Question

Divide. Write your answer as a fraction or mixed number in simplest form.
÷−85 2425

Answer 1

To divide the fraction \(-\frac{85}{2425}\), we first rewrite the operation as follows:

\[
-\frac{85}{2425} \div 1
\]

This doesn't make any changes, so we consider \(-\frac{85}{2425}\) as a division of two numbers where we can rewrite the division as multiplication by the reciprocal:

\[
-\frac{85}{2425} \div 1 = -\frac{85}{2425} \cdot 1
\]

Now, simplifying \(-\frac{85}{2425}\):

1. Find the greatest common divisor (GCD) of 85 and 2425.

- 85 can be factored into \(5 \times 17\).
- 2425 can be factored by dividing it by 5 first:
\[
2425 \div 5 = 485
\]
- Next, we can factor 485, which is \(5 \times 97\) (since 485 can be divided again by 5).

Thus, \(2425 = 5^2 \times 17 \times 97\).

2. Now we find the GCD of 85 and 2425 which is 85, since 85 is a factor of 2425.

3. Now simplify the fraction:
\[
-\frac{85 \div 85}{2425 \div 85} = -\frac{1}{29}
\]

Thus, the answer to \(-\frac{85}{2425}\) in simplest form is:

\[
-\frac{1}{29}
\]