Use the properties of operations and rules for multiplying and dividing to solve:
(−2) × (1/5) ÷ (2/3) × (−5/6) ÷ (3/4) =
possible ones are.
-2/3
-1/6
2/3
1/6
To solve this expression, we can follow the order of operations, which is to perform operations inside parentheses first, then multiplication and division from left to right.
Starting with the expression:
(−2) × (1/5) ÷ (2/3) × (−5/6) ÷ (3/4)
First, let's simplify the multiplication and division of fractions:
1/5 × -5/6 = -5/30 = -1/6 (numerator multiplied by numerator and denominator multiplied by denominator)
2/3 ÷ 3/4 = 8/9 (numerator multiplied by reciprocal of denominator)
Now, we can simplify the remaining operations:
-2 × -1/6 × 8/9 = 2/3 (multiplied numerators and denominators)
Therefore, the solution is 2/3.
To solve the given expression step-by-step, follow these steps:
Step 1: Multiply the first two fractions:
(-2) × (1/5) = -2/5
Step 2: Multiply the result from Step 1 by the next fraction:
-2/5 ÷ (2/3) = (-2/5) × (3/2)
Multiply the numerators together: -2 × 3 = -6
Multiply the denominators together: 5 × 2 = 10
The result is -6/10, which can be simplified to -3/5.
Step 3: Multiply the result from Step 2 by the next fraction:
-3/5 × (-5/6) = (-3/5) × (5/6)
Multiply the numerators together: -3 × 5 = -15
Multiply the denominators together: 5 × 6 = 30
The result is -15/30, which can be simplified to -1/2.
Step 4: Divide the result from Step 3 by the last fraction:
-1/2 ÷ (3/4) = (-1/2) ÷ (3/4)
To divide fractions, you multiply by the reciprocal of the second fraction:
(-1/2) × (4/3)
Multiply the numerators together: -1 × 4 = -4
Multiply the denominators together: 2 × 3 = 6
The result is -4/6, which can be simplified to -2/3.
Therefore, (-2) × (1/5) ÷ (2/3) × (-5/6) ÷ (3/4) simplifies to -2/3.