The provided image contains a series of mathematical problems involving fractions and mixed numbers. Let's solve them step by step.

(a)

$3 \frac{4}{5} - 4 \frac{1}{2} + 2 \frac{8}{9}$

1. Convert all mixed numbers to improper fractions:

   • $3 \frac{4}{5} = \frac{19}{5}$
   • $4 \frac{1}{2} = \frac{9}{2}$
   • $2 \frac{8}{9} = \frac{26}{9}$

2. Find the least common denominator (LCD):
   LCD of 5, 2, and 9 = 90.

3. Convert to equivalent fractions:

   • $\frac{19}{5} = \frac{342}{90}$
   • $\frac{9}{2} = \frac{405}{90}$
   • $\frac{26}{9} = \frac{260}{90}$

4. Perform the operations:
   $\frac{342}{90} - \frac{405}{90} + \frac{260}{90} = \frac{342 - 405 + 260}{90} = \frac{197}{90}$

5. Simplify the result:
   $\frac{197}{90}$ (already in simplest form).

(b)

$4 \frac{1}{2} + 3 \frac{2}{3} \times 1 \frac{2}{3} + 1 \frac{3}{11}$

1. Convert all mixed numbers to improper fractions:

   • $4 \frac{1}{2} = \frac{9}{2}$
   • $3 \frac{2}{3} = \frac{11}{3}$
   • $1 \frac{2}{3} = \frac{5}{3}$
   • $1 \frac{3}{11} = \frac{14}{11}$

2. Perform the multiplication: $\frac{11}{3} \times \frac{5}{3} = \frac{55}{9}$

3. Find the LCD for $\frac{9}{2}$, $\frac{55}{9}$, and $\frac{14}{11}$:
   LCD = 198.

4. Convert to equivalent fractions:

   • $\frac{9}{2} = \frac{891}{198}$
   • $\frac{55}{9} = \frac{1210}{198}$
   • $\frac{14}{11} = \frac{252}{198}$

5. Perform the addition: $\frac{891}{198} + \frac{1210}{198} + \frac{252}{198} = \frac{891 + 1210 + 252}{198} = \frac{2353}{198}$

6. Simplify the result:
   $\frac{2353}{198}$ (already in simplest form).

(c)

$1 \frac{3}{13} \times 2 \frac{1}{6} - 1 \frac{5}{8}$

1. Convert all mixed numbers to improper fractions:

   • $1 \frac{3}{13} = \frac{16}{13}$
   • $2 \frac{1}{6} = \frac{13}{6}$
   • $1 \frac{5}{8} = \frac{13}{8}$

2. Perform the multiplication: $\frac{16}{13} \times \frac{13}{6} = \frac{208}{78} = \frac{104}{39}$

3. Find the LCD for $\frac{104}{39}$ and $\frac{13}{8}$:
   LCD = 312.

4. Convert to equivalent fractions:

   • $\frac{104}{39} = \frac{832}{312}$
   • $\frac{13}{8} = \frac{507}{312}$

5. Perform the subtraction: $\frac{832}{312} - \frac{507}{312} = \frac{325}{312}$

6. Simplify the result:
   $\frac{325}{312}$ (already in simplest form).

Would you like me to continue solving (d), (e), and (f) or clarify any part of the solutions above? 😊

Related Questions:

1. What are the rules for converting mixed numbers to improper fractions?
2. How is the least common denominator calculated, and why is it important?
3. What is the process for simplifying fractions after performing operations?
4. How do you handle multiplication and addition/subtraction of fractions in combined problems?
5. Can all fractions be simplified into mixed numbers?

Tip:

When solving problems with mixed numbers and fractions, always double-check your conversions to improper fractions to avoid errors later in the calculations.