To solve the problem of adding the fractions [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{1}{2}\)[/tex], we will go through the steps methodically:
1. Find the Least Common Denominator (LCD):
- The denominators here are 4 and 2.
- The smallest number that both 4 and 2 divide into is 4.
- Thus, the LCD of 4 and 2 is 4.
2. Adjust the fractions to have the same denominator:
- The fraction [tex]\(\frac{3}{4}\)[/tex] already has the denominator 4, so it remains [tex]\(\frac{3}{4}\)[/tex].
- For the fraction [tex]\(\frac{1}{2}\)[/tex], we need to convert it to have the denominator 4. To do this, multiply both the numerator and the denominator by 2:
[tex]\[
\frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4}
\][/tex]
3. Add the numerators:
- Now that they have a common denominator, we can add the numerators directly:
[tex]\[
\frac{3}{4} + \frac{2}{4} = \frac{3 + 2}{4} = \frac{5}{4}
\][/tex]
4. Simplify if necessary:
- The fraction [tex]\(\frac{5}{4}\)[/tex] is already in its simplest form as 5 and 4 have no common divisors other than 1.
- Therefore, the result can be written as [tex]\(\frac{5}{4}\)[/tex].
So the result of [tex]\(\frac{3}{4} + \frac{1}{2} = \frac{5}{4}\)[/tex], which can also be expressed as a mixed number [tex]\(1 \frac{1}{4}\)[/tex] if preferred.
This is the detailed step-by-step solution for adding the fractions [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{1}{2}\)[/tex].
