To solve the problem [tex]\(-\frac{2}{15} + \frac{5}{12}\)[/tex], we follow these steps:
1. Identify the fractions involved:
- The first fraction is [tex]\(-\frac{2}{15}\)[/tex].
- The second fraction is [tex]\(\frac{5}{12}\)[/tex].
2. Find a common denominator:
- The denominators are 15 and 12.
- The least common multiple (LCM) of 15 and 12 is 60.
3. Convert each fraction to an equivalent fraction with the common denominator of 60:
- For [tex]\(-\frac{2}{15}\)[/tex]:
- [tex]\(-\frac{2}{15} = -\frac{2 \times 4}{15 \times 4} = -\frac{8}{60}\)[/tex].
- For [tex]\(\frac{5}{12}\)[/tex]:
- [tex]\(\frac{5}{12} = \frac{5 \times 5}{12 \times 5} = \frac{25}{60}\)[/tex].
4. Add the fractions:
- [tex]\(-\frac{8}{60} + \frac{25}{60}\)[/tex]:
- Combine the numerators: [tex]\(-8 + 25 = 17\)[/tex].
- The denominator remains the same: [tex]\(60\)[/tex].
Therefore, [tex]\(-\frac{8}{60} + \frac{25}{60} = \frac{17}{60}\)[/tex].
5. Simplify the result if possible:
- The fraction [tex]\(\frac{17}{60}\)[/tex] cannot be simplified further because 17 is a prime number and not a divisor of 60.
6. Convert the fraction to a decimal (if needed):
- [tex]\(\frac{17}{60} \approx 0.2833333333333333\)[/tex].
Thus, [tex]\(-\frac{2}{15} + \frac{5}{12}\)[/tex] is approximately [tex]\(0.2833333333333333\)[/tex] as a decimal.
