To solve the problem of adding the fractions [tex]\(\frac{1}{4} + \frac{5}{8}\)[/tex], follow these detailed steps:
1. Find a common denominator:
- The denominators of the fractions are 4 and 8.
- The least common multiple (LCM) of 4 and 8 is 8. Therefore, 8 is the common denominator.
2. Convert each fraction to have the common denominator:
- For [tex]\(\frac{1}{4}\)[/tex], we need to convert it to a fraction with the denominator of 8. Multiply both the numerator and the denominator by 2:
[tex]\[
\frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8}
\][/tex]
- For [tex]\(\frac{5}{8}\)[/tex], the denominator is already 8, so we do not need to change the fraction. It remains:
[tex]\[
\frac{5}{8}
\][/tex]
3. Add the numerators:
- With both fractions having the same denominator, we can now add the numerators:
[tex]\[
\frac{2}{8} + \frac{5}{8} = \frac{2 + 5}{8} = \frac{7}{8}
\][/tex]
4. Simplify the result (if necessary):
- The fraction [tex]\(\frac{7}{8}\)[/tex] is already in its simplest form.
5. Convert fraction to decimal (optional):
- To find the decimal equivalent of [tex]\(\frac{7}{8}\)[/tex], divide the numerator by the denominator:
[tex]\[
\frac{7}{8} = 0.875
\][/tex]
Therefore, the sum of [tex]\(\frac{1}{4} + \frac{5}{8}\)[/tex] is [tex]\(\frac{7}{8}\)[/tex], or as a decimal, 0.875.
