \frac{7}{8} \)[/tex] can also be written as a decimal:
[tex]\[
\frac{7}{8} = 0.875
\][/tex]
Therefore, the detailed step-by-step solution for adding [tex]\( \frac{3}{4} \)[/tex] and [tex]\( \frac{1}{8} \)[/tex] results in [tex]\( \frac{7}{8} \)[/tex] or 0.875.
