Divide:
f. `4 (2)/(7) div 2 (2)/(5)`

Answer

To solve the problem \( 4 \frac{2}{7} \div 2 \frac{2}{5} \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed numbers into improper fractions.

For \( 4 \frac{2}{7} \):
\[ 4 \frac{2}{7} = \frac{(4 \times 7) + 2}{7} = \frac{28 + 2}{7} = \frac{30}{7} \]

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

### Step 2: Rewrite the Division as Multiplication
Now we can rewrite the division of fractions as multiplication by the reciprocal of the second fraction:
\[ \frac{30}{7} \div \frac{12}{5} = \frac{30}{7} \times \frac{5}{12} \]

### Step 3: Multiply the Numerators and Denominators
Now we multiply the numerators and the denominators:
\[ \frac{30 \times 5}{7 \times 12} = \frac{150}{84} \]

### Step 4: Simplify the Fraction
Next, we simplify the fraction \( \frac{150}{84} \). We can find the greatest common divisor (GCD) of 150 and 84, which is 6.

Now we divide both the numerator and the denominator by 6:
\[ \frac{150 \div 6}{84 \div 6} = \frac{25}{14} \]

### Step 5: Convert Back to Mixed Number (if necessary)
Since \( \frac{25}{14} \) is an improper fraction, we can convert it back to a mixed number:
\[ 25 \div 14 = 1 \quad \text{(whole part)} \]
\[ 25 - (14 \times 1) = 11 \quad \text{(remainder)} \]
So, \( \frac{25}{14} = 1 \frac{11}{14} \).

### Final Answer
Thus, the result of \( 4 \frac{2}{7} \div 2 \frac{2}{5} \) is:
\[ 1 \frac{11}{14} \]

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