(-2) ×(1/5)÷(2/3)×(-5/6)÷(3/4)=
(-2) ×(1/5)÷(2/3)×(-5/6)÷(3/4) = (1*-2/(5*2/3))*(-5/6)÷(3/4)
= (-2/10)/(2/3)*(-5/6)÷(3/4) = -1/5*3/2*-5/6÷(3/4)
= -1/5*-5/4*4/3 = (-1*-5*-4)/(5*4*3) = -20/60 = -1/3
Therefore, (-2) ×(1/5)÷(2/3)×(-5/6)÷(3/4) = -1/3.
To simplify the expression (-2) ×(1/5)÷(2/3)×(-5/6)÷(3/4), follow these steps:
Step 1: Start by working within the parentheses:
-2 × (1/5) ÷ (2/3) × (-5/6) ÷ (3/4)
Step 2: Multiply the numbers outside the parentheses:
-2 × (1/5) ÷ (2/3) × (-5/6) ÷ (3/4) = -2/5 ÷ (2/3) × (-5/6) ÷ (3/4)
Step 3: Simplify the division (÷) operation:
-2/5 ÷ (2/3) × (-5/6) ÷ (3/4) = -2/5 × (3/2) × (-5/6) ÷ (3/4)
Step 4: Multiply the fractions together, both numerator and denominator:
-2/5 × (3/2) × (-5/6) ÷ (3/4) = (-2 × 3 × -5) / (5 × 2 × 6) ÷ (3/4)
Step 5: Perform the multiplication in the numerator:
(-2 × 3 × -5) / (5 × 2 × 6) ÷ (3/4) = 30 / (5 × 2 × 6) ÷ (3/4)
Step 6: Simplify the multiplication in the denominator:
30 / (5 × 2 × 6) ÷ (3/4) = 30 / 60 ÷ (3/4)
Step 7: Simplify the division (÷) operation:
30 / 60 ÷ (3/4) = 30 / 60 × (4/3)
Step 8: Simplify the expression and perform the division in the numerator:
30 / 60 × (4/3) = 1/2 × (4/3)
Step 9: Multiply the fractions together:
1/2 × (4/3) = (1 × 4) / (2 × 3)
Step 10: Perform the multiplication in the numerator and denominator:
(1 × 4) / (2 × 3) = 4/6
Step 11: Simplify the fraction:
4/6 = 2/3
Therefore, (-2) ×(1/5)÷(2/3)×(-5/6)÷(3/4) simplifies to 2/3.
To solve this expression, you need to follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, and Addition and Subtraction from left to right).
Let's break it down step by step:
Step 1: Evaluate (-2) × (1/5).
This is a multiplication problem. Multiply -2 by 1/5, which gives us -2/5.
Step 2: Evaluate the numerator of the previous result multiplied by the next fraction.
We have (-2/5) × (-5/6). Multiply the numerators and denominators together: (-2 × -5) / (5 × 6) = 10 / 30.
Step 3: Simplify the fraction if possible.
The fraction 10/30 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 10. Canceling out the common factor of 10, we get 1 / 3.
Step 4: Divide the previous result by the next fraction.
We have (1/3) ÷ (3/4). To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. So, (1/3) × (4/3) = 4/9.
Therefore, the final answer is 4/9.