Use the properties of operations and rules for multiplying and dividing to solve:(−2)×(1/5)÷(2/3)×(−5/6)÷(3/4)
To solve this expression using the properties of operations and rules for multiplying and dividing, we can follow these steps:
Step 1: Solve the multiplication and division from left to right.
(-2) × (1/5) = -2/5
Step 2: Now let's simplify the expression: (-2/5) ÷ (2/3) = (-2/5) × (3/2)
Step 3: Multiply the numerators and denominators: (-2/5) × (3/2) = (-2 × 3) / (5 × 2) = -6/10
Step 4: Simplify the fraction: -6/10 can be simplified as -3/5
Step 5: Lastly, divide (-3/5) ÷ (3/4) = (-3/5) × (4/3)
Step 6: Multiply the numerators and denominators: (-3/5) × (4/3) = (-3 × 4) / (5 × 3) = -12/15
Step 7: Simplify the fraction: -12/15 can be simplified as -4/5
Therefore, the expression (-2) × (1/5) ÷ (2/3) × (-5/6) ÷ (3/4) simplifies to -4/5.
To solve the expression (-2)×(1/5)÷(2/3)×(-5/6)÷(3/4), let's follow the rules for multiplying and dividing the fractional numbers:
Step 1: Start by multiplying the first two numbers:
(-2) × (1/5) = -2/5
Step 2: Continue by dividing the result from Step 1 by the next number:
-2/5 ÷ (2/3)
To divide fractions, you multiply the first fraction by the reciprocal (or inverse) of the second fraction. The reciprocal of 2/3 is 3/2, so:
-2/5 ÷ (2/3) = -2/5 × (3/2)
Step 3: Multiply the result from Step 2 by the next number:
-2/5 × (3/2) = -6/10
Step 4: Continue by dividing the result from Step 3 by the next number:
-6/10 ÷ (-5/6)
Again, we multiply the first fraction by the reciprocal of the second:
-6/10 ÷ (-5/6) = -6/10 × (-6/5)
Step 5: Multiply the result from Step 4 by the final number:
-6/10 × (-6/5) = 36/50
Simplifying the result:
36/50 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
36/50 = (36/2)/(50/2) = 18/25
So, the solution to the expression (-2)×(1/5)÷(2/3)×(-5/6)÷(3/4) is 18/25.