the expression 12/35 x 3/5 is a fraction a/b where b is positive and a and b have no common factors.

To simplify the expression \(\frac{12}{35} \times \frac{3}{5}\), follow these steps:

1. **Multiply the numerators**:
   \[
   12 \times 3 = 36
   \]

2. **Multiply the denominators**:
   \[
   35 \times 5 = 175
   \]

So, the product is:
\[
\frac{36}{175}
\]

3. **Simplify the fraction** if possible:
   - The numerator is 36, and the denominator is 175.
   - We need to check if 36 and 175 have any common factors.

   The prime factorization of 36 is:
   \[
   36 = 2^2 \times 3^2
   \]
   The prime factorization of 175 is:
   \[
   175 = 5^2 \times 7
   \]
   Since 36 and 175 have no common prime factors, \(\frac{36}{175}\) is already in its simplest form.

So, the expression \(\frac{12}{35} \times \frac{3}{5}\) simplifies to \(\frac{36}{175}\), where \(a = 36\) and \(b = 175\), and \(a\) and \(b\) have no common factors.

Would you like more details or have any questions?

Here are some related questions to consider:
1. How do you find the greatest common divisor (GCD) of two numbers?
2. What is the prime factorization method?
3. How can you simplify complex fractions?
4. What are some examples of improper fractions and their simplifications?
5. How can you convert a fraction to a decimal?

**Tip:** Always check for common factors when simplifying fractions to ensure they are in their simplest form.

Learn how to multiply fractions 12/35 and 3/5 with a detailed step-by-step solution. This problem covers basic fraction multiplication and simplification using prime factorization. Suitable for students in Grades 6-8.

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