(-2)×(1/5)÷(2/3)×(-5/6)÷(3/4)
To simplify the given expression, we follow the order of operations (PEMDAS):
First, we perform the multiplication and division from left to right:
(-2) × (1/5) ÷ (2/3) × (-5/6) ÷ (3/4)
= (-2) × (1/5) × (-5/6) × (3/4) ÷ (2/3)
Next, we simplify each multiplication:
= (-2/1) × (1/5) × (-5/6) × (3/4) ÷ (2/3)
= (-2 × 1 × -5 × 3) / (1 × 5 × 6 × 4) ÷ (2/3)
= 30 / 120 ÷ (2/3)
Now, we perform division, which is equivalent to multiplying by the reciprocal:
= 30 / 120 × (3/2)
= (30 × 3) / (120 × 2)
= 90 / 240
Finally, we simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD):
= 3 / 8
Therefore, (-2) × (1/5) ÷ (2/3) × (-5/6) ÷ (3/4) simplifies to 3/8.
To simplify the expression (-2)×(1/5)÷(2/3)×(-5/6)÷(3/4), follow these steps:
Step 1: Multiply -2 by 1/5:
-2 × 1/5 = -2/5
Step 2: Divide the result from Step 1 by 2/3:
(-2/5) ÷ (2/3) =
-2/5 × 3/2 =
-6/10 =
-3/5
Step 3: Multiply the result from Step 2 by -5/6:
(-3/5) × (-5/6) =
15/30 =
1/2
Step 4: Divide the result from Step 3 by 3/4:
(1/2) ÷ (3/4) =
1/2 × 4/3 =
4/6 =
2/3
Therefore, (-2)×(1/5)÷(2/3)×(-5/6)÷(3/4) equals 2/3.