Use the properties of operations and rules for multiplying and dividing to solve:

Question

(−2)×(1/5)÷(2/3)×(−5/6)÷(3/4)

−1/6

2/3

−2/3

1/6

Answer 1

To solve the expression $(-2)\times (1/5)÷(2/3)\times (-5/6)÷(3/4)$, we will follow the order of operations and simplify step by step.

1. First, let's rewrite the division as multiplication by the reciprocal: $$(-2)\times (1/5)\times (3/2)\times (-5/6)\times (4/3)$$

2. Now, combine the multiplications: $$=(-2)\times (1/5)\times (3/2)\times (-5/6)\times (4/3)$$

3. We can multiply the fractions and constants together one step at a time. Start with $(-2)\times (1/5)$: $$=(-2/5)$$

4. Next, multiply $(-2/5)$ by $(3/2)$: $$=(-2/5)\times (3/2)=(-2\times 3)/(5\times 2)=(-6/10)=(-3/5)$$

5. Now, multiply $(-3/5)$ by $(-5/6)$: $$=(-3/5)\times (-5/6)=(3\times 5)/(5\times 6)=(15/30)=(1/2)$$

6. Finally, multiply $(1/2)$ by $(4/3)$: $$=(1/2)\times (4/3)=(1\times 4)/(2\times 3)=4/6=(2/3)$$

So, the final answer is: $$\boxed{{\displaystyle 2/3}}$$