Let's solve the expression $11 \frac{3}{10} + 13 + 25 \frac{5}{12}$.

Step 1: Convert the mixed numbers to improper fractions

• $11 \frac{3}{10} = \frac{113}{10}$
• $25 \frac{5}{12} = \frac{305}{12}$

So, the expression becomes: $\frac{113}{10} + 13 + \frac{305}{12}$

Step 2: Convert the whole number 13 to a fraction

$13 = \frac{130}{10} = \frac{156}{12}$

Step 3: Find the common denominator

The least common denominator (LCD) of 10 and 12 is 60.

• Convert $\frac{113}{10}$ to have a denominator of 60: $\frac{113}{10} = \frac{113 \times 6}{10 \times 6} = \frac{678}{60}$
• Convert $\frac{305}{12}$ to have a denominator of 60: $\frac{305}{12} = \frac{305 \times 5}{12 \times 5} = \frac{1525}{60}$
• Convert $13 = \frac{156}{12}$ to have a denominator of 60: $\frac{156}{12} = \frac{156 \times 5}{12 \times 5} = \frac{780}{60}$

Step 4: Add the fractions

Now, sum the fractions: $\frac{678}{60} + \frac{780}{60} + \frac{1525}{60} = \frac{678 + 780 + 1525}{60} = \frac{2983}{60}$

Step 5: Simplify the result

The fraction $\frac{2983}{60}$ is already in its simplest form, and as a mixed number, it becomes: $49 \frac{43}{60}$

Thus, the sum is: $49 \frac{43}{60}$

Would you like more details on any step?

5 Related Questions:

1. How do you convert mixed numbers into improper fractions?
2. What is the process of finding the least common denominator (LCD)?
3. How do you convert whole numbers to fractions for addition?
4. How can you simplify large fractions to mixed numbers?
5. Why is it important to work with a common denominator when adding fractions?

Tip:

When working with mixed numbers, always convert them to improper fractions first to make calculations easier.