Use the properties of operations and rules for multiplying and dividing to solve: (−2)×(1/5)÷(2/3)×(−5/6)÷(3/4) (1 point)
2/3
1/6
-1/6
-2/3
To solve this expression, we start by simplifying the multiplication and division from left to right:
(-2) × (1/5) = -2/5
-2/5 ÷ (2/3) = (-2/5) × (3/2) = -6/10 = -3/5
-3/5 × (-5/6) = 15/30 = 1/2
1/2 ÷ (3/4) = (1/2) × (4/3) = 4/6 = 2/3
Therefore, the final answer is 2/3.
To solve the expression (−2)×(1/5)÷(2/3)×(−5/6)÷(3/4), we can follow the order of operations.
Step 1: Multiply the numbers with like signs and multiply numbers without signs.
(-2) * (-5) = 10 (since two negative numbers multiplied give a positive result)
Step 2: Multiply all the numbers together.
10 * (1/5) * (2/3) * (3/4) = (10 * 1 * 2 * 3) / (5 * 3 * 4)
Step 3: Simplify the expression.
= 60 / 60
Step 4: Divide the numerator by the denominator.
= 1
So, the simplified expression is 1.
To solve the expression (-2)×(1/5)÷(2/3)×(-5/6)÷(3/4), we need to apply the properties of operations and rules for multiplying and dividing.
Step 1: Multiply the numbers together from left to right.
(-2)×(1/5) = (-2/1)×(1/5) = -2/5
Step 2: Divide the obtained result by the numbers that follow in the expression.
-2/5 ÷ (2/3) × (-5/6) ÷ (3/4)
To divide fractions, we multiply by the reciprocal of the second fraction.
-2/5 ÷ (2/3) = -2/5 × (3/2) = -6/10 = -3/5
Step 3: Continue to divide and multiply the obtained result by the remaining numbers.
-3/5 × (-5/6) = 15/30 = 1/2
Step 4: Finally, divide the resulting fraction by (3/4).
1/2 ÷ (3/4) = 1/2 × (4/3) = 4/6 = 2/3
Therefore, the value of the expression (-2)×(1/5)÷(2/3)×(-5/6)÷(3/4) is 2/3.