Use the properties of operations and rules for multiplying and dividing to solve:
(−2)×(1/5)÷(2/3)×(−5/6)÷(3/4)
2/3
Start Fraction 2 over 3 End Fraction
−2/3
negative Start Fraction 2 over 3 End Fraction
1/6
Start Fraction 1 over 6 End Fraction
−1/6
negative Start Fraction 1 over 6 End Fraction
Step 1: Multiply the first two fractions: (-2) × (1/5) = -2/5
Step 2: Divide the result from step 1 by the third fraction: (-2/5) ÷ (2/3)
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. Thus, we multiply by (3/2):
(-2/5) × (3/2) = -6/10
Simplify the result by dividing both the numerator and denominator by their greatest common divisor, which is 2:
-6 ÷ 2 = -3
10 ÷ 2 = 5
So, -6/10 simplifies to -3/5.
Step 3: Multiply the result from step 2 by the fourth fraction: (-3/5) × (-5/6)
Multiply the numerators together and the denominators together:
(-3 × -5) / (5 × 6) = 15/30
Simplify the result by dividing both the numerator and denominator by their greatest common divisor, which is 15:
15 ÷ 15 = 1
30 ÷ 15 = 2
So, 15/30 simplifies to 1/2.
Step 4: Divide the result from step 3 by the fifth fraction: (1/2) ÷ (3/4)
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. Thus, we multiply by (4/3):
(1/2) × (4/3) = 4/6
Simplify the result by dividing both the numerator and denominator by their greatest common divisor, which is 2:
4 ÷ 2 = 2
6 ÷ 2 = 3
So, 4/6 simplifies to 2/3.
Therefore, the final result is 2/3.