(8/9) x (-3/4) divide (1/9) x (-4/5) divide (3/5)
To simplify this expression, we can start by canceling out common factors in the numerators and denominators:
First, let's simplify (8/9) x (-3/4):
8/9 x -3/4 = (8 x -3)/(9 x 4) = -24/36
Next, let's simplify (1/9) x (-4/5):
1/9 x -4/5 = (1 x -4)/(9 x 5) = -4/45
Finally, let's simplify (-24/36) ÷ (-4/45):
To divide by a fraction, we multiply by its reciprocal:
(-24/36) ÷ (-4/45) = (-24/36) x (45/-4)
Now, let's simplify:
(-24/36) x (45/-4) = (24/36) x (45/4) = (1/3) x (45/4)
Again, let's simplify:
(1/3) x (45/4) = 45/12 = 15/4
Therefore, (8/9) x (-3/4) ÷ (1/9) x (-4/5) ÷ (3/5) simplifies to 15/4.
To solve this problem step-by-step, we will first perform the divisions from left to right.
1. (8/9) x (-3/4) = -24/36 = -2/3
Next, we will move on to the second division.
2. (1/9) x (-4/5) = -4/45
Finally, we will perform the last division.
3. (-2/3) ÷ (3/5) = (-2/3) x (5/3) = -10/9
So, the final result is -10/9.
To simplify the given expression, we'll follow the order of operations, which is also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
Step 1: Simplify the numerator and denominator of each division separately.
Let's start with the numerator:
(8/9) x (-3/4) = -24/36
Next, let's simplify the denominator:
(1/9) x (-4/5) x (3/5) = -12/225
Step 2: Divide the numerator by the denominator:
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
(-24/36) ÷ (-12/225) = (-24/36) x (225/-12)
Next, let's simplify each fraction before multiplication:
-24/36 = -2/3
225/-12 = -75/4
Step 3: Multiply the fractions:
(-2/3) x (-75/4) = (2/3) x (75/4)
Now, we need to multiply the numerators and denominators to find the product:
(2 x 75) / (3 x 4) = 150/12
Step 4: Simplify the fraction (if possible):
In this case, both the numerator (150) and denominator (12) share a common factor of 6.
150 ÷ 6 / 12 ÷ 6 = 25/2
Therefore, the simplified expression is 25/2 or 25 divided by 2.