Use the properties of operations and rules for multiplying and dividing to solve: (−2)×(1/5)÷(2/3)×(−5/6)÷(3/4)
To solve the expression (-2)×(1/5)÷(2/3)×(-5/6)÷(3/4), we will follow the order of operations, which is parentheses, multiplication/division (from left to right), and addition/subtraction (from left to right).
First, let's simplify the multiplication:
(-2)×(1/5) = -2/5
Next, let's simplify the divisions:
-2/5 ÷ 2/3 = -2/5 × 3/2 (Note that dividing by a fraction is the same as multiplying by its reciprocal.)
We can simplify this:
-2/5 × 3/2 = (-2 × 3) / (5 × 2) = -6/10 = -3/5
Finally, let's simplify the last division:
-3/5 ÷ 3/4 = -3/5 × 4/3 (Again, dividing by a fraction is the same as multiplying by its reciprocal.)
We can simplify this expression:
-3/5 × 4/3 = (-3 × 4) / (5 × 3) = -12/15 = -4/5
So, the final simplified result is -4/5.
To solve the expression (-2)×(1/5)÷(2/3)×(-5/6)÷(3/4), we will follow the order of operations, which is parentheses, exponents, multiplication and division (from left to right), and finally addition and subtraction (from left to right).
Step 1: Start by simplifying the multiplication from left to right:
(-2)×(1/5) = -2/5
Step 2: Next, simplify the division from left to right:
-2/5 ÷ (2/3) = -2/5 × (3/2)
To multiply fractions, multiply the numerators together and the denominators together:
-2/5 × 3/2 = -6/10
Step 3: Simplify the next division:
-6/10 ÷ (-5/6)
To divide fractions, multiply the first fraction by the reciprocal of the second. The reciprocal of -5/6 is -6/5:
-6/10 × (-6/5) = 36/50
Step 4: Finally, simplify the last division:
36/50 ÷ (3/4)
To divide fractions, multiply the first fraction by the reciprocal of the second. The reciprocal of 3/4 is 4/3:
36/50 × (4/3) = 144/150
To simplify the fraction, find the greatest common divisor (GCD) of the numerator and denominator, and divide both numerator and denominator by the GCD:
144/150 = (72/75) ÷ (6/6) = 72/75
Therefore, the expression (-2)×(1/5)÷(2/3)×(-5/6)÷(3/4) simplifies to 72/75.