Use the properties of operations and rules for multiplying and dividing to solve:(−2)×(1/5)÷(2/3)×(−5/6)÷(3/4)

Answer 1

To solve this expression using the properties of operations and rules for multiplying and dividing, we can follow these steps:

Step 1: Solve the multiplication and division from left to right.

(-2) × (1/5) = -2/5

Step 2: Now let's simplify the expression: (-2/5) ÷ (2/3) = (-2/5) × (3/2)

Step 3: Multiply the numerators and denominators: (-2/5) × (3/2) = (-2 × 3) / (5 × 2) = -6/10

Step 4: Simplify the fraction: -6/10 can be simplified as -3/5

Step 5: Lastly, divide (-3/5) ÷ (3/4) = (-3/5) × (4/3)

Step 6: Multiply the numerators and denominators: (-3/5) × (4/3) = (-3 × 4) / (5 × 3) = -12/15

Step 7: Simplify the fraction: -12/15 can be simplified as -4/5

Therefore, the expression (-2) × (1/5) ÷ (2/3) × (-5/6) ÷ (3/4) simplifies to -4/5.