Question

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

Explanation:

Assuming the problem is to find a common operation (like addition, subtraction, multiplication, or division) between the mixed numbers \( 2\frac{1}{3} \) and \( 1\frac{4}{5} \), let's take addition as an example (since the problem isn't specified, we'll proceed with addition for illustration).

Step 1: Convert mixed numbers to improper fractions

To add mixed numbers, first convert them to improper fractions. For \( 2\frac{1}{3} \):
\( 2\frac{1}{3}=\frac{2\times3 + 1}{3}=\frac{6 + 1}{3}=\frac{7}{3} \)
For \( 1\frac{4}{5} \):
\( 1\frac{4}{5}=\frac{1\times5 + 4}{5}=\frac{5 + 4}{5}=\frac{9}{5} \)

Step 2: Find a common denominator

The denominators are 3 and 5. The least common denominator (LCD) of 3 and 5 is \( 3\times5 = 15 \).

Step 3: Rewrite fractions with the LCD

Rewrite \( \frac{7}{3} \) with denominator 15: \( \frac{7}{3}=\frac{7\times5}{3\times5}=\frac{35}{15} \)
Rewrite \( \frac{9}{5} \) with denominator 15: \( \frac{9}{5}=\frac{9\times3}{5\times3}=\frac{27}{15} \)

Step 4: Add the fractions

Now add the two fractions: \( \frac{35}{15}+\frac{27}{15}=\frac{35 + 27}{15}=\frac{62}{15} \)

Step 5: Convert back to a mixed number (optional)

\( \frac{62}{15}=4\frac{2}{15} \) (since \( 15\times4 = 60 \) and \( 62-60 = 2 \))

Answer:

If adding, the result is \( \frac{62}{15} \) or \( 4\frac{2}{15} \). (If the intended operation was different, the steps would adjust accordingly, but this shows the process for addition.)