Use the properties of operations and rules for multiplying and dividing to solve: (-2) x (1/2) divide (2/3) x (-5/6) divide (3/4)
To solve the expression (-2) x (1/2) ÷ (2/3) x (-5/6) ÷ (3/4), we can follow the order of operations (PEMDAS/BODMAS) and simplify step by step:
First, perform the multiplications from left to right:
(-2) x (1/2) = -1
(2/3) x (-5/6) = (-10/18) = (-5/9)
(3/4) = (3/4)
Now, substitute the simplified values back into the expression:
-1 ÷ (-5/9) ÷ (3/4)
To divide by a fraction (a/b), we can multiply by its reciprocal (b/a). So, let's invert (-5/9), which will give us (-9/5):
-1 x (-9/5) ÷ (3/4)
When dividing by a fraction, we multiply by its reciprocal. So, let's invert (3/4), giving us (4/3):
-1 x (-9/5) x (4/3)
Now, let's simplify the expression further:
-1 x (-9/5) = 9/5
9/5 x (4/3) = (9/5) x (4/3) = 36/15 = 12/5
Therefore, (-2) x (1/2) ÷ (2/3) x (-5/6) ÷ (3/4) simplifies to 12/5 or 2.4.
Let's break down the given expression step by step:
Step 1: Compute the multiplication (-2) x (1/2).
When multiplying a number by a fraction, you can simply multiply the numerator (top number) with the number and leave the denominator (bottom number) unchanged.
(-2) x (1/2) = -2/2
Step 2: Simplify -2/2.
To simplify a fraction, divide both the numerator and denominator by their greatest common divisor (GCD), which is 2 in this case.
-2/2 = -1/1 = -1
Step 3: Compute (2/3) x (-5/6).
Again, multiply the numerators and denominators separately.
(2/3) x (-5/6) = (2 x -5) / (3 x 6) = -10/18
Step 4: Simplify -10/18.
Find the GCD of 10 and 18, which is 2.
Divide both the numerator and denominator by 2.
-10/18 = -5/9
Step 5: Compute (-1) / (-5/9).
Dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of -5/9 is -9/5.
(-1) / (-5/9) = (-1) x (-9/5) = 9/5
Step 6: Compute 9/5 x (3/4).
Multiply the numerators and denominators separately.
(9/5) x (3/4) = (9 x 3) / (5 x 4) = 27/20
Therefore, the solution is 27/20.
To solve the given expression: (-2) x (1/2) ÷ (2/3) x (-5/6) ÷ (3/4), we will apply the properties of operations and rules for multiplying and dividing fractions.
Step 1: Multiply the fractions:
(-2) x (1/2) = -2/2 = -1
Step 2: Divide the fractions:
(-1) ÷ (2/3) = (-1) x (3/2) = -3/2
Step 3: Multiply the fractions:
(-3/2) x (-5/6) = (3/2) x (5/6) = 15/12
Step 4: Divide the fractions:
(15/12) ÷ (3/4) = (15/12) x (4/3)
Now, we need to simplify the final expression.
Step 5: Simplify the result:
15/12 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3.
After simplification: (15/12) x (4/3) = (5/4) x (4/1) = 5/1 = 5.
Therefore, the value of the expression (-2) x (1/2) ÷ (2/3) x (-5/6) ÷ (3/4) is 5.