49/52 times 13/-63 how do i simplify before multipling

To simplify \(\frac{49}{52} \times \frac{13}{-63}\), follow these steps:

1. **Factor the numerators and denominators**: Break down the numbers into their prime factors.

   - \( 49 = 7 \times 7 \)
   - \( 52 = 2^2 \times 13 \)
   - \( 13 \) is already prime.
   - \( 63 = 7 \times 9 = 7 \times 3^2 \)

   Now, the expression looks like this:
   \[
   \frac{7 \times 7}{2^2 \times 13} \times \frac{13}{-7 \times 3^2}
   \]

2. **Cancel out common factors**: Look for terms that can cancel out between the numerators and denominators.

   - The \(13\) in the numerator of the second fraction cancels with the \(13\) in the denominator of the first fraction.
   - One \(7\) from the numerator of the first fraction cancels with the \(7\) in the denominator of the second fraction.

   After cancellation, you're left with:
   \[
   \frac{7}{2^2} \times \frac{1}{-3^2}
   \]
   This simplifies to:
   \[
   \frac{7}{4} \times \frac{1}{-9}
   \]

3. **Multiply the remaining fractions**: Now multiply the numerators and the denominators.

   \[
   \frac{7 \times 1}{4 \times -9} = \frac{7}{-36}
   \]

   So, the simplified result is:
   \[
   \frac{-7}{36}
   \]

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Here are five related questions:
1. How do you simplify complex fractions with variables?
2. What are common factoring techniques in algebra?
3. How do you multiply and divide fractions involving negative numbers?
4. Can you explain how to work with fractions that have radicals?
5. How do you find the least common denominator for adding fractions?

**Tip**: Always cancel common factors before multiplying to simplify calculations.

Learn how to simplify and multiply the fractions 49/52 and 13/-63. This step-by-step solution covers fraction simplification, prime factorization, and multiplication of fractions with negative numbers. Suitable for students in Grades 6-8.

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