Find: d. `(4)/(25) div (16)/( 35)`

Answer

To solve the problem \( \frac{4}{25} \div \frac{16}{35} \), we can follow these steps:

### Step 1: Write the division of fractions
We start by writing the division of the two fractions:
\[ \frac{4}{25} \div \frac{16}{35} \]

### Step 2: Change division to multiplication
To divide by a fraction, we multiply by its reciprocal. The reciprocal of \( \frac{16}{35} \) is \( \frac{35}{16} \). Therefore, we can rewrite the expression as:
\[ \frac{4}{25} \times \frac{35}{16} \]

### Step 3: Multiply the fractions
Now we multiply the numerators and the denominators:
\[ \frac{4 \times 35}{25 \times 16} \]

### Step 4: Calculate the products
Calculating the products in the numerator and denominator:
- Numerator: \( 4 \times 35 = 140 \)
- Denominator: \( 25 \times 16 = 400 \)

So we have:
\[ \frac{140}{400} \]

### Step 5: Simplify the fraction
Now, we simplify \( \frac{140}{400} \). We can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 20:
- \( 140 \div 20 = 7 \)
- \( 400 \div 20 = 20 \)

Thus, we get:
\[ \frac{7}{20} \]

### Final Answer
The result of \( \frac{4}{25} \div \frac{16}{35} \) is:
\[ \frac{7}{20} \]

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