Use the properties of operations and rules for multiplying and dividing to solve:
(9) ÷ (5/4) x (7/9) x (-5) ÷ (7/2)
To solve this expression using the properties of operations and rules for multiplying and dividing, let's follow the order of operations (PEMDAS/BODMAS) and solve step by step.
First, let's simplify the multiplication and division from left to right:
(9) ÷ (5/4) x (7/9) x (-5) ÷ (7/2)
9 ÷ (5/4) = 9 x (4/5) = 36/5
(36/5) x (7/9) = (36 x 7) / (5 x 9) = 252/45
(-5) ÷ (7/2) = -5 x (2/7) = -10/7
Now, let's multiply the remaining fractions:
(252/45) x (-10/7) = (252 x -10) / (45 x 7) = -2520/315 = -8
So, the final answer to the expression (9) ÷ (5/4) x (7/9) x (-5) ÷ (7/2) is -8.
To solve the expression (9) ÷ (5/4) x (7/9) x (-5) ÷ (7/2), we will follow the order of operations.
Step 1: Simplify the expression inside parentheses first.
(9) ÷ (5/4) x (7/9) x (-5) ÷ (7/2)
First, let's simplify the division (9) ÷ (5/4):
9 ÷ (5/4)
To divide by a fraction, multiply by its reciprocal.
9 x (4/5)
The 5's cancel out:
9 x (4/1) = 9 x 4 = 36
Now the expression becomes:
36 x (7/9) x (-5) ÷ (7/2)
Step 2: Proceed left to right with multiplication and division.
Multiply 36 by 7/9:
36 x (7/9)
When multiplying fractions, multiply the numerators together and the denominators together.
(36 x 7) / (9) = 252 / 9
We can simplify this fraction by dividing the numerator and denominator by their greatest common factor, which is 9.
252 ÷ 9 = 28
Now the expression becomes:
28 x (-5) ÷ (7/2)
Step 3: Multiply 28 by -5:
28 x (-5) = -140
Now the expression becomes:
-140 ÷ (7/2)
Step 4: Divide -140 by 7/2:
To divide by a fraction, we multiply by its reciprocal.
-140 x (2/7)
Multiply the numerators and denominators together:
(-140 x 2) / 7 = -280 / 7
We can simplify this fraction by dividing the numerator and denominator by their greatest common factor, which is 7.
-280 ÷ 7 = -40
Therefore, (9) ÷ (5/4) x (7/9) x (-5) ÷ (7/2) simplifies to -40.
To solve the given expression, we need to follow the properties of operations and rules for multiplying and dividing. Here's how we can solve it step by step:
Step 1: Solve the division first.
(9) ÷ (5/4)
To divide by a fraction, we multiply by its reciprocal.
Reciprocal of (5/4) = (4/5)
So, (9) ÷ (5/4) = (9) x (4/5).
Step 2: Simplify the multiplication.
(9) x (4/5) = (9/1) x (4/5)
Multiplying across the numerator and denominator:
(9/1) x (4/5) = (9 x 4) / (1 x 5) = 36/5
Step 3: Continue with the remaining multiplication and division.
(36/5) x (7/9) x (-5) ÷ (7/2)
Multiply all the numerators together: (36 x 7 x -5)
Multiply all the denominators together: (5 x 9 x 7 x 2)
The negative sign in front of 5 indicates a negative result.
Final answer: - (36 x 7 x 5) / (5 x 9 x 7 x 2)
Multiplying across the numerator and denominator:
= - (36 x 7 x 5) / (5 x 9 x 7 x 2)
Simplifying the multiplication:
= - (36 x 5) / (9 x 2)
= - (180) / (18)
= - 10
Therefore, the result is -10.