To solve the problem of adding the fractions [tex]\( \frac{1}{3} + \frac{1}{4} \)[/tex], we follow these steps:
1. Find a common denominator:
- The denominators of the fractions [tex]\( \frac{1}{3} \)[/tex] and [tex]\( \frac{1}{4} \)[/tex] are 3 and 4, respectively.
- The least common denominator (LCD) of 3 and 4 is 12.
2. Convert each fraction to an equivalent fraction with the common denominator:
- For [tex]\( \frac{1}{3} \)[/tex], we need to multiply both the numerator and the denominator by 4 to make the denominator 12. This gives us [tex]\( \frac{1 \times 4}{3 \times 4} = \frac{4}{12} \)[/tex].
- For [tex]\( \frac{1}{4} \)[/tex], we need to multiply both the numerator and the denominator by 3 to make the denominator 12. This gives us [tex]\( \frac{1 \times 3}{4 \times 3} = \frac{3}{12} \)[/tex].
3. Add the fractions:
- Now that both fractions have the same denominator, we can add the numerators while keeping the denominator the same.
- Thus, [tex]\( \frac{4}{12} + \frac{3}{12} = \frac{4 + 3}{12} = \frac{7}{12} \)[/tex].
So, [tex]\( \frac{1}{3} + \frac{1}{4} = \frac{7}{12} \)[/tex].
Given the answer choices:
- [tex]\( \frac{4}{12} + \frac{3}{12} = \frac{7}{12} \)[/tex]
- [tex]\( \frac{1}{3} + \frac{1}{4} = \frac{2}{7} \)[/tex]
- [tex]\( \frac{1}{3} + \frac{1}{4} = \frac{2}{12} \)[/tex]
- [tex]\( \frac{4}{10} + \frac{3}{10} = \frac{7}{74} \)[/tex]
The correct answer is the first one:
[tex]\[ \frac{4}{12} + \frac{3}{12} = \frac{7}{12} \][/tex]
