I see that you've uploaded a worksheet related to adding and subtracting mixed fractions. I will guide you through solving these problems step by step.

Let's start with problem 1 as an example:

1. $2 \frac{1}{5} + 1 \frac{3}{4}$

Step-by-step solution:

1. Convert both mixed numbers to improper fractions:

   • $2 \frac{1}{5} = \frac{11}{5}$ (because $2 \times 5 + 1 = 11$)
   • $1 \frac{3}{4} = \frac{7}{4}$ (because $1 \times 4 + 3 = 7$)

2. Find a common denominator for $\frac{11}{5}$ and $\frac{7}{4}$. The least common denominator (LCD) is 20.

   • $\frac{11}{5} = \frac{44}{20}$
   • $\frac{7}{4} = \frac{35}{20}$

3. Add the fractions:

   • $\frac{44}{20} + \frac{35}{20} = \frac{79}{20}$

4. Convert $\frac{79}{20}$ back to a mixed number:

   • $\frac{79}{20} = 3 \frac{19}{20}$

So, the solution to $2 \frac{1}{5} + 1 \frac{3}{4}$ is $3 \frac{19}{20}$.

Would you like me to work through the other problems as well?

Related Questions:

1. How do you find the least common denominator when adding fractions?
2. How do you convert a mixed number into an improper fraction?
3. What is the difference between adding and subtracting mixed fractions?
4. How do you simplify improper fractions to mixed numbers?
5. Can you use cross-multiplication to find a common denominator?

Tip:

Always simplify the final result to its lowest terms by checking if the numerator and denominator have any common factors.