Divide:
g. `2 (4)/(7) div (45)/(14)`

Answer

To solve the problem \( 2 \frac{4}{7} \div \frac{45}{14} \), we will follow these steps:

### Step 1: Convert the mixed number to an improper fraction
The mixed number \( 2 \frac{4}{7} \) can be converted to an improper fraction.

\[ 2 \frac{4}{7} = \frac{(2 \times 7) + 4}{7} = \frac{14 + 4}{7} = \frac{18}{7} \]

### Step 2: Rewrite the division of fractions
Now, we need to divide \( \frac{18}{7} \) by \( \frac{45}{14} \). According to the rule of dividing fractions, we can rewrite the division as multiplication by the reciprocal:

\[ \frac{18}{7} \div \frac{45}{14} = \frac{18}{7} \times \frac{14}{45} \]

### Step 3: Multiply the fractions
Now, we multiply the fractions:

\[ \frac{18 \times 14}{7 \times 45} \]

### Step 4: Simplify the multiplication
Before multiplying, we can simplify the fractions.

1. The number 14 and 7 can be simplified:
\[ \frac{14}{7} = 2 \quad \text{(since 14 divided by 7 is 2)} \]

2. Now, substituting this back into the multiplication:
\[ \frac{18 \times 2}{45} \]

### Step 5: Calculate the numerator
Now, calculate the numerator:
\[ 18 \times 2 = 36 \]

So, we have:
\[ \frac{36}{45} \]

### Step 6: Simplify the fraction
Now, we simplify \( \frac{36}{45} \). Both 36 and 45 can be divided by 9:
\[ \frac{36 \div 9}{45 \div 9} = \frac{4}{5} \]

### Final Answer
Thus, the final answer is:
\[ \frac{4}{5} \]

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