Let's solve each of the fractional expressions step by step.

1. First Expression:

$\frac{2}{3} + \frac{1}{12}$ To add fractions, we need a common denominator. The least common denominator (LCD) of 3 and 12 is 12.

• Convert $\frac{2}{3}$ to have the denominator of 12: $\frac{2}{3} = \frac{8}{12}$ Now, add the fractions: $\frac{8}{12} + \frac{1}{12} = \frac{9}{12}$ Simplify: $\frac{9}{12} = \frac{3}{4}$ So, the result is: $\frac{2}{3} + \frac{1}{12} = \frac{3}{4}$

2. Second Expression:

$\frac{2}{3} - \frac{1}{2}$ Again, find a common denominator. The LCD of 3 and 2 is 6.

• Convert the fractions: $\frac{2}{3} = \frac{4}{6}, \quad \frac{1}{2} = \frac{3}{6}$ Now, subtract: $\frac{4}{6} - \frac{3}{6} = \frac{1}{6}$ So, the result is: $\frac{2}{3} - \frac{1}{2} = \frac{1}{6}$

3. Third Expression:

$\frac{7}{9} - \frac{1}{3}$ Find a common denominator. The LCD of 9 and 3 is 9.

• Convert $\frac{1}{3}$ to have a denominator of 9: $\frac{1}{3} = \frac{3}{9}$ Now, subtract: $\frac{7}{9} - \frac{3}{9} = \frac{4}{9}$ So, the result is: $\frac{7}{9} - \frac{1}{3} = \frac{4}{9}$

Final Answers:

1. $\frac{2}{3} + \frac{1}{12} = \frac{3}{4}$
2. $\frac{2}{3} - \frac{1}{2} = \frac{1}{6}$
3. $\frac{7}{9} - \frac{1}{3} = \frac{4}{9}$

Would you like more details on any of these steps?

Here are 5 related questions:

1. How do you find the least common denominator (LCD) of two fractions?
2. Can you explain how to subtract fractions with different denominators?
3. How do you simplify a fraction after performing addition or subtraction?
4. What happens when the numerator is larger than the denominator in a subtraction problem?
5. How can you convert mixed fractions into improper fractions for easier calculation?

Tip: Always simplify fractions to their lowest terms after performing operations!