Sure, let's solve these fraction problems step-by-step.
### Problem 1: [tex]\(\frac{7}{6} + \frac{3}{5}\)[/tex]
1. Find a common denominator:
The denominators are 6 and 5. The least common multiple (LCM) of 6 and 5 is 30.
2. Convert each fraction to the common denominator:
- [tex]\(\frac{7}{6}\)[/tex] becomes [tex]\(\frac{7 \times 5}{6 \times 5} = \frac{35}{30}\)[/tex]
- [tex]\(\frac{3}{5}\)[/tex] becomes [tex]\(\frac{3 \times 6}{5 \times 6} = \frac{18}{30}\)[/tex]
3. Add the fractions:
- [tex]\(\frac{35}{30} + \frac{18}{30} = \frac{35 + 18}{30} = \frac{53}{30}\)[/tex]
So, [tex]\(\frac{7}{6} + \frac{3}{5} = \frac{53}{30}\)[/tex].
### Problem 2: [tex]\(\frac{9}{12} - \frac{1}{3}\)[/tex]
1. Find a common denominator:
The denominators are 12 and 3. The least common multiple (LCM) of 12 and 3 is 12.
2. Convert each fraction to the common denominator:
- [tex]\(\frac{9}{12}\)[/tex] remains as [tex]\(\frac{9}{12}\)[/tex]
- [tex]\(\frac{1}{3}\)[/tex] becomes [tex]\(\frac{1 \times 4}{3 \times 4} = \frac{4}{12}\)[/tex]
3. Subtract the fractions:
- [tex]\(\frac{9}{12} - \frac{4}{12} = \frac{9 - 4}{12} = \frac{5}{12}\)[/tex]
So, [tex]\(\frac{9}{12} - \frac{1}{3} = \frac{5}{12}\)[/tex].
### Final Answers:
1. [tex]\(\frac{7}{6} + \frac{3}{5} = \frac{53}{30}\)[/tex]
2. [tex]\(\frac{9}{12} - \frac{1}{3} = \frac{5}{12}\)[/tex]
