To simplify the expression [tex]\(\frac{1}{2} + \frac{1}{4}\)[/tex], follow these steps:
1. Find a common denominator:
- The denominators of the fractions are 2 and 4.
- The least common multiple (LCM) of 2 and 4 is 4.
2. Convert each fraction to have the common denominator:
- For [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[
\frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4}
\][/tex]
- The fraction [tex]\(\frac{1}{4}\)[/tex] already has the common denominator of 4.
3. Add the numerators:
- Now that both fractions have the same denominator, add their numerators:
[tex]\[
\frac{2}{4} + \frac{1}{4} = \frac{2 + 1}{4} = \frac{3}{4}
\][/tex]
4. Simplify the result (if necessary):
- The fraction [tex]\(\frac{3}{4}\)[/tex] is already in its simplest form because 3 and 4 have no common divisors other than 1.
Therefore, the simplified form of [tex]\(\frac{1}{2} + \frac{1}{4}\)[/tex] is [tex]\(\frac{3}{4}\)[/tex].
