Question

2\frac{1}{4} and 3\frac{1}{5}

Explanation:

Assuming the problem is to add the mixed numbers \( 2\frac{1}{4} \) and \( 3\frac{1}{5} \).

Step 1: Convert mixed numbers to improper fractions

For \( 2\frac{1}{4} \):
\( 2\frac{1}{4}=\frac{2\times4 + 1}{4}=\frac{8+1}{4}=\frac{9}{4} \)

For \( 3\frac{1}{5} \):
\( 3\frac{1}{5}=\frac{3\times5+1}{5}=\frac{15 + 1}{5}=\frac{16}{5} \)

Step 2: Find a common denominator

The least common denominator of 4 and 5 is \( 4\times5 = 20 \).

Step 3: Rewrite fractions with the common denominator

\( \frac{9}{4}=\frac{9\times5}{4\times5}=\frac{45}{20} \)
\( \frac{16}{5}=\frac{16\times4}{5\times4}=\frac{64}{20} \)

Step 4: Add the fractions

\( \frac{45}{20}+\frac{64}{20}=\frac{45 + 64}{20}=\frac{109}{20} \)

Step 5: Convert back to a mixed number (if needed)

\( \frac{109}{20}=5\frac{9}{20} \)

(If the problem was multiplication or another operation, the steps would adjust accordingly. Since the operation wasn't specified clearly from the image, addition is a common operation with mixed numbers. If it was another operation, for example, multiplication:

Step 1: Convert to improper fractions (same as above)

\( 2\frac{1}{4}=\frac{9}{4} \), \( 3\frac{1}{5}=\frac{16}{5} \)

Step 2: Multiply the fractions

\( \frac{9}{4}\times\frac{16}{5}=\frac{9\times16}{4\times5}=\frac{144}{20}=\frac{36}{5}=7\frac{1}{5} \)

Since the problem's operation is unclear, but assuming addition as a common scenario, the result of addition is shown above. If it was another operation, the steps would change.)

Answer:

If adding: \( 5\frac{9}{20} \) (or \( \frac{109}{20} \))
If multiplying: \( 7\frac{1}{5} \) (or \( \frac{36}{5} \))

(Note: Since the operation in the problem was not clearly stated from the image, both common operations (addition and multiplication) with mixed numbers are provided as possible solutions.)