Use the properties of operations and rules for multiplying and dividing to solve: (8/9)×(−3/4)÷(1/9)×(−4/5)÷(3/5)
To solve (8/9)×(−3/4)÷(1/9)×(−4/5)÷(3/5), we can simplify step by step using the properties of operations and rules for multiplying and dividing.
First, let's multiply the fractions together from left to right:
(8/9) × (−3/4) = (8 × −3)/(9 × 4) = −24/36
Next, let's divide the result by the next fraction:
(−24/36) ÷ (1/9) = (−24/36) × (9/1) = (−24 × 9)/(36 × 1) = −216/36
Now, let's multiply this result by the next fraction:
(−216/36) × (−4/5) = (−216 × −4)/(36 × 5) = 864/180
Finally, let's divide the result by the last fraction:
(864/180) ÷ (3/5) = (864/180) × (5/3) = (864 × 5)/(180 × 3) = 4320/540
To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 60:
4320/540 = (4320 ÷ 60)/(540 ÷ 60) = 72/9
Therefore, (8/9)×(−3/4)÷(1/9)×(−4/5)÷(3/5) simplifies to 72/9 or 8.
To solve the given expression, we need to follow the order of operations (PEMDAS/BODMAS) and use the properties of multiplication and division.
Step 1: Simplify the expression within the parentheses:
(8/9) × (-3/4) ÷ (1/9) × (-4/5) ÷ (3/5)
Step 2: Multiply the fractions from left to right:
= (8 × -3) / (9 × 4) ÷ (1 × -4) / (9 × 5) ÷ (3 × 5)
= -24/36 ÷ -4/45 ÷ 15/25
Step 3: Simplify each fraction:
= -2/3 ÷ -1/45 ÷ 3/5
Step 4: Invert the second fraction and multiply:
= -2/3 × -45/1 ÷ 3/5
= 90/3 ÷ 3/5
= 30/1 ÷ 3/5
Step 5: Invert the third fraction and multiply:
= 30/1 × 5/3
= 150/3
= 50
Therefore, the value of (8/9) × (-3/4) ÷ (1/9) × (-4/5) ÷ (3/5) is equal to 50.