Let's solve the expression step by step:

$2 \frac{6}{31} - \frac{5}{24} + \frac{25}{31} - 1 \frac{1}{24} + 0.25$

Step 1: Convert mixed fractions to improper fractions

• $2 \frac{6}{31} = \frac{62}{31}$
• $1 \frac{1}{24} = \frac{25}{24}$

Now the expression is: $\frac{62}{31} - \frac{5}{24} + \frac{25}{31} - \frac{25}{24} + 0.25$

Step 2: Convert 0.25 to a fraction

$0.25 = \frac{1}{4}$

Now the expression is: $\frac{62}{31} - \frac{5}{24} + \frac{25}{31} - \frac{25}{24} + \frac{1}{4}$

Step 3: Find the common denominators

The common denominator between 31, 24, and 4 is 744 (the least common multiple).

Now, express each fraction with denominator 744:

• $\frac{62}{31} = \frac{62 \times 24}{31 \times 24} = \frac{1488}{744}$
• $\frac{5}{24} = \frac{5 \times 31}{24 \times 31} = \frac{155}{744}$
• $\frac{25}{31} = \frac{25 \times 24}{31 \times 24} = \frac{600}{744}$
• $\frac{25}{24} = \frac{25 \times 31}{24 \times 31} = \frac{775}{744}$
• $\frac{1}{4} = \frac{1 \times 186}{4 \times 186} = \frac{186}{744}$

Step 4: Combine the fractions

Now, substitute these values into the expression: $\frac{1488}{744} - \frac{155}{744} + \frac{600}{744} - \frac{775}{744} + \frac{186}{744}$

Combine the numerators: $1488 - 155 + 600 - 775 + 186 = 1344$

Thus, the result is: $\frac{1344}{744}$

Step 5: Simplify the fraction

$\frac{1344}{744} = \frac{1344 \div 24}{744 \div 24} = \frac{56}{31}$

So, the final answer is: $\boxed{\frac{56}{31} \text{ or approximately } 1.806}$

Would you like further details or any clarification?

Here are 5 related questions for further practice:

1. How do you add and subtract mixed numbers with different denominators?
2. What is the importance of finding the least common multiple in fraction addition?
3. How do you convert decimals to fractions?
4. How can you simplify complex fractions more efficiently?
5. What are the steps to convert improper fractions back into mixed numbers?

Tip: When working with fractions, always check if you can simplify at each step to make calculations easier!