(8/9)×(-3/4)÷(1/9)×(-4/5)÷(3/5)
To solve this expression, perform the multiplication and division operations from left to right:
(8/9) × (-3/4) ÷ (1/9) × (-4/5) ÷ (3/5)
First, calculate the multiplication:
(8/9) × (-3/4) = -24/36
Next, calculate the division:
(-24/36) ÷ (1/9) = -24/36 × 9/1 = -216/36
Then, calculate the next division:
(-216/36) ÷ (-4/5) = -216/36 × (-5/4) = 1080/144
Finally, calculate the last division:
(1080/144) ÷ (3/5) = 1080/144 × 5/3 = 900/72 = 25/2
Therefore, the result of the expression (8/9) × (-3/4) ÷ (1/9) × (-4/5) ÷ (3/5) is equal to 25/2.
To solve this expression step-by-step, we'll follow the order of operations (also known as PEMDAS: Parentheses, Exponents, Multiplication and Division from left to right, and Addition and Subtraction from left to right):
Step 1: Multiply the fractions from left to right:
(8/9) × (-3/4) = -24/36 or -2/3
Step 2: Divide by the next fraction from left to right:
(-2/3) ÷ (1/9) = -18/3 or -6
Step 3: Multiply the next fraction from left to right:
-6 × (-4/5) = 24/5 or 4 4/5
Step 4: Divide by the last fraction:
(4 4/5) ÷ (3/5) = (24/5) ÷ (3/5) = 24/3 or 8
Therefore, the final result of the expression (8/9) × (-3/4) ÷ (1/9) × (-4/5) ÷ (3/5) is 8.
To simplify the given expression:
1. Begin by multiplying the two fractions in the numerator: (8/9) × (-3/4) = -24/36.
2. Then, divide the result by the fraction in the denominator: (-24/36) ÷ (1/9) = -24/36 × 9/1 = (-24 × 9)/(36 × 1) = -216/36 = -6/1 = -6.
3. Now, multiply the result by the next fraction: -6 × (-4/5) = 24/5.
4. Lastly, divide the new result by the final fraction: 24/5 ÷ (3/5) = 24/5 × 5/3 = (24 × 5)/(5 × 3) = 120/15 = 8.
Therefore, the final answer is 8.