Compute (−1/5) × (−25/13) × (26/45).

Step-by-step solution

1. 1

   Determine the sign first. There are exactly two negative factors, $-1$ and $-25$. An even number of negatives gives a positive product, so the answer is positive and the signs can be dropped for the rest of the computation.

2. 2

   Set up the magnitudes as one fraction.

   $\frac{1\times 25\times 26}{5\times 13\times 45}$

3. 3

   Cancel in pairs. Take the easiest matches first:

   $\frac{25}{5}=5,\qquad \frac{26}{13}=2$

   That leaves $\dfrac{5\times 2}{45}=\dfrac{10}{45}$.

4. 4

   Reduce to lowest terms. Both $10$ and $45$ are divisible by $5$:

   $\frac{10}{45}=\frac{2}{9}$

   $\boxed{\dfrac{2}{9}}$

5. 5

   Verify without cancelling. $\tfrac{1\times 25\times 26}{5\times 13\times 45}=\tfrac{650}{2925}$, and dividing both by $325$ gives $\tfrac{2}{9}$ ✓. Numerically $2/9=0.2222$, and $0.2\times 1.923\times 0.578\approx 0.222$ — consistent.