Use the properties of operations and rules for multiplying and dividing to solve:
(−2)×(1/5)÷(2/3)×(−5/6)÷(3/4)
(1 point)
Responses
1/6
−2/3
2/3
−1/6
To solve this expression, we can follow the order of operations: perform the multiplication and division from left to right.
First, multiply -2 and 1/5:
(-2) × (1/5) = -2/5
Next, divide -2/5 by 2/3:
(-2/5) ÷ (2/3) = (-2/5) × (3/2) = -6/10 = -3/5
Then, multiply -3/5 by -5/6:
(-3/5) × (-5/6) = (3/5) × (5/6) = 15/30 = 1/2
Finally, divide 1/2 by 3/4:
(1/2) ÷ (3/4) = (1/2) × (4/3) = 4/6 = 2/3
Therefore, the solution is 2/3.
To solve the expression (-2)×(1/5)÷(2/3)×(-5/6)÷(3/4), we can use the properties of operations and the rules for multiplying and dividing. Let's break it down step by step:
Step 1: Multiply -2 by 1/5:
(-2) × (1/5) = -2/5
Step 2: Divide -2/5 by 2/3:
(-2/5) ÷ (2/3) = (-2/5) × (3/2)
To divide by a fraction, we can multiply by its reciprocal (flipped version). So, dividing by 2/3 is the same as multiplying by 3/2.
(-2/5) × (3/2) = (-2/5) × (3/2) = (-6/10) = -3/5
Step 3: Multiply -3/5 by -5/6:
(-3/5) × (-5/6) = (3/5) × (5/6)
When you multiply two negative numbers, the result is positive.
(3/5) × (5/6) = (3 × 5) / (5 × 6) = 15/30
Simplify the fraction 15/30:
15/30 = (3 × 5) / (6 × 5) = 3/6
Step 4: Divide 3/6 by 3/4:
(3/6) ÷ (3/4) = (3/6) × (4/3)
To divide by a fraction, we can multiply by its reciprocal (flipped version). So, dividing by 3/4 is the same as multiplying by 4/3.
(3/6) × (4/3) = (3 × 4) / (6 × 3) = 12/18
Simplify the fraction 12/18:
12/18 = (2 × 2 × 3) / (2 × 3 × 3) = 4/9
So, the final answer is 4/9.
To solve the expression (-2)×(1/5)÷(2/3)×(-5/6)÷(3/4), we need to follow the order of operations (PEMDAS/BODMAS).
Step 1: Perform the multiplication and division from left to right.
(-2) * (1/5) = -2/5
Now we have: (-2/5) ÷ (2/3) × (-5/6) ÷ (3/4)
Step 2: Continue with the division operation.
(-2/5) ÷ (2/3) = (-2/5) * (3/2)
To divide by a fraction, we multiply by its reciprocal.
(-2/5) * (3/2) = (-2/5) * (3/2) = -6/10
Now we have: (-6/10) × (-5/6) ÷ (3/4)
Step 3: Continue with the multiplication operation.
(-6/10) × (-5/6) = (-6 * -5) / (10 * 6) = 30/60 = 1/2
Now we have: (1/2) ÷ (3/4)
Step 4: Divide the two remaining fractions by multiplying by the reciprocal.
(1/2) ÷ (3/4) = (1/2) * (4/3) = 4/6 = 2/3
Therefore, the solution to the expression (-2)×(1/5)÷(2/3)×(-5/6)÷(3/4) is 2/3.