To add the fractions [tex]\( \frac{2}{3} \)[/tex] and [tex]\( \frac{1}{4} \)[/tex], we follow these steps:
1. Find the Least Common Denominator (LCD):
- The denominators of the fractions are 3 and 4.
- We need to find the least common multiple (LCM) of these denominators.
- The LCM of 3 and 4 is 12.
2. Convert each fraction to an equivalent fraction with the LCD as the new denominator:
- For [tex]\( \frac{2}{3} \)[/tex]:
[tex]\[
\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}
\][/tex]
- For [tex]\( \frac{1}{4} \)[/tex]:
[tex]\[
\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}
\][/tex]
3. Add the fractions with the common denominator:
- Now that both fractions have the same denominator (12), we can add them directly:
[tex]\[
\frac{8}{12} + \frac{3}{12} = \frac{8 + 3}{12} = \frac{11}{12}
\][/tex]
So, the sum of [tex]\( \frac{2}{3} \)[/tex] and [tex]\( \frac{1}{4} \)[/tex] is [tex]\( \frac{11}{12} \)[/tex].
