Compute (−3/4) × (12/−5) × (−25/6).

Step-by-step solution

1. 1

   Settle the sign before touching the digits. Count the negative factors: $-3$, $-5$ and $-25$ — three of them. An odd number of negatives makes the product negative, so the answer will carry a minus sign and the rest of the work can be done with positive numbers only.

2. 2

   Write the magnitudes as a single fraction.

   $\frac{3\times 12\times 25}{4\times 5\times 6}$

   Multiplying this out gives $\tfrac{900}{120}$, but cancelling first is much lighter.

3. 3

   Cancel across numerator and denominator. In a product of fractions any top factor may cancel with any bottom factor:

   $\frac{12}{4}=3,\qquad \frac{25}{5}=5,\qquad \frac{3}{6}=\frac12$

   leaving $\tfrac12\times 3\times 5=\tfrac{15}{2}$.

4. 4

   Reattach the sign.

   $\frac{-3}{4}\cdot\frac{12}{-5}\cdot\frac{-25}{6}=-\frac{15}{2}$

   $\boxed{-\dfrac{15}{2}=-7.5}$

5. 5

   Check with the uncancelled form. $\tfrac{900}{120}=\tfrac{15}{2}$ after dividing both by $60$, and the sign is negative — the two routes agree. As a rough check, the three magnitudes are roughly $0.75\times 2.4\times 4.17\approx 7.5$.