(8/9)×(−3/4)÷(1/9)×(−4/5)÷(3/5)
To solve this expression, we must multiply and divide the fractions in the correct order according to the order of operations (PEMDAS/BODMAS).
First, we multiply the fractions 8/9 and -3/4:
(8/9) × (-3/4) = (-24/36) or (-2/3)
Next, we divide the result by the fraction 1/9:
(-2/3) ÷ (1/9) = (-2/3) × (9/1) = (-18/3) or -6
Then, we multiply the result by the fraction -4/5:
-6 × (-4/5) = (24/5) or 4.8
Finally, we divide the result by the fraction 3/5:
4.8 ÷ (3/5) = (4.8) × (5/3) = 24/3 or 8
Therefore, the expression (8/9) × (-3/4) ÷ (1/9) × (-4/5) ÷ (3/5) equals 8.
(−3/5)×(5/16)×(7/12)÷(−3/16)×(−5/7)
To simplify the expression (8/9) × (-3/4) ÷ (1/9) × (-4/5) ÷ (3/5), we can follow these steps:
Step 1: Multiply the fractions from left to right:
(8/9) × (-3/4) = -24/36
Step 2: Divide the result from step 1 by the next fraction:
(-24/36) ÷ (1/9) = -216/36
Step 3: Multiply the result from step 2 by the next fraction:
(-216/36) × (-4/5) = 864/180
Step 4: Divide the result from step 3 by the last fraction:
(864/180) ÷ (3/5) = 2880/540
Step 5: Simplify the resulting fraction if possible (if there is a common factor in the numerator and denominator, divide both by that factor):
2880/540 = 16/3
Therefore, the simplified result of the expression (8/9) × (-3/4) ÷ (1/9) × (-4/5) ÷ (3/5) is 16/3.
To solve the expression (8/9) × (-3/4) ÷ (1/9) × (-4/5) ÷ (3/5), we can follow the order of operations which is commonly known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction):
Step 1: Simplify the multiplication and division from left to right.
First, let's perform the multiplication of the fractions:
(8/9) × (-3/4) = -24/36
Now, let's simplify the division of the fractions:
-24/36 ÷ (1/9) = -24/36 × 9/1 = -216/36
Next, let's simplify the multiplication of the fractions:
-216/36 × (-4/5) = 864/180
Finally, let's simplify the division of the fractions:
864/180 ÷ (3/5) = 864/180 × 5/3 = 4800/540
Step 2: Simplify the fraction.
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 4800 and 540 is 60. Dividing both the numerator and the denominator by 60, we get:
4800/540 ÷ 60/60 = 80/9
So, the final answer is 80/9.