(8/9)x(-3/4)divided (1/9)x(-4/5)divided (3/5)
To simplify the expression:
(8/9)x(-3/4) ÷ (1/9)x(-4/5) ÷ (3/5)
First, multiply the fractions in the numerator and in the denominator:
(8/9) x (-3/4) = -24/36
(1/9) x (-4/5) = -4/45
Therefore, the expression becomes:
(-24/36) ÷ (-4/45) ÷ (3/5)
To divide fractions, you invert the divisor and multiply:
(-24/36) ÷ (-4/45) is the same as (-24/36) x (-45/4).
The multiplication of these fractions simplifies to:
= (24/4) x (45/36)
= 6 x (45/36)
= (6/1) x (45/36)
Multiplying the numerator gives:
= 270/36
Reducing this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 18:
= (270/18) / (36/18)
= 15/2
Finally, we multiply 15/2 by 3/5:
= (15/2) x (3/5)
Multiplying the numerators, and denominators, we get:
= (15 x 3) / (2 x 5)
= 45/10
Therefore, the simplified expression is 45/10 or 9/2.
To solve this expression, we need to apply the order of operations, which is parentheses, exponents, multiplication and division (from left to right), and finally addition and subtraction (from left to right).
First, let's simplify the expression within the parentheses:
- Starting with (8/9) x (-3/4):
Multiplying the numerators and the denominators, we get (-3 x 8) / (4 x 9) = -24 / 36.
- Next, simplifying (1/9) x (-4/5):
Multiplying the numerators and the denominators, we get (-4 x 1) / (5 x 9) = -4 / 45.
Now, let's divide these two results:
(-24 / 36) divided by (-4 / 45)
Remember that division is the same as multiplying by the reciprocal, so it becomes:
(-24 / 36) x (45 / -4)
Multiplying the numerators and the denominators, we get (-24 x 45) / (36 x -4) = -1080 / -144 = 7.5.
Finally, let's divide the result by (3/5):
(7.5) divided by (3/5)
Again, division is the same as multiplying by the reciprocal:
(7.5) x (5/3)
Multiplying the numerators and the denominators, we get (7.5 x 5) / 3 = 37.5 / 3 = 12.5.
Therefore, the expression (8/9) x (-3/4) divided by (1/9) x (-4/5) divided by (3/5) simplifies to 12.5.
To solve this expression, we need to follow the order of operations, which is commonly remembered using the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division - from left to right, Addition and Subtraction - from left to right).
The expression you provided is:
(8/9) * (-3/4) ÷ (1/9) * (-4/5) ÷ (3/5)
Let's break it down step by step:
Step 1: Parentheses
There are no parentheses in the expression, so we can move on to the next step.
Step 2: Multiplication and Division (from left to right)
Now we need to evaluate the multiplications and divisions in the expression. We read the expression from left to right and perform the operations as we go.
(8/9) * (-3/4) ÷ (1/9) * (-4/5) ÷ (3/5)
First, let's evaluate the multiplication:
(8/9) * (-3/4) = -24/36 = -2/3
The expression now becomes:
(-2/3) ÷ (1/9) * (-4/5) ÷ (3/5)
Now, let's continue with the divisions:
(-2/3) ÷ (1/9) = -18/3 = -6
The expression now becomes:
-6 * (-4/5) ÷ (3/5)
We can simplify the multiplication:
-6 * (-4/5) = 24/5
The expression now becomes:
24/5 ÷ (3/5)
Now, let's evaluate the division:
24/5 ÷ (3/5) = (24/5) * (5/3) = 120/15 = 8
So the solution to the expression is 8.