Use the properties of operations and rules for multiplying and dividing to solve: (8/9)×(−3/4)÷(1/9)×(−4/5)÷(3/5). And show your work.
To solve the expression (8/9)×(-3/4)÷(1/9)×(-4/5)÷(3/5), we can simplify each multiplication and division operation step by step.
First, let's multiply (8/9) and (-3/4):
(8/9) × (-3/4) = (8 × -3) / (9 × 4) = -24/36
Next, let's divide the result by (1/9):
(-24/36) ÷ (1/9) = (-24/36) × (9/1) = (-24 × 9) / (36 × 1) = -216/36
Now, let's multiply the result by (-4/5):
(-216/36) × (-4/5) = (-216 × -4) / (36 × 5) = 864/180
Lastly, let's divide the result by (3/5):
(864/180) ÷ (3/5) = (864/180) × (5/3) = (864 × 5) / (180 × 3) = 4320/540
To simplify the fraction 4320/540, we can divide both the numerator and the denominator by their greatest common divisor, 60:
4320/540 = (4320/60) / (540/60) = 72/9 = 8
Therefore, the expression (8/9)×(-3/4)÷(1/9)×(-4/5)÷(3/5) is equal to 8.
To solve the expression (8/9) × (-3/4) ÷ (1/9) × (-4/5) ÷ (3/5), we can follow the order of operations (PEMDAS) and apply the properties of operations and rules for multiplying and dividing.
Step 1: Begin by multiplying the fractions from left to right.
(8/9) × (-3/4) = -24/36
Step 2: Reduce the fraction:
-24/36 = -2/3
Step 3: Next, divide by (1/9):
-2/3 ÷ (1/9) = -2/3 × 9/1
Step 4: Multiply the fractions:
-2/3 × 9/1 = -18/3
Step 5: Simplify the fraction:
-18/3 = -6
Step 6: Finally, divide by (4/5) and (3/5) from left to right:
-6 ÷ (4/5) = -6 × 5/4
= -30/4
= -15/2
Step 7: Simplify the fraction:
-15/2 ÷ (3/5) = -15/2 × 5/3
= -75/6
= -25/2
Therefore, the value of (8/9) × (-3/4) ÷ (1/9) × (-4/5) ÷ (3/5) is -25/2.