`2(2/5) // 2(1/5) =2`

Answer

To solve the equation \( \frac{2 \frac{2}{5}}{2 \frac{1}{5}} = 2 \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed numbers \( 2 \frac{2}{5} \) and \( 2 \frac{1}{5} \) into improper fractions.

- For \( 2 \frac{2}{5} \):
\[ 2 \frac{2}{5} = 2 \times 5 + 2 = 10 + 2 = \frac{12}{5} \]

- For \( 2 \frac{1}{5} \):
\[ 2 \frac{1}{5} = 2 \times 5 + 1 = 10 + 1 = \frac{11}{5} \]

### Step 2: Substitute the Improper Fractions into the Equation
Now substitute the improper fractions back into the equation:
\[ \frac{\frac{12}{5}}{\frac{11}{5}} \]

### Step 3: Simplify the Division of Fractions
To divide fractions, we multiply by the reciprocal:
\[ \frac{12}{5} \div \frac{11}{5} = \frac{12}{5} \times \frac{5}{11} \]

### Step 4: Cancel Common Factors
In the multiplication, we can cancel the \( 5 \) in the numerator and the denominator:
\[ \frac{12}{1} \times \frac{1}{11} = \frac{12}{11} \]

### Step 5: Check if the Result Equals 2
Now we need to check if \( \frac{12}{11} \) equals \( 2 \). To do this, we can convert \( 2 \) into a fraction:
\[ 2 = \frac{22}{11} \]

### Step 6: Compare the Two Fractions
Now we compare \( \frac{12}{11} \) with \( \frac{22}{11} \):
\[ \frac{12}{11} \neq \frac{22}{11} \]

### Conclusion
The left-hand side does not equal the right-hand side, so the equation \( \frac{2 \frac{2}{5}}{2 \frac{1}{5}} = 2 \) is not true.